A digital signal processing method, system, terminal and storage medium

Abstract

The application provides a digital signal processing method, system, terminal and storage medium, relates to the field of digital signal processing, and in particular to a digital signal processing method.The method comprises the following steps: acquiring an original digital signal; and using a second-order derivative interpolation method to perform interpolation processing on the original digital signal by using a second-order derivative of a function, so as to obtain first data.The application can improve the interpolation accuracy of the interpolation algorithm in digital signal processing and reduce the error between the data obtained through interpolation and the real data.

Description

Technical Field

[0001] This application relates to the field of digital signal processing, and in particular to a digital signal processing method, system, terminal, and storage medium. Background Technology

[0002] In practical digital signal sampling, because the sampled data is discrete—that is, sample values ​​are acquired at equal time intervals (e.g., a sampling frequency of 1000Hz, meaning a sample value is acquired every 1ms)—some useful sample values ​​will not be collected, hindering precise time-domain analysis. There are two solutions in practical applications: one is to increase the sampling frequency. This method generally yields data that meets the requirements for precise analysis, but the data volume is large, consuming more storage space and reducing work efficiency, failing to meet the practical application needs of digital signal acquisition and analysis. The other method is to use the acquired known digital signal samples to estimate the unknown required digital signal samples. Interpolation, as an important method of numerical approximation, can estimate the approximate value of unknown samples by considering the values ​​of a finite number of samples. Common digital signal interpolation algorithms include Lagrange interpolation, Newton interpolation, and Hermitian interpolation. These interpolation methods are all linear interpolation, computationally simple and stable, but their interpolation errors are large, and their smoothness is poor, leading to digital signal distortion, peak loss, and the introduction of spurious frequency components.

[0003] Therefore, how to improve the interpolation accuracy of interpolation algorithms in digital signal processing and reduce the error between the interpolated data and the real data is a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0004] To address the aforementioned technical problems, this application provides a digital signal processing method that can improve the interpolation accuracy of interpolation algorithms in digital signal processing and reduce the error between the interpolated data and the actual data. This application also provides a digital signal processing system, terminal, and storage medium, which have the same technical effects.

[0005] The first objective of this application is to provide a digital signal processing method.

[0006] The aforementioned objective of this application is achieved through the following technical solution:

[0007] A digital signal processing method, comprising:

[0008] Acquire the raw digital signal;

[0009] The first data is obtained by interpolating the original digital signal using the second derivative of the function.

[0010] Preferably, in the digital signal processing method, the step of using the second derivative interpolation method to interpolate the original digital signal using the second derivative of a function to obtain the first data includes:

[0011] In each interval formed by two adjacent data nodes of the original digital signal, a second-order derivative interpolation function is constructed.

[0012] Construct the system of matrix equations for solving the second-order derivative interpolation function;

[0013] Substitute each data node of the original digital signal into the matrix equations and solve for the second-order differential value.

[0014] Substitute the second derivative value into the second derivative interpolation function to calculate the second derivative interpolation function for each interval;

[0015] Determine the interval in which the interpolation node is located, and calculate the function value corresponding to the interpolation node based on the second derivative interpolation function of the interval in which the interpolation node is located;

[0016] The original digital signal is interpolated based on the interpolation node and the function value corresponding to the interpolation node to obtain the first data.

[0017] Preferably, in the digital signal processing method, constructing a second-order derivative interpolation function in each interval formed by two adjacent data nodes of the original digital signal includes:

[0018] Suppose the original digital signal contains n data nodes, namely (x1, y1), (x2, y2), ..., (x... n ,y n ), where n is a positive integer greater than 1, to obtain each interval [x] formed by two adjacent data nodes of the original digital signal. i ,x i+1 (i = 1, 2, ..., n-1);

[0019] Construct the intervals [x] i ,x i+1 The second derivative interpolation function S of (i = 1, 2, ..., n-1) i (x)=a i +b i (xx i )+c i (xx i ) 2 +d i (xx i ) 3 (x i ≤x≤x i+1 In the formula, x represents the independent variable of the interpolation function, and a i,b i ,c i ,d i The coefficients of the second-order derivative interpolation function are as follows:

[0020]

[0021] In the formula, m i The value is the second derivative, with a step size h. i =x i+1 -x i (i = 1, 2, ..., n-1).

