LTI system circuit simulation system, method, device and storage medium

Abstract

The embodiment of the present application provides an LTI system circuit simulation system, method, device and storage medium, which belongs to the field of experimental teaching technology. The system includes: a time domain analysis subsystem and a frequency domain analysis subsystem; the time domain analysis subsystem includes: a signal decomposition module, a linear system property proof module, a convolution theorem derivation module and an LTI system circuit signal processing module; the present application more intuitively and dynamically displays the decomposition of the input signal into a weighted sum of multiple unit impulse functions, and displays the process of the input signal being gradually expanded by the unit impulse function, and displays the first result, second result, third result, fourth result and fifth result step by step and sampling point by sampling point, as well as the comparison results of the equivalence between the results, to help users understand the expansion process of each step and its final result, making abstract mathematical concepts intuitive and visible.

Description

Technical Field

[0001] The present application relates to the field of experimental teaching technology, and in particular to an LTI system circuit simulation system, method, device and storage medium. Background Art

[0002] Linear Time-Invariant (LTI) systems are a core concept in signal processing and systems theory, with widespread applications in fields such as communications, control, and audio processing. Traditional LTI system teaching methods typically rely on classroom lectures and textbooks. However, existing LTI system teaching methods are limited in effectiveness, often struggling to establish an intuitive connection between mathematical formulas and actual system behavior. Summary of the Invention

[0003] In order to solve the above technical problems, embodiments of the present application provide an LTI system circuit simulation system, method, device and storage medium.

[0004] In a first aspect, an embodiment of the present application provides an LTI system circuit simulation system, the system comprising: a time domain analysis subsystem and a frequency domain analysis subsystem;

[0005] The time domain analysis subsystem includes: a signal decomposition module, a linear system property proof module, a convolution theorem derivation module and an LTI system circuit signal processing module;

[0006] The signal decomposition module is used to decompose the input signal into a weighted sum of multiple unit impulse functions and display the process of the input signal being gradually expanded by the unit impulse functions;

[0007] The linear system property proving module is configured to obtain a first response signal after the weighted sum of the unit impulse functions is processed by the LTI system circuit signal processing module, and use the first response signal as a first result; and a plurality of second response signals obtained after the LTI system circuit signal processing module processes the signal components of the input signals according to the unit impulse functions and the corresponding weights, and use the sum of the second response signals as a second result;

[0008] The linear system property proof module is further used to display the first result, the second result, and the comparison result of the equivalence between the first result and the second result step by step and sampling point by sampling point;

[0009] The convolution theorem derivation module is configured to use the signal components of each input signal as a weight, obtain a response after each unit impulse function is processed by the LTI system circuit signal processing module as a third response signal, perform weighted superposition of the signal components of each input signal on the third response signal, and obtain the weighted superposition sum as a third result;

[0010] The convolution theorem derivation module is further used to display the second result and the third result, as well as a comparison result of the equivalence between the second result and the third result;

[0011] The frequency domain analysis subsystem is configured to obtain a unit impulse response signal after the unit impulse function is processed by the LTI system circuit signal processing module, edit and change the frequency domain characteristics of the unit impulse response signal, convolve the changed unit impulse response signal with the input signal, and use the convolved signal with the changed frequency domain characteristics as a fourth result; and, input the input signal to the LTI system circuit signal processing module to obtain an output signal, and use the output signal as a fifth result;

[0012] The frequency domain analysis subsystem is further used to display the fourth result and the fifth result, as well as a comparison result of the frequency domain differences between the fourth result and the fifth result.

[0013] In one embodiment, the signal decomposition module includes: a first signal generation submodule, a first impulse function generation submodule, a first step function control submodule, a first signal decomposition submodule and a first animation module;

[0014] The first signal generating submodule is used to generate an input signal and specify a unit impulse function type;

[0015] The first impulse function generating submodule is configured to generate a unit impulse function according to the unit impulse function type and determine a corresponding time interval;

[0016] The first signal decomposition submodule is configured to decompose the input signal into a sum of multiple weighted unit impulse functions using a signal decomposition formula;

[0017] The signal decomposition formula is:

[0018] ;

[0019] in, is the input signal, is the unit impulse function, Δt is the time interval, N is the number of discrete points of integration, and k is the index of the discrete point;

[0020] The first step function control submodule is configured to gradually increase the time interval using a unit step formula and superimpose a weighted unit impulse function;

[0021] The unit step formula is:

[0022] ;

[0023] in, is a unit step function, is a signal component of the input signal expanded by a unit impulse function;

[0024] The first animation module is used to dynamically display, step by step according to the sampling points, the various weighted impulse signals formed by the decomposition of the input signal by the unit impulse function at each sampling point, as well as the process of expanding the unit impulse function of the complete input signal based on each unit impulse function and the weighted sum of each unit impulse function.

[0025] In one embodiment, the linear system property proof module includes: a second signal generation submodule, a second impulse function generation submodule, a second signal decomposition submodule, a linear property reasoning module, and a second animation module;

[0026] The second signal generating submodule is used to generate an input signal and specify a unit impulse function type;

[0027] The second impulse function generating submodule is configured to generate a unit impulse function according to the unit impulse function type and determine a corresponding time interval;

[0028] The second signal decomposition submodule is used to decompose the input signal into a sum of multiple weighted unit impulse functions;

[0029] The linear property reasoning module is configured to obtain the first result by using a first summation formula, and obtain the second result by using a second summation formula;

[0030] The first summation formula is:

[0031] ;

[0032] Where x(t) is the input signal, is the impulse function, is the processing function of the signal processing module of the LTI system circuit, Δt is the time interval, N is the number of discrete points of integration, and k is the index of the discrete point;

[0033] The second summation formula is:

[0034] ;

[0035] The second animation module is used to dynamically display the comparison results of each sampling point between the first result and the second result in steps according to the sampling points, and the comparison results of the equivalence between the first result and the second result.

