A gain control method for a second-order discrete low-pass filter based on RBF

Abstract

The application discloses a kind of second-order discrete low-pass filter gain control method based on RBF, belong to digital signal processing technical field.The method includes: real-time acquisition input signal and the actual output signal of second-order discrete low-pass filter current time, calculate the deviation of input signal and output signal at current time;Deviation is used as the input of RBF network, the output of each neuron of network is calculated using radial basis function, the gain compensation amount is obtained by weighting operation to output layer connection weight;The adjustable core gain coefficient is iteratively corrected by gain compensation amount, and the updated adjustable core gain coefficient is substituted into difference equation to calculate signal filtering at next time.The application can effectively solve the problem that the amplitude of output signal of second-order discrete low-pass filter fluctuates with the change of input signal frequency without changing the pole position of filter and the high-frequency noise reduction performance, significantly improves the amplitude maintaining performance of filtering system.

Description

Technical Field

[0001] This invention relates to the field of digital signal processing technology, and in particular to a gain control method for a second-order discrete low-pass filter based on RBF. Background Technology

[0002] In signal processing, measurement and control technology, and other fields, second-order discrete low-pass filters are widely used in sensor signal acquisition and processing, high-frequency noise suppression, and other specific applications due to their advantages such as simple structure, low computational load, and ease of implementation. Compared with first-order filter structures, second-order discrete low-pass filters have superior high-frequency attenuation characteristics and filtering smoothing effect, while preserving the waveform characteristics of the signal before filtering. They are one of the most commonly used basic filtering units in the field of signal processing.

[0003] Most current second-order discrete low-pass filters are designed with fixed parameters, meaning the filter coefficients remain constant throughout operation and cannot dynamically adapt to the deviation between the input and output signals in real time. Therefore, when the frequency of the input signal changes, the amplitude of the filtered output signal will deviate from the amplitude of the input signal. This causes the filter gain to change while filtering high-frequency noise, resulting in a deviation between the amplitude of the filtered output signal and the original input signal. The root cause of this problem is that for any frequency AC signal input, the magnitude of its transfer function changes with the discrete angular frequency, leading to different gain values ​​for different frequency components after passing through the filter. This results in insufficient amplitude preservation in the low-frequency range, affecting the accuracy and reliability of subsequent signal processing.

[0004] Current technologies for improving filter amplitude deviation mainly focus on traditional methods such as frequency domain correction and linear compensation. These methods are generally not very versatile, difficult to adapt to real-time discrete iterative scenarios, and cannot adaptively compensate for the gain changes of the filter caused by changes in the frequency of the input signal.

[0005] To effectively address the issue of fluctuations in the output amplitude of traditional second-order discrete low-pass filters due to variations in input signal frequency, a control method is needed to acquire signal numerical errors in real time and dynamically correct filter gain deviations, thereby achieving stable amplitude control of the filtered signal. However, the stability constraints of the system must be fully considered during the dynamic adjustment of the filter gain. If the filter pole positions change during the adjustment process, signal oscillations or even divergence can easily occur. Therefore, how to achieve dynamic adaptive gain correction while ensuring absolute filter stability is another critical technical challenge that urgently needs to be addressed in this field. Summary of the Invention

[0006] To address the issue that the amplitude of the output signal in a traditional second-order discrete low-pass filter changes with the frequency of the input signal during filtering, this invention provides a gain control method for a second-order discrete low-pass filter based on an RBF (Restricted Baseline Filter). This method quantizes the offset between the input and output signals in real time, using this offset as the input to the RBF network. A nonlinear mapping is then performed to obtain the current signal gain compensation, and the updated gain coefficient is substituted into the filter for filtering. This method effectively suppresses amplitude fluctuations caused by frequency changes in the second-order discrete low-pass filter while preserving the original filter's high-frequency noise reduction and smoothing filtering performance. This significantly improves the steady-state output amplitude of the effective signal after filtering and enhances the system's operational stability.

[0007] This invention employs a second-order discrete low-pass filter to perform signal smoothing filtering. This filter adopts an autoregressive structure, and its discrete-time difference equation is as follows: ; In the formula, , For feedback with a fixed coefficient, This is the adjustable core gain coefficient dynamically corrected by the RBF network.