[0022] Preferably, in the digital signal processing method, constructing the matrix equation system for solving the second-order derivative interpolation function includes:

[0023] Based on the data nodes (x1, y1), (x2, y2), ..., (x n ,y n Constructing matrix equation one: S(x) i )=y i (i = 1, 2, ..., n), where y represents the function value corresponding to data node x, i represents the number of data nodes, and n is a positive integer greater than 1;

[0024] Based on the fact that S(x), S′(x), and S″(x) have second-order continuous derivatives in the original digital signal, construct the second square matrix equation:

[0025]

[0026] In the formula, i represents the number of data nodes, and n is a positive integer greater than 1;

[0027] Based on the fact that S(x) is a data point with an integer period in the original digital signal, construct matrix equation three:

[0028]

[0029] In the formula, n is a positive integer greater than 1.

[0030] Preferably, in the digital signal processing method, the step of substituting each data node of the digital signal into the matrix equation system to obtain the second-order differential value includes:

[0031] Substituting the data node into matrix equation one, matrix equation two, and matrix equation three, the second differential value m is obtained by solving. i =S i "(x i );

[0032] Accordingly, substituting the second derivative value into the second derivative interpolation function to calculate the second derivative interpolation function for each interval includes:

[0033] Based on the second derivative value, the data node, and the step size, a is obtained by solving the problem. i ,b i ,c i ,d i And according to the a i ,b i ,c i ,d i The second-order derivative interpolation function S for each interval is calculated. i (x);

[0034] Accordingly, determining the interval where the interpolation node is located, and calculating the function value corresponding to the interpolation node based on the second derivative interpolation function of the interval where the interpolation node is located, includes:

[0035] Determine the interpolation node x′ k The interval [x] i ,x i+1 (i = 1, 2, ..., n-1), based on the interpolation node x′ k The second derivative interpolation function S in the interval i (x) calculates the interpolation node x′ k The corresponding function value y′ k , where k represents the number of interpolation nodes;

[0036] Accordingly, the step of interpolating the original digital signal based on the interpolation node and the function value corresponding to the interpolation node to obtain the first data includes:

[0037] According to the interpolation node x′ k and the interpolation node x′ k The corresponding function value y′ k The original digital signal is interpolated to obtain the first data.

[0038] Preferably, in the digital signal processing method, acquiring the original digital signal specifically includes:

[0039] According to the sampling frequency F s The time series is T, and the time length is T. Time interval ΔT = 1 / F s The original digital signal was obtained by sampling: Where, N A N represents the number of sampling points. A =TF s .

[0040] Preferably, in the digital signal processing method, the step of using the second derivative interpolation method to interpolate the original digital signal using the second derivative of the function to obtain the first data specifically includes:

[0041] The original digital signal was processed using the second-derivative interpolation method. Interpolation is performed to obtain the first data: Where, N B N represents the number of sampling points after interpolation. B =TF′ s F′ s This indicates the sampling frequency after interpolation, and the time series corresponding to the first data is...

[0042] Preferably, in the digital signal processing method, after obtaining the original digital signal data through sampling, the method further includes:

[0043] For the original digital signal, according to the segmented time interval T Dmin If segmentation is performed, the sampling frequency F′ of the interpolated data will be... s According to the segmented time interval T Dmin The calculation yielded:

[0044]

[0045] In the formula, M takes the form of a positive integer greater than or equal to 2;

[0046] Choosing the cutoff time point as the interpolation point, and using the second-derivative interpolation method, the sampling frequency F is... s The original digital signal is interpolated at a sampling frequency of F′. s The data yields the first set of data: (Z′1, Z′2, ..., Z′) N′ ), where the subscript N′ has the value: N′=[TF′ s [] represents the floor function, and [] represents the floor function. The time series corresponding to the first data is (t′1, t′2, ..., t′). N′ );

[0047] For the first data, according to the segmented time interval T Dmin The data is truncated to obtain the second data.