[0036] In one embodiment, the convolution theorem derivation module includes: a third signal generation submodule, a third impulse function generation submodule, a third signal decomposition submodule, a convolution theorem proving module and a third animation module;

[0037] The third signal generating submodule is used to generate an input signal and specify a unit impulse function type;

[0038] The third impulse function generating submodule is configured to generate a unit impulse function according to the unit impulse function type and determine a corresponding time interval;

[0039] The third signal decomposition submodule is used to decompose the input signal into a sum of multiple weighted unit impulse functions;

[0040] The convolution theorem proving module is configured to obtain the second result through the second summation formula;

[0041] The convolution theorem proving module is further configured to obtain a third result through a third summation formula;

[0042] The third summation formula is:

[0043]

[0044] Where x(t) is the input signal, is the unit impulse function, is the processing function of the LTI system circuit signal processing module, h(t) is the impulse response obtained after the unit impulse signal is processed by the LTI system circuit signal processing module, Δt is the time interval, N is the number of discrete points of integration, and k is the index of the discrete point;

[0045] The third animation module is used to dynamically display the comparison results between the second result and the third result of each sampling point in steps, the comparison results of the equivalence between the second result and the third result, and the convolution process of the complete impulse response and the input signal based on the weighted sum of the signal components of each impulse response signal and each input signal.

[0046] In one embodiment, the frequency domain analysis subsystem includes: a spectrum editing module;

[0047] The spectrum editing module is used to click or drag the frequency on the spectrum graph to adjust it and display the adjusted frequency in real time;

[0048] The spectrum editing module is further configured to edit and change the frequency domain characteristics of the unit impulse response signal, convolve the changed unit impulse response signal with the input signal, and use the convolved signal with the changed frequency domain characteristics as a fourth result.

[0049] In one embodiment, the frequency domain analysis subsystem further includes: a comparison and display module;

[0050] The comparison and display module is configured to input the input signal into the LTI system circuit signal processing module to obtain an output signal, and use the output signal as a fifth result;

[0051] The comparison display module is further used to display a comparison result signal generated by comparing the fifth result and the fourth result, and dynamically display a change process of the spectrum diagram.

[0052] In one embodiment, the system further comprises: a user interaction subsystem;

[0053] The user interaction subsystem is used to control the sampling interval, total sampling time, window function type and windowing range during signal processing and display, and provides stepping, backtracking, comparison and zooming functions.

[0054] In a second aspect, an embodiment of the present application provides an LTI system circuit simulation method, which is applied to the LTI system circuit simulation system of the first aspect, wherein the method includes:

[0055] Decomposing the input signal into a weighted sum of multiple unit impulse functions by the signal decomposition module, and displaying the process of gradually expanding the input signal by the unit impulse functions;

[0056] Obtaining, by the linear system property proving module, a first response signal after the weighted sum of the unit impulse functions is processed by the LTI system circuit signal processing module, and using the first response signal as a first result; and obtaining, by the LTI system circuit signal processing module, a plurality of second response signals after processing the unit impulse functions and the corresponding signal components of the input signals as weights, and using the sum of the second response signals as a second result;

[0057] Furthermore, the first result, the second result, and a comparison result of the equivalence between the first result and the second result are displayed step by step and sampling point by sampling point by the linear system property proof module;

[0058] Using the convolution theorem derivation module as a weight, a response obtained after each unit impulse function is processed by the LTI system circuit signal processing module is used as a third response signal, performing weighted superposition of the signal components of each input signal on the third response signal, and obtaining a weighted superposition sum as a third result;

[0059] The second result and the third result, as well as a comparison result of equivalence between the second result and the third result, are also displayed through the convolution theorem derivation module;

[0060] Obtaining, through the frequency domain analysis subsystem, a unit impulse response signal of the unit impulse function after being processed by the LTI system circuit signal processing module, editing and changing a frequency domain characteristic of the unit impulse response signal, convolving the changed unit impulse response signal with the input signal, and using the convolved signal with the changed frequency domain characteristic as a fourth result; and, sending the input signal to the LTI system circuit signal processing module to obtain an output signal, and using the output signal as a fifth result;

[0061] The fourth result and the fifth result, as well as the comparison results of the frequency domain differences between the fourth result and the fifth result, are displayed by the frequency domain analysis subsystem.

[0062] In a third aspect, an embodiment of the present application provides an electronic device, including a memory and a processor, wherein the memory is used to store a computer program, and when the computer program is run by the processor, the LTI system circuit simulation method provided in the second aspect is executed.

[0063] In a fourth aspect, an embodiment of the present application provides a computer-readable storage medium storing a computer program. When the computer program is run on a processor, the LTI system circuit simulation method provided in the second aspect is executed.

[0064] The LTI system circuit simulation system, method, device and storage medium provided by the present application more intuitively and dynamically display the decomposition of the input signal into the weighted sum of multiple unit impulse functions, and display the process of the input signal being gradually expanded by the unit impulse function, and display the first result, second result, third result, fourth result and fifth result step by step and sampling point by sampling point, as well as the comparison results of the equivalence between each result, to help users understand the expansion process of each step and its final result, making abstract mathematical concepts intuitive and visible. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] In order to more clearly illustrate the technical solution of this application, the following is a brief introduction to the drawings required for use in the embodiments. It should be understood that the following drawings only illustrate certain embodiments of this application and should not be regarded as limiting the scope of protection of this application. In each of the drawings, similar components are numbered similarly.

[0066] Figure 1 A schematic diagram of the structure of an LTI system circuit simulation system provided by an embodiment of the present application is shown;

[0067] Figure 2 Another structural diagram of the LTI system circuit simulation system provided by an embodiment of the present application is shown;

[0068] Figure 3 A schematic diagram of a flow chart of the LTI system circuit simulation method provided by an embodiment of the present application is shown;

[0069] Figure 4 A structural schematic diagram of an electronic device provided in an embodiment of the present application is shown.

[0070] Icons: 10-LTI system circuit simulation system; 11-time domain analysis subsystem; 12-frequency domain analysis subsystem; 13-user interaction subsystem; 111-signal decomposition module; 112-linear system property proof module; 113-convolution theorem derivation module; 114-LTI system circuit signal processing module; 121-spectrum editing module; 122-comparison display module; 400-electronic device; 401-transceiver; 402-processor; 403-memory. DETAILED DESCRIPTION

[0071] The technical solutions in the embodiments of the present application will be described clearly and completely below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments.

[0072] The components of the embodiments of the present application generally described and illustrated in the drawings herein may be arranged and designed in a variety of different configurations. Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the claimed application, but rather merely represents selected embodiments of the present application. All other embodiments obtained by those skilled in the art based on the embodiments of the present application without creative effort are within the scope of protection of the present application.