[0008] Core gain coefficient This is an adjustable variable, dynamically adjusted by the real-time compensation amount output by the RBF gain compensation module. It can be adjusted... It achieves adaptive correction of the overall steady-state gain of the system while keeping the other coefficients of the filter constant. Without changing the original filtering performance and noise reduction performance of the filter, it accurately compensates for the amplitude gain deviation of the filtering system caused by frequency changes.

[0009] Taking the Z-transform of the time-domain difference equation of a second-order discrete low-pass filter, we can obtain the discrete-domain transfer function: .

[0010] Construct the characteristic equation from the denominator of the transfer function Solving for the filter poles, we can obtain the following: .

[0011] Due to the stability requirements of the filter, the feedback coefficient is fixed. , The modulus condition was met during the design phase. , Therefore, the filter remains stable. The poles are determined solely by the feedback fixed coefficients. , The decision is made in relation to the adjustable core gain coefficient. Regardless, the RBF network adjusts the adjustable core gain coefficient. The positions of the filter poles remain unchanged.

[0012] When a DC signal is input, Substituting into the transfer function, we obtain the system's DC gain: .

[0013] when ,Right now When the output signal amplitude is greater than the input signal amplitude; when ,Right now When the output signal amplitude is less than the input signal amplitude, the output signal amplitude is less than the input signal amplitude.

[0014] For an AC signal input of arbitrary frequency, let the discrete angular frequency be... Substitute The frequency domain complex transfer function is obtained, and its magnitude is: .

[0015] Similarly, for the transfer function expression of an AC signal input at any frequency, when the magnitude is greater than 1, the amplitude of the AC signal at the corresponding frequency will increase; when the magnitude is less than 1, the amplitude of the AC signal at the corresponding frequency will decrease.

[0016] As shown by the transfer function above, the amplitude of the output signal changes with the frequency of the input AC signal, thus different input signal frequencies lead to different gain in the filter's output signal. Therefore, an RBF network is introduced to construct an adaptive gain compensation control method. During the closed-loop iteration process, the filtered output signal is compared with the input signal in real time to calculate the deviation, thereby maintaining the consistency of the amplitudes of the input and output signals.

[0017] Furthermore, the filtered output signal is compared with the input signal, and settings are made accordingly. The input signal of the time filter is The filtered output signal is Calculate different Signal deviation at time This deviation can intuitively and in real time reflect the current filtering deviation status of the filter, and can be used as an input variable for the RBF gain compensation module.

[0018] Furthermore, an RBF network is used for bias fitting and compensation calculation. The hidden neuron centers, widths, and output layer connection weights of the RBF network are preset after offline training and remain unchanged during system operation. The offline training can be determined using conventional clustering and least squares methods in this field. The signal bias is constructed from the real-time difference between the input and output signals and used as the input to the RBF network. A Gaussian radial basis function is used to complete the nonlinear mapping of the bias. The output of the RBF network corresponds to the gain increment compensation, which is used to iteratively update the adjustable gain coefficient of the second-order discrete low-pass filter.

[0019] The Gaussian radial basis function expression used in this process is: ; In the formula, the independent variable Substitute the first Signal deviation at sampling time , , The first The center and width of each basis function This represents the output mapping value corresponding to a single neuron.

[0020] Based on the calculation of the basis function mapping of a single neuron, this invention outputs a gain compensation amount that matches the current signal deviation through a weighted summation method. The formula for calculating the gain compensation amount is as follows: ; In the formula, The connection weights corresponding to the j-th neuron are... The preset number of hidden layer neurons for the RBF network. This is the real-time gain compensation amount for the final output of the network.