[0048] Preferably, in the digital signal processing method, the step of using the second derivative interpolation method to interpolate the original digital signal using the second derivative of the function to obtain the first data specifically includes:

[0049] For the original digital signal, the second-derivative interpolation method is used to interpolate the sampling frequency F. sThe original digital signal is interpolated at a sampling frequency of F′. s The data yields the first set of data: (Z′1, Z′2, ..., Z′) N′ ), where the subscript N′ has the value: N′=[TF′ s [], [] is the floor function, F′ s Greater than F s The time series corresponding to the first data is (t′1, t′2, ..., t′). N′ ).

[0050] Preferably, in the digital signal processing method, after obtaining the first data, the method further includes:

[0051] The first data is subjected to anti-aliasing filtering to obtain the third data.

[0052] The second objective of this application is to provide a digital signal processing system.

[0053] The second objective of this application is achieved through the following technical solution:

[0054] A digital signal processing system, characterized in that it comprises:

[0055] The data acquisition module is used to acquire raw digital signals;

[0056] The interpolation processing module is used to interpolate the original digital signal using the second derivative of the function to obtain the first data.

[0057] The third objective of this application is to provide a digital signal processing terminal.

[0058] The aforementioned objective three of this application is achieved through the following technical solution:

[0059] A digital signal processing terminal includes: a storage medium and a processor;

[0060] The storage medium stores computer-executed instructions.

[0061] The processor executes computer execution instructions stored in the storage medium to implement any of the methods described above in the digital signal processing method.

[0062] The fourth objective of this application is to provide a computer-readable storage medium.

[0063] The fourth objective of this application is achieved through the following technical solution:

[0064] A computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, are used to implement any of the methods described above in the digital signal processing method.

[0065] The above technical solution utilizes a second-derivative interpolation method to perform interpolation processing on the original digital signal, achieving further processing of the original digital signal. This overcomes the problems of signal distortion, peak loss, and the introduction of spurious frequency components inherent in linear interpolation, ensuring interpolation accuracy and significantly reducing the error between the interpolated data and the actual data. Simultaneously, compared to higher-order linear interpolation methods, it greatly shortens processing time, improves the efficiency of digital signal processing, and is beneficial for data processing in online real-time monitoring. In summary, the above technical solution can improve the interpolation accuracy of interpolation algorithms in digital signal processing and reduce the error between the interpolated data and the actual data. Attached Figure Description

[0066] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0067] Figure 1 This is a flowchart illustrating a digital signal processing method provided in an embodiment of this application;

[0068] Figure 2 This is a schematic diagram of the interpolation process in the embodiments of this application;

[0069] Figure 3 This is a schematic diagram of the original digital signal in an embodiment of this application;

[0070] Figure 4 This is a schematic diagram of the first data in the embodiments of this application;

[0071] Figure 5 This is a schematic diagram of the structure of a digital signal processing system provided in an embodiment of this application;

[0072] Figure 6 This is a schematic diagram of the structure of a digital signal processing terminal provided in the embodiments of this application. Detailed Implementation

[0073] To enable those skilled in the art to better understand the technical solutions in this application, the technical solutions in the embodiments of this application will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0074] In the embodiments provided in this application, it should be understood that the disclosed methods and systems can be implemented in other ways. The system embodiments described below are merely illustrative. For example, the division of modules is only a logical functional division, and in actual implementation, there may be other division methods, such as: multiple modules or components can be combined, or integrated into another system, or some features can be ignored or not executed. In addition, the coupling, direct coupling, or communication connection between the various components shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or modules, and can be electrical, mechanical, or other forms.

[0075] The embodiments in this application are written in a progressive manner.