[0073] Hereinafter, the terms "including", "having" and their cognates, which may be used in various embodiments of the present application, are intended only to indicate specific features, numbers, steps, operations, elements, components or combinations of the foregoing items, and should not be understood as first excluding the existence of one or more other features, numbers, steps, operations, elements, components or combinations of the foregoing items or the possibility of adding one or more features, numbers, steps, operations, elements, components or combinations of the foregoing items.

[0074] Furthermore, the terms “first,” “second,” “third,” etc., are merely used for distinguishing descriptions and are not to be understood as indicating or implying relative importance.

[0075] Unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by those skilled in the art to which the various embodiments of the present application belong. The terms (such as those defined in generally used dictionaries) will be interpreted as having the same meaning as in the context of the relevant technical field and will not be interpreted as having an idealized meaning or an overly formal meaning unless clearly defined in the various embodiments of the present application.

[0076] LTI systems (Linear Time-Invariant Systems) are a core concept in signal processing and systems theory, with widespread applications in fields such as communications, control, and audio processing. Traditional LTI system teaching methods typically include theoretical explanations, mathematical derivations, simple simulations, and laboratory practice. However, these traditional methods have the following shortcomings: high abstraction, where pure mathematical derivations and theoretical explanations are often too abstract, making it difficult for users to intuitively understand system behavior; insufficient interactivity, where static charts and traditional experimental equipment often make it difficult to adjust system parameters in real time and immediately observe their impact; low visualization, where traditional methods struggle to dynamically display signal changes in both the time and frequency domains, limiting users' understanding of the system's comprehensive characteristics; and a disconnect between theory and practice, where users often struggle to intuitively connect mathematical formulas with actual system behavior. Therefore, to address the above issues, this application proposes an LTI system circuit simulation system 10, method, device, and storage medium.

[0077] Example 1

[0078] The embodiment of the present application provides an LTI system circuit simulation system 10, such as Figure 1As shown, the system includes: a time domain analysis subsystem 11 and a frequency domain analysis subsystem 12; the time domain analysis subsystem 11 includes: a signal decomposition module 111, a linear system property proof module 112, a convolution theorem derivation module 113 and an LTI system circuit signal processing module 114; the signal decomposition module 111 is used to decompose the input signal into a weighted sum of multiple unit impulse functions and display the process of the input signal being gradually expanded by the unit impulse function; the linear system property proof module 112 is used to obtain the first response signal after the weighted sum of each unit impulse function is processed by the LTI system circuit signal processing module 114, and the first response signal is used as the first result, and, according to each unit impulse function and the corresponding signal component of each input signal as the weight, the LTI system circuit The signal processing module 114 obtains multiple second response signals after processing, and takes the sum of the second response signals as the second result; the linear system property proof module 112 is also used to display the first result, the second result and the comparison result of the equivalence between the first result and the second result step by step and sampling point by sampling point; the convolution theorem derivation module 113 is used to use the signal components of each input signal as weights, and take the response of each unit impulse function obtained after being processed by the LTI system circuit signal processing module 114 as the third response signal, perform weighted superposition of the signal components of each input signal on the third response signal, and take the obtained weighted superposition sum as the third result; the convolution theorem derivation module 113 is also used to display the second result and the third result, as well as the comparison result of the equivalence between the second result and the third result.

[0079] The frequency domain analysis subsystem 12 is used to obtain the unit impulse response signal after the unit impulse function is processed by the LTI system circuit signal processing module 114, edit and change the frequency domain characteristics of the unit impulse response signal, convolve the changed unit impulse response signal with the input signal, and use the convolved signal with the changed frequency domain characteristics as the fourth result, and send the input signal to the LTI system circuit signal processing module 114 to obtain the output signal, and use the output signal as the fifth result; the frequency domain analysis subsystem 12 is also used to display the fourth result and the fifth result, as well as the comparison results of the frequency domain differences between the fourth result and the fifth result.

[0080] It's important to note that LTI systems possess a fundamental property: their behavior can be completely described by a unit impulse response. For an LTI system, the input signal is x(t), the output signal is y(t), and the impulse response generated by the unit impulse response is h(t). The output signal can be expressed as the convolution of the input and impulse response signals: y(t) = (x * h)(t).

[0081] Therefore, if we use a specially selected unit pulse signal to input into the LTI system, obtain the impulse response h(t), and then convolve any input signal with the impulse response, the output signal of the system can be simulated through the convolution operation. Therefore, we set the original formula: y(t) = T[x(t)], and derive the convolution theorem according to the following steps: (1) x(t) = ∫x(τ)δ(t-τ) dτ; (2) y(t) = T[x(t)]= T[∫x(τ)δ(t-τ) dτ]; (3) y(t) = ∫T[x(τ)δ(t-τ)]dτ (using linear properties); (4) y(t) = ∫x(τ)T[δ(t-τ)] dτ (again using linear properties); (5) y(t) = ∫x(τ)h(t-τ) dτ, and the final convolution theorem formula is: y(t) = ∫x(τ)h(t-τ) dτ.

[0082] This solution uses graphical visualization in its experiments, dynamically demonstrating the sampling characteristics of a unit impulse signal and the convolution of the unit impulse response with the input signal, step by step. This helps provide a detailed understanding of the signal decomposition and convolution steps. By visualizing the input signal and system impulse response in both the time and frequency domains, users can more clearly see how convolution is used to calculate the system's output signal.

[0083] Furthermore, by interactively changing the frequency domain characteristics of the system's impulse response signal on the spectrum graph and convolving it with the input signal, the frequency domain characteristics of the system's output signal are altered. Furthermore, the original system's output signal is compared with the convolution result in the frequency domain to demonstrate the consistency of the two output signals at the unmodified frequency points and the precise differences at the modified frequency points, intuitively demonstrating that the system's behavior is completely described by its impulse response. These visualizations and interactive methods help users gain a deeper understanding of the behavior of LTI systems and the mathematical nature of convolution.

[0084] In one embodiment, the signal decomposition module 111 includes: a first signal generation submodule, a first impulse function generation submodule, a first step function control submodule, a first signal decomposition submodule, and a first animation module; the first signal generation submodule is used to generate an input signal and specify a unit impulse function type; the first impulse function generation submodule is used to generate a unit impulse function according to the unit impulse function type and determine the corresponding time interval; the first signal decomposition submodule is used to decompose the input signal into a sum of multiple weighted unit impulse functions using a signal decomposition formula;

[0085] The signal decomposition formula is:

[0086] ;

[0087] in, is the input signal, is the unit impulse function, Δt is the time interval, N is the number of discrete points of integration, and k is the index of the discrete point.