[0021] It should be noted that while existing technologies combine RBF neural networks with filters—such as combining active power filters with RBF networks for harmonic suppression, using RBF networks for offline coefficient design optimization of FIR digital filters, and using RBF networks for fault-tolerant gain adjustment of Kalman filters—the types of filters targeted, the technical problems solved, and the technical paths employed by these solutions differ substantially from this invention. Active power filters belong to the harmonic compensation devices in the field of power electronics, and their control objective is power quality improvement; FIR digital filters have a non-recursive structure, and RBF networks are only used for coefficient optimization during the design phase, not for real-time compensation during operation; Kalman filters are state estimators, and their gain adjustment aims to ensure filter convergence rather than amplitude preservation. None of these existing technologies have solved the technical problem of output amplitude fluctuations caused by changes in the input signal frequency during the operation of a second-order discrete low-pass filter.

[0022] The transfer function of the second-order discrete low-pass filter is extracted and transformed into a structure where a fixed filter subunit is multiplied by an independently adjustable gain, as shown in the following form: ; In the formula, For fixed filter subunits, It is the adjustable core gain coefficient of the filter. In discrete iterative calculations, at different times... Recorded as .

[0023] To achieve dynamic compensation of gain deviation, this invention applies the real-time gain compensation amount output by the RBF network to the core adjustable coefficient of the filter. This completes the dynamic iterative update of the parameters. Assume the adjustable core coefficients of the filter at the current moment are... Gain compensation amount at the current moment Then, construct the iterative update formula for the adjustable core gain coefficient: ; In the formula, The adjusted core gain coefficient of the iteratively updated filter is substituted into the filter iteration calculation at the next sampling time. By dynamically adjusting the core gain coefficient, the overall equivalent gain of the filter is changed, which inversely cancels the gain deviation caused by the change in the input signal frequency, thus completing the output amplitude self-correction compensation. The above steps are executed cyclically to form a closed-loop iterative control, dynamically correcting the filter gain coefficient and realizing stable amplitude control of the output signal.

[0024] Furthermore, to prevent transient overshoot caused by sudden changes in the gain coefficient due to transient abnormal disturbances in the RBF network, the adjustable core gain coefficient can be iteratively updated. Add clamping constraints to satisfy: ; In the formula, and These are the preset lower and upper limits of gain, respectively.

[0025] Dynamic adjustment via RBF network During the process, filter poles and The value of will not change, so the pole position will not change, thus it will not cause oscillation divergence, and the gain adjustment can be completed while ensuring the stability of the system.

[0026] The beneficial effects of this invention are: 1. This invention, under the premise of fixed pole configuration of a second-order discrete low-pass filter, allows adjustment of the equivalent gain by adjusting the core gain coefficient, with the poles determined only by the feedback fixed coefficient. , The decision is made in relation to the adjustable core gain coefficient. They are independent of each other, the pole positions do not change, and there is no need to change the feedback structure and hardware topology of the filter.

[0027] 2. Introducing an RBF network to adjust the core gain coefficient Iterative correction can effectively solve the problem of output amplitude fluctuation caused by changes in the frequency of the input signal in traditional second-order discrete low-pass filters, resulting in better consistency between the amplitudes of the input and output signals.

[0028] 3. It avoids the complex tuning process of multi-parameter joint adjustment, and has a simple control structure, low computational load, and fast response speed, making it suitable for engineering scenarios with real-time requirements. Attached Figure Description

[0029] Figure 1 This is a system flowchart of the second-order discrete low-pass filter gain control method based on RBF of the present invention.

[0030] Figure 2 This is a block diagram of the functional modules in the signal filtering process.

[0031] Figure 3 A comparison of the amplitudes of the filter output signal and the input signal without the introduction of RBF.

[0032] Figure 4 A comparison of the amplitudes of the filter output signal and the input signal after the introduction of RBF. Detailed Implementation

[0033] The invention will now be further described with reference to the accompanying drawings. These drawings are simplified schematic diagrams, illustrating only the basic structure of the invention, and therefore only show the components relevant to the invention.

[0034] Figure 1 The system flowchart of the RBF-based second-order discrete low-pass filter gain control method of the present invention is as follows: First, the input signal of the second-order discrete low-pass filter and the actual output signal at the current moment are acquired in real time. The difference between the signal values ​​of the output signal and the input signal at the same moment is calculated to obtain the deviation. The real-time deviation is input into the RBF neural network to obtain the gain compensation amount at the current moment. Then, the adjustable gain coefficient is adjusted according to the gain compensation amount. The process involves iterative correction; finally, the updated gain coefficient is used to correct the filtered output, completing the filtering calculation for the next time step. This process is repeated to obtain an output signal with amplitude matching and noise suppression.