[0076] like Figure 1 As shown, this application provides a digital signal processing method, including:

[0077] S101. Acquire the raw digital signal;

[0078] In S101, specifically, different signal sources can be used to acquire corresponding digital signals as the original digital signals. These digital signals can be vibration data acquired through a vibration sensor, or temperature data acquired through a temperature sensor, etc. The specific acquisition method does not affect the implementation of this embodiment.

[0079] S102. Using the second derivative interpolation method, the original digital signal is interpolated using the second derivative of the function to obtain the first data.

[0080] In S102, the second-derivative interpolation method is used to construct an interpolation function using the idea of ​​the second derivative of a function, thereby achieving data interpolation. Specifically, the second-derivative interpolation function can be used to interpolate the original digital signal. For example, the original data signal can be divided into multiple intervals, a second-derivative interpolation function corresponding to each interval can be established, and the second-derivative interpolation function can be solved to obtain the interpolation node and the function value corresponding to each interval. Using the interpolation node and the function value corresponding to the interpolation node, the original digital signal is interpolated to obtain the first data.

[0081] Interpolation, as an important method of numerical approximation, can estimate the approximate value of an unknown sample by considering the values ​​of a finite number of samples. Common digital signal interpolation algorithms include Lagrange interpolation, Newton interpolation, and Hermitian interpolation. These interpolation methods are all linear interpolation, computationally simple and stable, but they have relatively large interpolation errors and poor smoothness, leading to problems such as digital signal distortion, peak loss, and the introduction of spurious frequency components.

[0082] The above embodiments utilize second-derivative interpolation to perform interpolation processing on the original digital signal, achieving further processing of the original digital signal. This overcomes the problems of signal distortion, peak loss, and the introduction of false frequency components inherent in linear interpolation, ensuring interpolation accuracy and significantly reducing the error between the interpolated data and the actual data. Simultaneously, compared to higher-order linear interpolation methods, it greatly shortens the processing time, improves the efficiency of digital signal processing, and is beneficial for data processing in online real-time monitoring. In summary, the above embodiments can improve the interpolation accuracy of interpolation algorithms in digital signal processing and reduce the error between the interpolated data and the actual data.

[0083] like Figure 2 As shown, based on the above embodiments, one implementation of the step of using the second derivative interpolation method to interpolate the original digital signal using the second derivative of the function to obtain the first data may include the following steps:

[0084] S201. Construct a second-order derivative interpolation function for each interval formed by two adjacent data nodes of the original digital signal;

[0085] In S201, specifically, the original digital signal can be assumed to contain n data nodes, namely (x1, y1), (x2, y2), ..., (x... n ,y n ), where n is a positive integer greater than 1, to obtain each interval [x] formed by two adjacent data nodes of the original digital signal. i ,x i+1 (i = 1, 2, ..., n-1);

[0086] Construct the intervals [x] i ,x i+1 The second derivative interpolation function S of (i = 1, 2, ..., n-1) i (x)=a i +b i (xx i )+c i (xx i ) 2 +d i (xx i ) 3 (xi ≤x≤x i+1 In the formula, x represents the independent variable of the interpolation function, and a i ,b i ,c i ,d i The coefficients of the second-order derivative interpolation function are as follows:

[0087]

[0088] In the formula, m i The value is the second derivative, with a step size h. i =x i+1 -x i (i = 1, 2, ..., n-1).

[0089] S202. Construct the matrix equation system for solving the second-order derivative interpolation function;

[0090] In S202, specifically, the data nodes (x1, y1), (x2, y2), ..., (x n ,y n Constructing matrix equation one: S(x) i )=y i (i = 1, 2, ..., n), where y represents the function value corresponding to data node x, i represents the number of data nodes, and n is a positive integer greater than 1;

[0091] Based on the fact that S(x), S′(x), and S″(x) have second-order continuous derivatives in the original digital signal, construct the second square matrix equation:

[0092]

[0093] In the formula, i represents the number of data nodes, and n is a positive integer greater than 1;

[0094] Based on the fact that S(x) is a data point with an integer period in the original digital signal, construct matrix equation three:

[0095]

[0096] In the formula, n is a positive integer greater than 1.