[0088] A first step function control submodule is used to gradually increase the time interval through a unit step formula and superimpose a weighted unit impulse function;

[0089] The unit step formula is:

[0090] ;

[0091] in, is a unit step function, It is the signal component of the input signal expanded by the unit impulse function;

[0092] The first animation module is used to dynamically display, step by step according to the sampling points, the various weighted impulse signals formed by the unit impulse function decomposition of the input signal at each sampling point, as well as the process of expanding the unit impulse function to finally form the complete input signal based on the unit impulse functions and the weighted sum of the unit impulse functions.

[0093] It should be noted that the impulse function expansion formula of the input signal x(t) δ(t) has an important property: the sampling property, which means that the impulse function can extract the value of the function x(t) at t=τ, as shown in the following formula:

[0094]

[0095] Any continuous-time signal x(t) can be represented as a weighted sum of an infinite number of unit impulse functions, as shown in the following basic formula:

[0096]

[0097] The integral form shows that x(t) can be regarded as the superposition of the weighted sum of the unit impulse functions at all time points, where x(τ) is the weighting coefficient.

[0098] In order to better demonstrate the expansion process, this solution introduces the window function To limit the integral range, so that it gradually expands from a finite range to an infinite range. The window function is defined as follows:

[0099]

[0100] Use window functions to decompose the underlying formula into finite and infinite parts:

[0101]

[0102] When T approaches infinity, this formula will approach the basic formula:

[0103]

[0104] For the convenience of step-by-step display, the input signal is decomposed into the sum of multiple weighted unit impulse functions through the signal decomposition formula. At the same time, for the convenience of step-by-step control in the experimental device to display the superposition of each component, the time interval is gradually increased through the unit step formula, and the weighted unit impulse functions are superimposed. The unit step function of the unit step formula has the following effect: when t≥kΔt, =1, allowing the signal to pass. When t<kΔt, =0, blocking the signal from passing.

[0105] Through the unit step function control the start time of each component, so as to facilitate the display of the superposition of each component by controlling the trigger of the unit step function in the experimental device.

[0106] Furthermore, this solution dynamically displays step by step the weighted impulse signals formed by the decomposition of the input signal by the unit impulse function at each sampling point according to the sampling points. First, determine the total duration Ts of the input signal. Then, gradually increase the value of T, such as T = Δt, T = 2Δt, T = 3Δt,..., until T is greater than or equal to Ts. The specific process is as follows: The first step: Initial display. At the beginning, a relatively small T = Δt can be selected, which only contains one unit impulse function. The specific formula is as follows:

[0107]

[0108] The second step: Gradually increase the integration range, gradually increase the value of T, increasing by one Δt each time; when T = 2Δt, display by controlling the unit step function. The specific formula is as follows:

[0109]

[0110] When T = 3Δt, display by controlling the unit step function, continue to increase the value of T until the entire signal range is covered. Finally, when T approaches infinity, the integration covers the entire time axis. The specific formula is as follows:

[0111]

[0112] It should be understood that the user freely generates a path of original signal through the first signal generation sub-module , and specify the type of unit impulse function and the time interval Δt, where the type of unit impulse function includes: rectangular function or normal distribution function. The first impulse function generation sub-module generates a unit impulse function according to the type of unit impulse function, and uses a graphical interface to display a single impulse function and its corresponding weight .

[0113] Gradually increase the integration range by controlling the step function. The specific process is as follows: (1) The user gradually increases the value of T by one Δt each time, and dynamically displays the increase of the T value. (2) Update the graph in real time to display the new impulse function and its weight. (3) Superimpose the new impulse function on the graph to gradually construct the entire signal.

[0114] Gradually increase the time interval by the unit step formula, and superimpose the weighted unit impulse functions, where the unit step function of the unit step formula has the following effect: when t≥kΔt, = 1, allowing the signal to pass. When t < kΔt, = 0, blocking the signal from passing.

[0115] It is further understood that when k = 0, only x(0)δ(t) is allowed to pass. As the value of k increases, more components are gradually introduced. This process simulates the gradual expansion of the integration range. The user can adjust the value of k through the control interface. As the value of k increases, the LTI system circuit simulation system 10 calculates and displays the cumulative effect of the passed components in real time, and the user can intuitively see how the signal is gradually constructed.

[0116] In one embodiment, the linear system property proof module 112 includes: a second signal generation sub-module, a second impulse function generation sub-module, a second signal decomposition sub-module, a linear property reasoning module, and a second animation module; the second signal generation sub-module is used to generate an input signal and specify the type of unit impulse function; the second impulse function generation sub-module is used to generate a unit impulse function according to the type of unit impulse function and determine the corresponding time interval; the second signal decomposition sub-module is used to decompose the input signal into the sum of multiple weighted unit impulse functions; the linear property reasoning module is used to obtain a first result through a first summation formula, and a second result through a second summation formula;

[0117] The first summation formula is:

[0118] ;

[0119] where, x(t) is the input signal, is the impulse function, is the processing function of the LTI system circuit signal processing module 114, Δt is the time interval, N is the number of discrete points of integration, and k is the index of the discrete point;

[0120] The second summation formula is:

[0121] ;

[0122] The second animation module is used to dynamically display the comparison results of each sampling point between the first result and the second result step by step according to the sampling points, and the comparison results of the equivalence between the first result and the second result.

[0123] It should be noted that in the above embodiment, the following formula is derived after windowing the continuous integral function:

[0124]

[0125] Assume that the processing function of the LTI system circuit signal processing module 114 is F, that is, y(t) = F[x(t)], and obtain the first result through the first summation formula. The first summation formula is as follows:

[0126]

[0127] The second summation formula is derived through the LTI system as follows:

[0128]

[0129] In order to facilitate the step-by-step control triggering and display of the superposition of each component in the experimental setup, the unit step function u(t) is used to explicitly represent the delay operation. The above formula is further rewritten as follows:

[0130]

[0131] pass Controlling the start time of each component makes it easier to demonstrate the superposition of each component in the experimental setup by controlling the triggering of the step function.