[0035] During the filtering process, the modules work together to dynamically correct the amplitude deviation of the second-order discrete low-pass filter caused by changes in the input signal frequency, without changing the original filter structure and high-frequency noise reduction performance.

[0036] Figure 2 This diagram shows the functional modules of a second-order discrete low-pass filter gain control system based on an RBF (Restricted Baseline Filter). These modules include: a signal acquisition module, a signal deviation calculation module, an RBF gain compensation module, and a gain coefficient iterative update module. The output of the signal acquisition module is connected to the input of the signal deviation calculation module, the output of the signal deviation calculation module is connected to the input of the RBF gain compensation module, and the output of the RBF gain compensation module is connected to the input of the gain coefficient iterative update module.

[0037] A second-order discrete low-pass filter is used to perform signal smoothing filtering. This filter adopts an autoregressive structure, and its discrete-time difference equation is as follows: ; In the formula, , For feedback with a fixed coefficient, This is the adjustable core gain coefficient dynamically corrected by the RBF network.

[0038] In a specific implementation example, the feedback fixed coefficient of the second-order discrete low-pass filter can be set as follows: =1.6、 =-0.64, at this time the characteristic equation is The extreme point is = =0.8 is a repeated root, and all roots lie within the unit circle in the Z-plane, satisfying the system stability requirements. Adjustable core gain coefficient. The initial value can be set to 0.2, which is the number of neurons in the hidden layer of the RBF network. It can be set to 8, the center of the basis functions. (j=1,2,...,8) can be evenly distributed within the interval [-1,1], with a width It can be set to 0.5, the output layer connection weight. After offline training, it was determined that its typical value range is within the interval [-5, 5]. It should be noted that the above parameter values ​​are merely illustrative and do not constitute any limitation on the scope of protection of this invention. Those skilled in the art can reasonably adjust the above parameters according to actual application scenarios and filtering performance requirements.

[0039] Performing a Z-transform on the above difference equation yields the discrete-domain transfer function model of the filter: .

[0040] From the transfer function and system stability conditions, it can be seen that as long as all poles are located inside the unit circle in the z-domain, the second-order discrete filter system can remain stable. For the second-order autoregressive discrete low-pass filter in this invention, its fixed feedback coefficients... , The modulus condition was met during the design phase. , Therefore, the filter remains stable and will not exhibit unstable phenomena such as signal divergence or signal oscillation, thus meeting the requirements for signal smoothing preprocessing in signal processing scenarios.

[0041] As can be seen from the preceding analysis, the poles of the autoregressive filter described in this invention are determined only by fixed feedback coefficients. , Determined, with adjustable gain coefficient They are independent of each other, when adjusted through the RBF network The poles will not change, thus avoiding oscillation and divergence problems during the adaptive adjustment process.

[0042] For an AC signal input of any frequency, referring to the amplitude-frequency modulus expression above: .

[0043] As can be seen from the amplitude-frequency magnitude expression, the amplitude of the output signal changes with the frequency of the input AC signal when any frequency AC signal is input. Therefore, this invention introduces an RBF neural network to construct an adaptive gain compensation control method, dynamically adjusting the adjustable gain coefficient. This allows the filter to achieve amplitude stabilization control under input signals of different frequencies, thereby ensuring consistency between the output amplitude and the input amplitude.

[0044] The input signal of a second-order discrete low-pass filter is acquired, and the actual output signal at the current moment is compared with the input signal. The amplitude difference between the signal before and after filtering is calculated in real time. Let... The input signal of the time filter is The output signal is Calculate the amplitude deviation Its expression is: .

[0045] This amplitude deviation can quantify the deviation between the filtering result and the input signal in real time. It can be used as the input variable of the RBF network. Based on the degree of real-time deviation change, a matching gain compensation amount can be adaptively generated for subsequent dynamic correction of the core gain coefficient.