[0097] S203. Substitute each data node of the original digital signal into the matrix equation system and solve to obtain the second derivative value;

[0098] In S203, specifically, the data node can be substituted into matrix equation one, matrix equation two, and matrix equation three to obtain the second-order differential value m. i =S i "(xi ).

[0099] S204. Substitute the second derivative value into the second derivative interpolation function to calculate the second derivative interpolation function for each interval;

[0100] In S204, specifically, a can be obtained by solving based on the second derivative value, the data node, and the step size. i ,b i ,c i ,d i And according to the a i ,b i ,c i ,d i The second-order derivative interpolation function S for each interval is calculated. i (x).

[0101] S205. Determine the interval where the interpolation node is located, and calculate the function value corresponding to the interpolation node based on the second derivative interpolation function of the interval where the interpolation node is located;

[0102] Specifically, in S205, the interpolation node x′ can be determined. k The interval [x] i ,x i+1 (i = 1, 2, ..., n-1), based on the interpolation node x′ k The second derivative interpolation function S in the interval i (x) calculates the interpolation node x′ k The corresponding function value y′ k , where k represents the number of interpolation nodes.

[0103] S206. Based on the interpolation node and the function value corresponding to the interpolation node, the original digital signal is interpolated to obtain the first data.

[0104] In S206, specifically, it can be based on the interpolation node x′ k and the interpolation node x′ k The corresponding function value y′ k The original digital signal is interpolated to obtain the first data.

[0105] The digital signal processing method based on second-order derivative interpolation proposed in the above embodiments can be applied to the needs of different scenarios. For example, in another embodiment based on the above embodiments, when it is necessary to truncate the signal, and there is no sampling point at the time when truncation is required, the method can be used for interpolation and truncation. For example, when truncating an entire period, the following methods can be used:

[0106] S301. Based on the sampling frequency F sThe time series is T, and the time length is T. Time interval ΔT = 1 / F s The original digital signal was obtained by sampling: Where, N A N represents the number of sampling points. A =TF s .

[0107] S302. The original digital signal is segmented according to a time interval of T. Dmin If segmentation is performed, the sampling frequency F′ of the interpolated data will be... s According to the segmented time interval T D min The calculation yielded:

[0108]

[0109] In the formula, M is a positive integer greater than or equal to 2, which can be selected according to the actual use case.

[0110] S303. Select the cutoff time point as the interpolation point, and use the second derivative interpolation method to interpolate the sampling frequency F. s The original digital signal is interpolated at a sampling frequency of F′. s The data yields the first set of data: (Z′1, Z′2, ..., Z′) N′ ), where the subscript N′ has the value: N′=[TF′ s [] represents the floor function, and [] represents the floor function. The time series corresponding to the first data is (t′1, t′2, ..., t′). N′ );

[0111] Wherein, the interpolated time interval ΔT′=1 / F′ s The first data represents the data obtained after interpolation.

[0112] S304. For the first data, according to the segmented time interval T Dmin The data is truncated to obtain the second data.

[0113] In S304, the first data obtained after interpolation is truncated to obtain the second data.

[0114] In this embodiment, when the original digital signal is truncated, and there is no sampling point at the truncation point, the second-order derivative interpolation method is used to interpolate the truncation point before data truncation is performed. In this way, the data segment is a complete data with a start and an end.

[0115] In another embodiment based on the above embodiments, when it is necessary to recover the peak value lost due to digital signal sampling, the lost peak value can be recovered by interpolation using this method, including:

[0116] S401. Based on the sampling frequency F s The time series is T, and the time length is T. Time interval ΔT = 1 / F s The original digital signal was obtained by sampling: Where, N A N represents the number of sampling points. A =TF s .

[0117] S402. For the original digital signal, use the second-derivative interpolation method to convert the sampling frequency F... s The original digital signal is interpolated at a sampling frequency of F′. s The data yields the first set of data: (Z′1, Z′2, ..., Z′) N′ ), where the subscript N′ has the value: N′=[TF′ s [], [] is the floor function, F′ s Greater than F s The time series corresponding to the first data is (t′1, t′2, ..., t′). N′ ).