[0132] In this embodiment, by selecting T=Δt, only one impulse function is included:

[0133]

[0134] Display separately and Compare the results.

[0135] Gradually increase the value of T, each time increasing by one Δt, and compare the obtained results with each sampling point until the entire signal range is covered. For example, when T=2Δt:

[0136]

[0137] The comparison results of the following two formulas are shown by controlling the step function.

[0138]

[0139]

[0140] Continue increasing the value of T until the entire signal range is covered. Eventually, when T is infinite, the integral covers the entire time axis, as shown in the following formula:

[0141]

[0142] It should be noted that the user performs the initial display in advance, and the steps of generating the input signal and unit impulse signal and display are shown above and will not be repeated here. The integral range needs to be gradually increased by controlling the step function. The specific steps are as follows: (1) The user gradually increases the T value, increasing it by one Δt each time, and dynamically displays the increase in the T value. (2) The graph is updated in real time to display the new impulse function and its weight. (3) The sum of the impulse function and its weight in each step is sent to the LTI system, and the first result is obtained through the first summation formula. (4) Each impulse function and its weight in each step is sent to the linear property reasoning module, and the second result is obtained through the second summation formula. (5) The first result and the second result are compared, and the comparison results of each sampling point between the first result and the second result are displayed, as well as the comparison results of the equivalence between the first result and the second result, and the important conclusion of exchanging the order of integration and signal processing is obtained.

[0143] It is further explained that this application adopts a dynamic step-by-step display formula to gradually show that y(t) = F[x(t)] = F[∫x(τ)δ(t-τ) dτ]= ∫F[x(τ)δ(t-τ)] dτ. When an impulse signal is expanded by the impulse function, the sum of the results of each impulse function and its weight after being processed by this linear signal system is equal to the result of the sum of each impulse function and its weight after being processed by the linear system. The basic formula is transformed equivalently to show this process more clearly step by step. Specifically, the integral of the basic formula is decomposed into finite and infinite parts, and a window function is introduced to gradually show the expansion of each step.

[0144] In one embodiment, the convolution theorem derivation module 113 includes: a third signal generation submodule, a third impulse function generation submodule, a third signal decomposition submodule, a convolution theorem proving module, and a third animation module; the third signal generation submodule is used to generate an input signal and specify a unit impulse function type; the third impulse function generation submodule is used to generate a unit impulse function according to the unit impulse function type and determine a corresponding time interval; the third signal decomposition submodule is used to decompose the input signal into a sum of multiple weighted unit impulse functions; the convolution theorem proving module is used to obtain a second result through a second summation formula; the convolution theorem proving module is further used to obtain a third result through a third summation formula;

[0145] The third summation formula is:

[0146]

[0147] Where x(t) is the input signal, is the unit impulse function, is the processing function of the LTI system circuit signal processing module 114, h(t) is the impulse response obtained after the unit impulse signal is processed by the LTI system circuit signal processing module 114, Δt is the time interval, N is the number of discrete points of integration, and k is the index of the discrete point; the third animation module is used to dynamically display the comparison results between the second result and the third result of each sampling point in step by step, and the comparison results of the equivalence between the second result and the third result, and, based on the weighted sum of the signal components of each impulse response signal and each input signal, finally form a complete convolution process of the impulse response and the input signal.

[0148] It should be noted that the following discrete point formula is obtained by windowing the integral function:

[0149]

[0150] Due to the linear nature of the LTI system, x(kΔt) can be regarded as a discrete point that is independent of the independent variable t. , which can be regarded as a scalar x(kΔt) multiplied by δ(t−kΔt). According to the linear properties of the LTI system, we have: F[ ]=x(kΔt)F[ ].

[0151] Due to the time-invariant nature of the LTI system, if the system's response to the unit impulse function δ(t) is h(t), that is, F[δ(t)]=h(t), then the impulse function with time offset is , the response is .

[0152] Therefore, combining these two points, we have F[ ]=x(kΔt)h[ ], so we get the following step-by-step formula of the convolution theorem:

[0153]

[0154] in represents the input signal, is the impulse response obtained after the unit impulse function is processed by the linear signal processing system, is the processing function of the LTI system circuit signal processing module 114.

[0155] In order to facilitate the step-by-step control triggering and display of the superposition of each component in the experimental setup, the unit step function u(t) will be used to explicitly represent the delay operation. The above formula is further rewritten as follows:

[0156]

[0157] pass Controlling the start time of each component makes it easier to demonstrate the superposition of each component in the experimental setup by controlling the triggering of the step function.

[0158] In this embodiment, by selecting a smaller T=Δt, only one impulse function is included:

[0159]

[0160] Display separately and Compare the results.

[0161] Gradually increase the value of T, each time increasing by one Δt, and compare the obtained results with each sampling point until the entire signal range is covered. For example, when T=2Δt:

[0162]

[0163] The comparison results of the following two formulas are shown by controlling the step function.

[0164]

[0165]

[0166] Continue increasing the value of T until the entire signal range is covered. Eventually, when T is infinite, the integral covers the entire time axis, as shown in the following formula:

[0167]

[0168] It should be noted that the result of infinite integration of step-by-step superposition is The convolution results are compared and displayed, and finally the step-by-step derivation of the complete convolution theorem is demonstrated.

[0169] It should be noted that the user performs the initial display in advance, and the steps of generating the input signal and unit impulse signal and display are shown above, which will not be repeated here. The integral range needs to be gradually increased by controlling the step function. The specific steps are as follows: (1) The user gradually increases the T value, increasing it by Δt each time, and dynamically displays the increase in the T value. (2) The graph is updated in real time to display the new impulse function and its weight. (3) Each impulse function and its weight in each step are sent to the signal processing system to display the results of each component. , and then sum each component through the second summation formula to obtain the second result. (4) Send each impulse function in each step to the signal processing system, multiply the obtained impulse response with the value corresponding to the input signal at that step, display the result of each component, and obtain the third result through the third summation formula (5) Dynamically display the comparison results between the second result and the third result of each sampling point in steps, and the comparison results of the equivalence between the second result and the third result, and, based on the weighted sum of the signal components of each impulse response signal and each input signal, finally form a complete convolution process of the impulse response and the input signal.