[0046] The signal deviation obtained during system operation is input into the RBF neural network. The hidden neuron center, width, and output layer connection weights of the network are preset and fixed after offline training and remain unchanged during operation. The nonlinear mapping operation is completed through the Gaussian function and used for subsequent iterative updates of the adjustable gain coefficient of the second-order discrete low-pass filter.

[0047] The Gaussian function expression used is: ; In the formula, Substitute the input variables for the RBF network into the first... Signal deviation formed by input and output signals at sampling time , , The first The center and width of each basis function For the first The output of each neuron.

[0048] The gain compensation amount is output by weighted summation to match the current signal deviation. The formula for calculating the gain compensation amount is as follows: ; In the formula, For the first The connection weights between each hidden layer neuron and the output layer; This represents the number of neurons in the hidden layer of the RBF network. This is the gain compensation amount for the core coefficient.

[0049] As an exemplary implementation of offline training of the RBF network, the following steps can be followed: First, apply sinusoidal signals of different frequencies as filter inputs, collect the filter outputs at each frequency point, and calculate the signal deviation and its corresponding gain compensation. Normalize the collected original signal deviations, mapping them to a unified interval [-1, 1], forming a training sample set that pairs the normalized input with the desired output. Then, set the number of neurons in the hidden layer of the RBF network. ,For example =8, and the basis functions are Gaussian radial basis functions. Basis function center (j=1,2,..., The signal is uniformly distributed at equal intervals within the expected range [-1, 1] after normalization of the signal bias, and the basis function width is... A value of 0.5 is used to ensure appropriate overlap in the responses of adjacent neurons, guaranteeing a smooth network output. Based on this, the least squares method is used to calculate the connection weights of the output layer, aiming to minimize the network output error. After training, all network parameters are stored and stored. During actual runtime, only forward computation is required, without iterative updates. It should be noted that the above training method is merely illustrative and does not constitute any limitation on the scope of protection of this invention. Those skilled in the art can adopt other equivalent offline training methods according to actual application scenarios.

[0050] The transfer function of a second-order discrete low-pass filter is extracted and transformed into a structure where a fixed filter subunit is multiplied by an independently adjustable gain. The expression is as follows: ; In the formula, For filter sub-units with fixed parameters, the noise reduction frequency domain characteristics of the system remain constant; This is the adjustable core gain coefficient of the filter.

[0051] The aforementioned gain compensation is input into the filter coefficient iterative correction unit to update the core adjustable coefficients. Let... The core coefficients of the time filter are Combined with the current gain compensation amount The coefficients after iterative updates are obtained, and their formula is: .

[0052] During iterative operation, the overall equivalent gain of the filter is adjusted by making small corrections cycle by cycle, thereby gradually reducing the amplitude deviation.

[0053] Furthermore, to enhance the system's engineering safety under abnormal operating conditions and prevent sudden gain changes caused by transient disturbances in the RBF network, clamping constraints can be added after the update and iteration as needed to ensure that the updated gain coefficients are optimized. Keep within the appropriate range: ; In the formula, and These are the preset lower and upper limits of gain, respectively.

[0054] The RBF network adaptively adjusts within the corresponding interval based on the real-time signal deviation. This improves the consistency between the amplitude of the output signal and the amplitude of the input signal of the filtering system, and maintains stable control of the filter gain while ensuring system stability.

[0055] Figure 3 The graph shows a comparison of the amplitudes of the filter output signal and the input signal without RBF gain compensation. It is clear from the graph that there is a significant difference between the amplitude of the filter output signal and the amplitude of the input signal. Figure 4The diagram showing the amplitude comparison between the filter output signal and the input signal after introducing RBF gain compensation in this invention demonstrates that, after RBF adaptive gain compensation, the amplitude of the filter output signal is consistent with that of the original input signal, achieving the effect of stable amplitude control of the filter.

[0056] In practical engineering applications, the aforementioned closed-loop iterative process is continuously executed until the system is powered off or an external interrupt command is received. The specific duration of the iterative control cycle is determined by the system's sampling period, and those skilled in the art can set it reasonably according to the real-time requirements of the actual application scenario.