[0118] Wherein, the interpolated time interval ΔT′=1 / F′ s The first data represents the data obtained after interpolation, which can effectively restore the lost peak values.

[0119] Take the following specific implementation as an example:

[0120] The original digital signal is a sinusoidal signal with an amplitude of 1 and a frequency of 22Hz; the digital signal obtained from a sampling frequency of 100Hz is as follows: Figure 3 As shown.

[0121] The signal exhibits peak loss due to digital sampling, with the minimum peak value being 0.77, representing a loss of 23%.

[0122] Using the second-derivative interpolation method proposed in this paper, a digital signal with a sampling frequency of 100Hz is interpolated to first data with a sampling frequency of 400Hz, such as... Figure 4 As shown.

[0123] The peak values ​​in the signal that were lost due to digital sampling were restored to 0.9852 by interpolation, reducing the peak loss from 23% to 1.5%, which greatly solved the problem of peak loss in the original digital signal.

[0124] In another embodiment based on the above embodiments, the second-order derivative interpolation method is applied to the field of vibration signal processing to provide another digital signal processing method, including:

[0125] S501. Based on the sampling frequency F s The time series is T, and the time length is T. Time interval ΔT = 1 / F s The original digital signal was obtained by sampling: Where, N A N represents the number of sampling points. A =TF s .

[0126] In S501, specifically, the original digital signal is a vibration signal, and the vibration source for acquiring the vibration signal can be a rotating component.

[0127] S502. Using the second-derivative interpolation method, the original digital signal... Interpolation is performed to obtain the first data: Where, N B N represents the number of sampling points after interpolation. B =TF′ s F′ s This indicates the sampling frequency after interpolation, and the time series corresponding to the first data is...

[0128] In S502, specifically, based on the original digital signal, according to the rotation period f n1 N1 points are sampled in each rotation cycle, and the original digital signal is processed using the second-order derivative interpolation method. Interpolation is performed to obtain the first data: The first data represents the data obtained after interpolation, where F′ s =f n1 N1, the rotation period f n1 It can be the frequency cycle, engine blade rotation cycle, cage rotation cycle, etc.; the time series of the data after interpolation is... Time interval ΔT′=1 / F′ s The corresponding original digital signal: Where t1=t′1, Z1 = Z′1,

[0129] In this embodiment, when the original digital signal is a vibration signal, the vibration signal is truncated to an integer period according to the rotation period of a certain rotating component, such as the frequency cycle, the engine blade rotation period, the cage rotation period, etc., by means of the above-mentioned second-order interpolation method.

[0130] In another embodiment based on the above embodiments, after obtaining the first data, the method further includes:

[0131] S601. Perform anti-aliasing filtering on the first data to obtain the third data.

[0132] In step S601, the first data is subjected to anti-aliasing filtering based on the interpolated sampling frequency to obtain the third data. Specifically, the anti-aliasing filtering can be performed using a low-pass filter, with a cutoff frequency less than half of the interpolated sampling frequency. The purpose of the anti-aliasing filtering is to reduce spectral aliasing, ultimately yielding the third data.

[0133] In other embodiments of this application, the sampling frequency can also be set to F in the original digital signal. s By using the second-derivative interpolation method described above, the sampling frequency is changed to F′. s This enables the variation of the sampling frequency of digital signals.

[0134] In engineering signals, there are both detected signals whose frequency is directly proportional to the rotational speed frequency V of the rotating machinery, such as fault signals from bearings, gears, and wheels, and signals from track damage interacting with the wheels. These are best detected using the rotational speed tracking sampling method, i.e., signal acquisition at equal circumferential angle intervals. There are also detected signals with a basically fixed frequency, independent of the rotational speed frequency of the rotating machinery, such as generalized resonance signals of machinery, and signals from track ripples interacting with the wheels. These are best detected using the astronomical clock sampling method, i.e., signal acquisition at equal time intervals. In other embodiments of this application, the acquisition of the original digital signal can use astronomical clock sampling, and the acquired rotational speed pulse signal can be converted into rotational speed tracking sampling data through second-order interpolation. In other embodiments of this application, rotational speed tracking sampling can also be used during the acquisition of the original digital signal, and the data can be converted into astronomical clock sampling data through second-order interpolation, thereby achieving sampling method conversion.