[0170] It is further explained that the present application uses a fixed window to derive a dynamic step-by-step display formula, which gradually shows that due to the superposition and homogeneity of the LTI system, the system's response to the input signal can be expressed as a weighted superposition of the unit impulse response of each input component as a weight, and further determines that the output y(t) can be regarded as the input signal x(t) and the system's unit impulse response T[δ ] to prove the convolution theorem. By employing a fixed window to perform an equivalent transformation of the original formula, at each time step, the system processes the input signal components, calculates the weighted sum of the components' contributions to the output, and then superimposes these weighted sums to obtain the system's response to the entire input signal. This interactive and dynamic display intuitively helps users gain a deeper understanding of the convolution process, as well as the additive and homogeneous properties of LTI systems, effectively reducing comprehension and improving learning outcomes.

[0171] In one embodiment, if Figure 2 As shown, the frequency domain analysis subsystem 12 includes: a spectrum editing module 121; the spectrum editing module 121 is used to click or drag the frequency on the spectrum graph to adjust it, and display the adjusted frequency in real time; the spectrum editing module 121 is also used to edit and change the frequency domain characteristics of the unit impulse response signal, convolve the changed unit impulse response signal with the input signal, and use the convolved signal with the changed frequency domain characteristics as the fourth result.

[0172] In one embodiment, the frequency domain analysis subsystem 12 also includes: a comparison display module 122; the comparison display module 122 is used to send the input signal to the LTI system circuit signal processing module 114 to obtain an output signal, and use the output signal as the fifth result; the comparison display module 122 is also used to display the comparison result signal generated by comparing the fifth result and the fourth result, and dynamically display the change process of the spectrum diagram.

[0173] It should be noted that the spectrum editing module 121 can implement the following functions: (1) frequency selection and adjustment, where the user can click or drag the frequency components on the spectrum graph to adjust and change their amplitude and phase. (2) real-time feedback, where the spectrum and time domain signal of the adjusted system output signal are displayed in real time, allowing the user to immediately see the effect of the adjustment.

[0174] To make operations more convenient and intuitive, the module uses some interactive methods to simplify the amplitude and phase adjustment process. For example, users can drag points on polar coordinates to adjust both amplitude and phase simultaneously. Polar coordinates are used to visually represent amplitude and phase in the spectrum graph. Each frequency component is represented as a vector, and users can adjust it by dragging the endpoints of the vector. If dragging radially, the length of the vector is changed to adjust the amplitude. If dragging angularly, the vector is rotated to adjust the phase. Users can also directly adjust formulas and mapping functions.

[0175] Users only need to perform simple drag operations to directly and clearly adjust frequency components in the visual interface of the spectrum graph, thereby successfully achieving the desired signal modification goals. This greatly improves the convenience and efficiency of operations, effectively reduces the difficulty of understanding, and improves learning effects.

[0176] In one embodiment, the system also includes: a user interaction subsystem 13; the user interaction subsystem 13 is used to control the sampling interval, total sampling time, type of window function and windowing range in the signal processing and display process, and provide stepping, backtracking, comparison and zooming functions.

[0177] In this embodiment, the first animation module, the second animation module and the third animation module are used to generate an animation sequence based on the output of the signal processing module, and create animation frames for the processing of each impulse function and its weight.

[0178] Each animation module includes the following components: a graphics rendering engine, responsible for converting mathematical data into visual graphics and plotting impulse functions, weights, and accumulated signals; a multi-view manager, which manages multiple views, such as time domain and frequency domain views, and allows for simultaneous display of signal representations from different angles; and an animation controller, which controls the playback, pausing, and speed adjustment of animations, achieving smooth animation transitions.

[0179] Each animation module is controlled by the user interaction subsystem 13 to allow the user to control the animation playback, and provide interactive functions such as stepping, backtracking, comparing and zooming to observe specific parts of the signal in detail, and support fast playback and jumping of the animation by storing intermediate calculation results.

[0180] This application more intuitively and dynamically displays the decomposition of the input signal into the weighted sum of multiple unit impulse functions, and shows the process of the input signal being gradually expanded by the unit impulse function. It displays the first result, second result, third result, fourth result and fifth result step by step, sampling point by sampling point, as well as the comparison results of the equivalence between each result, to help users understand the expansion process of each step and its final result, making abstract mathematical concepts intuitive and visible.

[0181] Example 2

[0182] An embodiment of the present application provides a method for simulating an LTI system circuit.

[0183] See also Figure 3 ,LTI system circuit simulation methods include:

[0184] S301 , decomposing an input signal into a weighted sum of multiple unit impulse functions through the signal decomposition module 111 , and displaying a process in which the input signal is gradually expanded by the unit impulse functions.

[0185] S302, obtaining the first response signal after the weighted sum of each unit impulse function is processed by the LTI system circuit signal processing module 114 through the linear system property proof module 112, and taking the first response signal as the first result, and, obtaining multiple second response signals after the signal components of each input signal as the corresponding unit impulse function and the corresponding weight are processed by the LTI system circuit signal processing module 114, and taking the sum of the second response signals as the second result.

[0186] S303 , the linear system property proving module 112 is further used to display the first result, the second result, and the comparison result of the equivalence between the first result and the second result step by step and sampling point by sampling point.

[0187] S304: The convolution theorem derivation module 113 uses the signal components of each input signal as a weight, and the response obtained after each unit impulse function is processed by the LTI system circuit signal processing module 114 is used as a third response signal. The third response signal is weightedly superimposed with the signal components of each input signal, and the obtained weighted superposition sum is used as the third result.

[0188] S305 , the convolution theorem derivation module 113 is further used to display the second result and the third result, as well as the comparison result of the equivalence between the second result and the third result.

[0189] S306. Obtain, through the frequency domain analysis subsystem 12, a unit impulse response signal of the unit impulse function after being processed by the LTI system circuit signal processing module 114, edit and change the frequency domain characteristics of the unit impulse response signal, convolve the changed unit impulse response signal with the input signal, and use the convolved signal with the changed frequency domain characteristics as a fourth result. S306. Send the input signal to the LTI system circuit signal processing module 114 to obtain an output signal, and use the output signal as a fifth result.

[0190] S307 , displaying the fourth result and the fifth result, as well as the comparison result of the frequency domain difference between the fourth result and the fifth result, through the frequency domain analysis subsystem 12 .

