Design method for FIR filter based on learning rate changing neural net

Abstract

The invention discloses a design method of an FIR filter based on a variable learning rate neural network, which introduces a variable learning rate algorithm to automatically adjust the value of the learning rate in the course of triangle basis function neural network training so as to improve the learning efficiency and the convergence rate of the neural network. A relative neural network modelis built according to the relationship between the triangle basis function neural network and the amplitude-frequency characteristic of a linear phase 4 type FIR filter. The sum of error squares of the amplitude-frequency response of the FIR linear phase filter and the ideal amplitude-frequency response in a whole passband and a stopband is minimized. An FIR high-pass filter and a band-pass filter are designed for optimization with the method, and the result shows that the FIR filter designed by the method has availability and superiority. The designed FIR filter has the advantages of high convergence rate, no overshoot impulse and fluctuation of the amplitude-frequency passband, narrow amplitude-frequency transition band and large attenuation of the stopband.

Description

technical field

[0001] The invention belongs to the technical field of electronic science and communication, and relates to a design method of a finite impulse response (FIR) filter, in particular to a design method of an FIR filter based on a variable learning rate neural network. Background technique

[0002] The finite impulse response (FIR) filter has strict linear phase characteristics, while the phase of the infinite impulse response (IIR) filter is nonlinear, so when designing a linear phase IIR filter, an all-pass network is required for phase correction. Therefore, in the In areas such as image processing and data transmission that require strict signal phase, FIR filters have wider engineering practical applications than IIR filters, and their design and implementation methods have also attracted extensive attention from the academic community. Commonly used methods for FIR filter design are window function weighting method and frequency sampling method, but these ...

Examples

Embodiment 1

[0084] Embodiment 1 assumes that the amplitude-frequency characteristic of a certain ideal high-pass filter is:

[0085]

[0086] The method of designing a 220-order high-pass filter is: uniformly take 111 sample values ​​for ω in [0, π], that is ω = π 110 n , n = 0,1,2 , · · · , 110 . In order to make the passband and stopband of the filter have no overshoot and ripple, two sample points 0.2 and 0.8 are taken in each transition band respectively. Therefore, the actual amplitude-frequency sampling sequence is: H o (n) = [zeros (1, 55), 0.2, 0.8, ones (1, 54)]. Take the network structure of the neural network as 1×111×1, and the global error performance index in the passband and stopband range is J=4.62×10 -6 , the initial value of the α learning rate is 0.001, and the sampling sequence is input into the neural ...

Embodiment 2

[0090] Embodiment 2 assumes that the amplitude-frequency characteristic of a certain ideal bandpass filter is:

[0091]

[0092] The method of designing a 180-order band-pass filter is: take 91 sample values ​​evenly in [0, π] for ω, that is ω = π 90 n , n = 0,1,2 , · · · , 90 . In order to make the passband and stopband of the filter have no overshoot and ripple, two sample points 0.2 and 0.8 are taken in each transition band respectively. Therefore, the actual amplitude-frequency sampling sequence is: H o (n)=[zeros(1, 28), 0.2, 0.8, ones(1, 31), 0.8, 0.2, zeros(1, 28)]. Take the network structure of the neural network as 1×91×1, and the global error performance index in the passband and stopband range is J=5.64×10 -7 , the initial value of the α learning rate is 0.001, and the sampling sequence is input into...

technical field

[0001] The invention belongs to the technical field of electronic science and communication, and relates to a design method of a finite impulse response (FIR) filter, in particular to a design method of an FIR filter based on a variable learning rate neural network. Background technique

[0002] The finite impulse response (FIR) filter has strict linear phase characteristics, while the phase of the infinite impulse response (IIR) filter is nonlinear, so when designing a linear phase IIR filter, an all-pass network is required for phase correction. Therefore, in the In areas such as image processing and data transmission that require strict signal phase, FIR filters have wider engineering practical applications than IIR filters, and their design and implementation methods have also attracted extensive attention from the academic community. Commonly used methods for FIR filter design are window function weighting method and frequency sampling method, but these ...

Examples

Embodiment 1

[0084] Embodiment 1 assumes that the amplitude-frequency characteristic of a certain ideal high-pass filter is:

[0085]

[0086] The method of designing a 220-order high-pass filter is: uniformly take 111 sample values ​​for ω in [0, π], that is ω = π 110 n , n = 0,1,2 , · · · , 110 . In order to make the passband and stopband of the filter have no overshoot and ripple, two sample points 0.2 and 0.8 are taken in each transition band respectively. Therefore, the actual amplitude-frequency sampling sequence is: H o (n) = [zeros (1, 55), 0.2, 0.8, ones (1, 54)]. Take the network structure of the neural network as 1×111×1, and the global error performance index in the passband and stopband range is J=4.62×10 -6 , the initial value of the α learning rate is 0.001, and the sampling sequence is input into the neural ...

Embodiment 2

[0090] Embodiment 2 assumes that the amplitude-frequency characteristic of a certain ideal bandpass filter is:

[0091]

[0092] The method of designing a 180-order band-pass filter is: take 91 sample values ​​evenly in [0, π] for ω, that is ω = π 90 n , n = 0,1,2 , · · · , 90 . In order to make the passband and stopband of the filter have no overshoot and ripple, two sample points 0.2 and 0.8 are taken in each transition band respectively. Therefore, the actual amplitude-frequency sampling sequence is: H o (n)=[zeros(1, 28), 0.2, 0.8, ones(1, 31), 0.8, 0.2, zeros(1, 28)]. Take the network structure of the neural network as 1×91×1, and the global error performance index in the passband and stopband range is J=5.64×10 -7 , the initial value of the α learning rate is 0.001, and the sampling sequence is input into...

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