[0135] The digital signal processing method provided in this application not only ensures the accuracy requirements of digital signal processing, but also can be applied to the needs of different scenarios. It is not limited to the implementation of the functions in the above embodiments, and can process all functions of digital signals through second-order derivative interpolation.

[0136] like Figure 5 As shown, in another embodiment of this application, a digital signal processing system is also provided, comprising:

[0137] Data acquisition module 10 is used to acquire raw digital signals;

[0138] The interpolation processing module 11 is used to interpolate the original digital signal using the second derivative of the function to obtain the first data.

[0139] like Figure 6As shown, in another embodiment of this application, a digital signal processing terminal is also provided, including: a storage medium 12 and a processor 13;

[0140] The storage medium 12 stores computer-executed instructions.

[0141] The processor 13 executes the computer execution instructions stored in the storage medium 12 to implement any of the methods described above in the digital signal processing method.

[0142] The processor 13 may include one or more processing cores. The processor 13 executes instructions, programs, code sets, or instruction sets stored in the storage medium 12, and calls data stored in the storage medium 12 to perform various functions and process data according to this application. The processor 13 may be at least one of a specific application integrated circuit, a digital signal processor, a digital signal processing device, a programmable logic device, a field-programmable gate array, a central processing unit, a controller, a microcontroller, and a microprocessor. It is understood that, for different devices, the electronic devices used to implement the functions of the processor 13 may also be other types.

[0143] The storage medium 12 can be used to store instructions, programs, code, code sets, or instruction sets. The storage medium 12 may include a program storage area and a data storage area. The program storage area may store instructions for implementing an operating system, instructions for at least one function, and instructions for implementing any of the aforementioned digital signal processing methods; the data storage area may store data involved in any of the aforementioned digital signal processing methods.

[0144] In another embodiment of this application, a computer-readable storage medium is also provided, wherein computer-executable instructions are stored therein, which, when executed by a processor, are used to implement any of the methods described above in the digital signal processing.

[0145] The computer-readable storage medium can be any medium capable of storing program code, such as a USB flash drive, portable hard drive, read-only memory, random access memory, or optical disc.

[0146] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A digital signal processing method, characterized in that, include: Acquire the raw digital signal; The first data is obtained by interpolating the original digital signal using the second derivative of the function through the second derivative of the function. The method of using second-order derivative interpolation, which involves interpolating the original digital signal using the second derivative of a function to obtain the first data, includes: In each interval formed by two adjacent data nodes of the original digital signal, a second-order derivative interpolation function is constructed. Construct the system of matrix equations for solving the second-order derivative interpolation function; Substitute each data node of the original digital signal into the matrix equations and solve for the second-order differential value. Substitute the second derivative value into the second derivative interpolation function to calculate the second derivative interpolation function for each interval; Determine the interval in which the interpolation node is located, and calculate the function value corresponding to the interpolation node based on the second derivative interpolation function of the interval in which the interpolation node is located; The original digital signal is interpolated based on the interpolation node and the function value corresponding to the interpolation node to obtain the first data; The construction of a second-order derivative interpolation function in each interval formed by two adjacent data nodes of the original digital signal includes: Suppose that the original digital signal contains n data nodes, namely... , The intervals formed by two adjacent data nodes of the original digital signal are obtained by assigning a positive integer greater than 1. ; Construct the intervals Second derivative interpolation function In the formula, This represents the independent variable of the interpolation function. The coefficients of the second-order derivative interpolation function are as follows: In the formula, The value is the second derivative, and the step size is... . The construction of the matrix equation system for solving the second-order derivative interpolation function includes: According to the data node Constructing Matrix Equation 1: In the formula, Represents data nodes The corresponding function value, Indicates the number of data nodes. It is a positive integer greater than 1; According to the above , , When the original digital signal has a second-order continuous derivative, construct the second square matrix equation: In the formula, Indicates the number of data nodes. It is a positive integer greater than 1; According to the above When the original digital signal contains a single integer period of data, matrix equation three is constructed: In the formula, It is a positive integer greater than 1.