[0191] This application more intuitively and dynamically displays the decomposition of the input signal into the weighted sum of multiple unit impulse functions, and shows the process of the input signal being gradually expanded by the unit impulse function. It displays the first result, second result, third result, fourth result and fifth result step by step, sampling point by sampling point, as well as the comparison results of the equivalence between each result, to help users understand the expansion process of each step and its final result, making abstract mathematical concepts intuitive and visible.

[0192] Example 3

[0193] In addition, an embodiment of the present application provides an electronic device, including a memory and a processor, wherein the memory stores a computer program, and when the computer program runs on the processor, it executes the LTI system circuit simulation method provided in Example 2.

[0194] For details, see Figure 4The electronic device 400 includes: a transceiver 401, a bus interface and a processor 402, the processor 402 is used to: decompose the input signal into a weighted sum of multiple unit impulse functions through the signal decomposition module 111, and display the process of the input signal being gradually expanded by the unit impulse function; obtain the first response signal after the weighted sum of each unit impulse function is processed by the LTI system circuit signal processing module 114 through the linear system property proof module 112, and use the first response signal as the first result; and, according to each unit impulse function and the corresponding signal component of each input signal as the weight, obtain multiple second response signals after being processed by the LTI system circuit signal processing module 114, and use the sum of the second response signals as the second result; also display the first result, the second result and the comparison result of the equivalence between the first result and the second result step by step sampling point by sampling point through the linear system property proof module 112; use the signal component of each input signal as the weight to derivate the convolution theorem of each unit impulse function. The response obtained after the excitation function is processed by the LTI system circuit signal processing module 114 is used as the third response signal, and the signal components of each input signal are weighted superimposed on the third response signal, and the obtained weighted superposition sum is used as the third result; the second result and the third result, as well as the comparison result of the equivalence between the second result and the third result are also displayed through the convolution theorem derivation module 113; the unit impulse response signal after the unit impulse function is processed by the LTI system circuit signal processing module 114 is obtained through the frequency domain analysis subsystem 12, the frequency domain characteristics of the unit impulse response signal are edited and changed, the changed unit impulse response signal is convolved with the input signal, and the convolution signal with the changed frequency domain characteristics is used as the fourth result, and the input signal is sent to the LTI system circuit signal processing module 114 to obtain the output signal, and the output signal is used as the fifth result; the fourth result and the fifth result, as well as the comparison result of the frequency domain difference between the fourth result and the fifth result are displayed through the frequency domain analysis subsystem 12.

[0195] In the embodiment of the present application, the electronic device 400 further includes a memory 403. Figure 4 In the embodiment, the bus architecture may include any number of interconnected buses and bridges, specifically connecting various circuits such as one or more processors represented by processor 402 and memory represented by memory 403. The bus architecture may also connect various other circuits such as peripheral devices, voltage regulators, and power management circuits, which are well known in the art and therefore will not be described further herein. The bus interface provides an interface. The transceiver 401 may be a plurality of components, i.e., a transmitter and a receiver, providing a unit for communicating with various other devices over a transmission medium. The processor 402 is responsible for managing the bus architecture and general processing, and the memory 403 may store data used by the processor 402 when performing operations.

[0196] The electronic device 400 provided in the embodiment of the present application can execute the steps of the LTI system circuit simulation method provided in the above method embodiment 2, which will not be described again here to avoid repetition.

[0197] The electronic device provided in this embodiment dynamically and intuitively displays the expansion process of the impulse function of the input signal x(t), decomposes the integral of the original formula into finite and infinite parts, and introduces a window function to gradually display the expansion of each step, helping users understand the expansion process of each step and its final result, making abstract mathematical concepts intuitive and visible.

[0198] Example 4

[0199] The present application also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the LTI system circuit simulation method provided in Example 2 is implemented.

[0200] In this embodiment, the computer-readable storage medium may be a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0201] The computer-readable storage medium provided in this embodiment can implement the LTI system circuit simulation method provided in Example 2, and will not be described again here to avoid repetition.

[0202] The embodiments of the present application are described above in conjunction with the accompanying drawings, but the present application is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the guidance of this application, ordinary technicians in this field can also make many forms without departing from the purpose of this application and the scope of protection of the claims, all of which are within the protection of this application.

Claims

1. An LTI system circuit simulation system, characterized in that: The system includes: a time domain analysis subsystem and a frequency domain analysis subsystem; The time domain analysis subsystem includes: a signal decomposition module, a linear system property proof module, a convolution theorem derivation module and an LTI system circuit signal processing module; The signal decomposition module is used to decompose the input signal into a weighted sum of multiple unit impulse functions and display the process of the input signal being gradually expanded by the unit impulse functions; The linear system property proving module is configured to obtain a first response signal after the weighted sum of the unit impulse functions is processed by the LTI system circuit signal processing module, and use the first response signal as a first result; and a plurality of second response signals obtained after the LTI system circuit signal processing module processes the signal components of the input signals according to the unit impulse functions and the corresponding weights, and use the sum of the second response signals as a second result; The linear system property proof module is further used to display the first result, the second result, and the comparison result of the equivalence between the first result and the second result step by step and sampling point by sampling point; The convolution theorem derivation module is configured to use the signal components of each input signal as a weight, obtain a response after each unit impulse function is processed by the LTI system circuit signal processing module as a third response signal, perform weighted superposition of the signal components of each input signal on the third response signal, and obtain the weighted superposition sum as a third result; The convolution theorem derivation module is further used to display the second result and the third result, as well as a comparison result of the equivalence between the second result and the third result; The frequency domain analysis subsystem is configured to obtain a unit impulse response signal after the unit impulse function is processed by the LTI system circuit signal processing module, edit and change the frequency domain characteristics of the unit impulse response signal, convolve the changed unit impulse response signal with the input signal, and use the convolved signal with the changed frequency domain characteristics as a fourth result; and, input the input signal to the LTI system circuit signal processing module to obtain an output signal, and use the output signal as a fifth result; The frequency domain analysis subsystem is further used to display the fourth result and the fifth result, as well as a comparison result of the frequency domain differences between the fourth result and the fifth result.