[0057] By transforming the transfer function of a second-order discrete low-pass filter into a structure multiplied by a fixed filter subunit and an independently adjustable gain, and relying on an RBF neural network to fit the nonlinear mapping relationship between signal deviation and gain compensation in real time, the gain coefficient is iteratively updated, and upper and lower limit constraints on the gain are used to ensure system stability. The entire solution requires no modification to the internal frequency domain parameters of the filter unit. While retaining the original signal noise reduction capability, it compensates for amplitude shifts, effectively solving the problem of filter gain changes in second-order discrete low-pass filtering under varying input signal frequencies. This significantly improves the consistency of signal amplitude before and after filtering, demonstrating good practical application value and promising prospects for widespread adoption.

[0058] The above description is based on the preferred embodiments of the present invention. Through the above description, those skilled in the art can make various changes and modifications without departing from the technical concept of the present invention. The technical scope of this invention is not limited to the contents of the specification, but must be determined according to the scope of the claims.

Claims

1. A gain control method for a second-order discrete low-pass filter based on RBF, characterized in that, Includes the following steps: Step 1: Real-time acquisition of input signals The actual output signal of the second-order discrete low-pass filter at the current moment ; Step 2: Calculate the deviation between the input signal and the output signal at the current moment. ; Step 3, the deviation amount As input to the RBF network, the RBF network has preset hidden neuron centers, widths, and output layer connection weights. The output of each neuron in the network is calculated using radial basis functions, and the output layer connection weights are weighted to obtain the filter output gain compensation. ; Step four, using the aforementioned gain compensation amount The adjustable core gain coefficient of the second-order discrete low-pass filter is iteratively corrected using the following formula: ； In the formula, for The filter's adjustable core gain coefficient at time t. The core gain coefficient of the updated filter is adjustable; Step 5: Adjust the gain coefficient of the updated filter. Substitute the values ​​into the difference equation of the second-order discrete low-pass filter to perform signal filtering calculations at the next time step; repeat steps one through five to form a closed-loop iterative control, dynamically correct the filter gain coefficient, and achieve stable amplitude control of the output signal.

2. The gain control method for a second-order discrete low-pass filter based on RBF according to claim 1, characterized in that, The second-order discrete low-pass filter adopts an autoregressive structure, and its discrete-time difference equation is as follows: ； In the formula, , For feedback with a fixed coefficient, The adjustable core gain coefficient, the Dynamically corrected by the RBF network.

3. The gain control method for a second-order discrete low-pass filter based on RBF according to claim 2, characterized in that, The transfer function of the second-order discrete low-pass filter is: ； Its extreme point is Two roots , And satisfy and The requirements are to ensure the stability of the filter throughout the entire range; the poles are determined only by the feedback fixed coefficients. , The decision is made in relation to the adjustable core gain coefficient. Regardless, the RBF network adjusts the adjustable core gain coefficient. The positions of the filter poles remain unchanged.

4. The gain control method for a second-order discrete low-pass filter based on RBF according to claim 1, characterized in that, The radial basis function used in step three is a Gaussian radial basis function, which is used to perform a nonlinear mapping on the signal deviation generated by the second-order discrete low-pass filter. The function expression is as follows: ； In the formula, Substitute the input variables for the RBF network into the first... Signal deviation at sampling time , , The first The center and width of each basis function For the first The output of each neuron.

5. The gain control method for a second-order discrete low-pass filter based on RBF according to claim 4, characterized in that, Step 3: After completing the radial basis mapping output of each neuron, the gain compensation amount for the amplitude shift of the adapted second-order discrete low-pass filter is obtained through weighted summation. The formula for calculating the gain compensation amount is as follows: ； In the formula, For the first The connection weights between each hidden layer neuron and the output layer; This represents the total number of neurons in the hidden layer of the RBF network. This is the gain compensation amount.

6. The gain control method for a second-order discrete low-pass filter based on RBF according to claim 1, characterized in that, In step four, the adjustable core gain coefficient is updated iteratively. Add clamping constraints to satisfy: ； In the formula, and These are the preset lower and upper limits of gain, respectively.

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