2. The method as described in claim 1, characterized in that, The step of substituting each data node of the original digital signal into the matrix equations and solving for the second-order differential value includes: Substituting the data nodes into matrix equation one, matrix equation two, and matrix equation three, the second differential value is obtained by solving. ; Accordingly, substituting the second derivative value into the second derivative interpolation function to calculate the second derivative interpolation function for each interval includes: Based on the second derivative value, the data node, and the step size, the solution is obtained. and according to the The second derivative interpolation function for each interval is calculated. ; Accordingly, determining the interval where the interpolation node is located, and calculating the function value corresponding to the interpolation node based on the second derivative interpolation function of the interval where the interpolation node is located, includes: Determine interpolation nodes Location According to the interpolation nodes The second derivative interpolation function of the interval The interpolation nodes are calculated. Corresponding function value ,in, Indicates the number of interpolation nodes; Accordingly, the step of interpolating the original digital signal based on the interpolation node and the function value corresponding to the interpolation node to obtain the first data includes: According to the interpolation node and the interpolation node Corresponding function value The original digital signal is interpolated to obtain the first data.

3. The method as described in claim 1, characterized in that, The acquisition of the original digital signal specifically includes: Based on sampling frequency The duration is The time series is Time interval The original digital signal was obtained by sampling: ,in, Indicates the number of sampling points. .

4. The method as described in claim 3, characterized in that, The method of using second-order derivative interpolation, which involves interpolating the original digital signal using the second derivative of a function to obtain the first data, specifically includes: The original digital signal was processed using the second-derivative interpolation method. Interpolation is performed to obtain the first data: ,in, This indicates the number of sampling points after interpolation. , This indicates the sampling frequency after interpolation, and the time series corresponding to the first data is... .

5. The method as described in claim 3, characterized in that, After obtaining the original digital signal through sampling, the process also includes: For the original digital signal, according to the segmented time interval as If segmentation is performed, the sampling frequency of the interpolated data will be... According to the segmented time interval The calculation yielded: In the formula, Take a positive integer greater than or equal to 2; Choosing the cutoff time point as the interpolation point, and using the second-derivative interpolation method, the sampling frequency is... The original digital signal is interpolated at a sampling frequency of The data yields the first data: , where subscript The value is: , The floor sign is used for rounding down. The time series corresponding to the first data is: ; For the first data, according to the segmented time interval The data is truncated to obtain the second data.

6. The method as described in claim 3, characterized in that, The method of using second-order derivative interpolation, which involves interpolating the original digital signal using the second derivative of a function to obtain the first data, specifically includes: For the original digital signal, the second-derivative interpolation method is used to adjust the sampling frequency to... The original digital signal is interpolated at a sampling frequency of The data yields the first data: , where subscript The value is: , The floor symbol is used for rounding down. Greater than The time series corresponding to the first data is .

7. The method as described in claim 1, characterized in that, After obtaining the first data, the process also includes: The first data is subjected to anti-aliasing filtering to obtain the third data.

8. A digital signal processing system, characterized in that, Applied to the digital signal processing method of claim 1, comprising: The data acquisition module is used to acquire raw digital signals; The interpolation processing module is used to interpolate the original digital signal using the second derivative of the function to obtain the first data.

9. A digital signal processing terminal, characterized in that, include: Storage media and processor; The storage medium stores computer-executed instructions. The processor executes computer execution instructions stored in the storage medium to implement the method as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions, which, when executed by a processor, are used to implement the method as described in any one of claims 1 to 7.

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