2. The LTI system circuit simulation system according to claim 1, characterized in that: The signal decomposition module includes: a first signal generation submodule, a first impulse function generation submodule, a first step function control submodule, a first signal decomposition submodule and a first animation module; The first signal generating submodule is used to generate an input signal and specify a unit impulse function type; The first impulse function generating submodule is configured to generate a unit impulse function according to the unit impulse function type and determine a corresponding time interval; The first signal decomposition submodule is configured to decompose the input signal into a sum of multiple weighted unit impulse functions using a signal decomposition formula; The signal decomposition formula is: ； in, is the input signal, is the unit impulse function, Δt is the time interval, N is the number of discrete points of integration, and k is the index of the discrete point; The first step function control submodule is configured to gradually increase the time interval using a unit step formula and superimpose a weighted unit impulse function; The unit step formula is: ； in, is a unit step function, is a signal component of the input signal expanded by a unit impulse function; The first animation module is used to dynamically display, step by step according to the sampling points, the various weighted impulse signals formed by the decomposition of the input signal by the unit impulse function at each sampling point, as well as the process of expanding the unit impulse function of the complete input signal based on each unit impulse function and the weighted sum of each unit impulse function.

3. The LTI system circuit simulation system according to claim 1, characterized in that: The linear system property proof module includes: a second signal generation submodule, a second impulse function generation submodule, a second signal decomposition submodule, a linear property reasoning module and a second animation module; The second signal generating submodule is used to generate an input signal and specify a unit impulse function type; The second impulse function generating submodule is configured to generate a unit impulse function according to the unit impulse function type and determine a corresponding time interval; The second signal decomposition submodule is used to decompose the input signal into a sum of multiple weighted unit impulse functions; The linear property reasoning module is configured to obtain the first result by using a first summation formula, and obtain the second result by using a second summation formula; The first summation formula is: ； Where x(t) is the input signal, is the impulse function, is the processing function of the signal processing module of the LTI system circuit, Δt is the time interval, N is the number of discrete points of integration, and k is the index of the discrete point; The second summation formula is: ； The second animation module is used to dynamically display the comparison results of each sampling point between the first result and the second result in steps according to the sampling points, and the comparison results of the equivalence between the first result and the second result.

4. The LTI system circuit simulation system according to claim 3, characterized in that: The convolution theorem derivation module includes: a third signal generation submodule, a third impulse function generation submodule, a third signal decomposition submodule, a convolution theorem proving module and a third animation module; The third signal generating submodule is used to generate an input signal and specify a unit impulse function type; The third impulse function generating submodule is configured to generate a unit impulse function according to the unit impulse function type and determine a corresponding time interval; The third signal decomposition submodule is used to decompose the input signal into a sum of multiple weighted unit impulse functions; The convolution theorem proving module is configured to obtain the second result through the second summation formula; The convolution theorem proving module is further configured to obtain a third result through a third summation formula; The third summation formula is: Where x(t) is the input signal, is the unit impulse function, is the processing function of the LTI system circuit signal processing module, h(t) is the impulse response obtained after the unit impulse signal is processed by the LTI system circuit signal processing module, Δt is the time interval, N is the number of discrete points of integration, and k is the index of the discrete point; The third animation module is used to dynamically display the comparison results between the second result and the third result of each sampling point in steps, the comparison results of the equivalence between the second result and the third result, and the convolution process of the complete impulse response and the input signal based on the weighted sum of the signal components of each impulse response signal and each input signal.

5. The LTI system circuit simulation system according to claim 1, characterized in that: The frequency domain analysis subsystem includes: a spectrum editing module; The spectrum editing module is used to click or drag the frequency on the spectrum graph to adjust it and display the adjusted frequency in real time; The spectrum editing module is further configured to edit and change the frequency domain characteristics of the unit impulse response signal, convolve the changed unit impulse response signal with the input signal, and use the convolved signal with the changed frequency domain characteristics as a fourth result.

6. The LTI system circuit simulation system according to claim 5, characterized in that: The frequency domain analysis subsystem further includes: a comparison and display module; The comparison and display module is configured to input the input signal into the LTI system circuit signal processing module to obtain an output signal, and use the output signal as a fifth result; The comparison display module is further used to display a comparison result signal generated by comparing the fifth result and the fourth result, and dynamically display a change process of the spectrum diagram.

7. The LTI system circuit simulation system according to any one of claims 1 to 6, characterized in that: The system further comprises: a user interaction subsystem; The user interaction subsystem is used to control the sampling interval, total sampling time, window function type and windowing range during signal processing and display, and provides stepping, backtracking, comparison and zooming functions.

8. A method for simulating an LTI system circuit, characterized in that: The method applied to the LTI system circuit simulation system according to any one of claims 1 to 7 includes: Decomposing the input signal into a weighted sum of multiple unit impulse functions by the signal decomposition module, and displaying the process of gradually expanding the input signal by the unit impulse functions; Obtaining, by the linear system property proving module, a first response signal after the weighted sum of the unit impulse functions is processed by the LTI system circuit signal processing module, and using the first response signal as a first result; and obtaining, by the LTI system circuit signal processing module, a plurality of second response signals after processing the unit impulse functions and the corresponding signal components of the input signals as weights, and using the sum of the second response signals as a second result; Furthermore, the first result, the second result, and a comparison result of the equivalence between the first result and the second result are displayed step by step and sampling point by sampling point by the linear system property proof module; Using the convolution theorem derivation module as a weight, a response obtained after each unit impulse function is processed by the LTI system circuit signal processing module is used as a third response signal, performing weighted superposition of the signal components of each input signal on the third response signal, and obtaining a weighted superposition sum as a third result; The second result and the third result, as well as a comparison result of equivalence between the second result and the third result, are also displayed through the convolution theorem derivation module; Obtaining, through the frequency domain analysis subsystem, a unit impulse response signal of the unit impulse function after being processed by the LTI system circuit signal processing module, editing and changing a frequency domain characteristic of the unit impulse response signal, convolving the changed unit impulse response signal with the input signal, and using the convolved signal with the changed frequency domain characteristic as a fourth result; and, sending the input signal to the LTI system circuit signal processing module to obtain an output signal, and using the output signal as a fifth result; The fourth result and the fifth result, as well as the comparison results of the frequency domain differences between the fourth result and the fifth result, are displayed by the frequency domain analysis subsystem.

9. An electronic device, characterized in that: The system comprises a memory and at least one processor, wherein the memory stores a computer program, and the processor is configured to execute the computer program to implement the LTI system circuit simulation method according to claim 8.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, and when the computer program is executed, the LTI system circuit simulation method according to claim 8 is implemented.

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