MATLAB: How can i obtain the frequency response for Savitzky-Golay filtering

cut-off frequencyfilterfrequencyfrequency responselow-pass filterMATLABMATLAB Compiler

I want to prove that this filter is a low pass filter by passing it from a heaviside and then i need the define the transfer function to get the bode plots.

How should i get the transfer function for heavyside.

Best Answer

Try this instead:

t = linspace(0, 10);
y = sin(2*pi*t/5) + randn(size(t))/10;
sgf = sgolayfilt(y, 3, 11);
figure
plot(t, y)
hold on
plot(t, sgf, '-r')
hold off
grid
L = numel(t);
Ts = mean(diff(t));
Fs = 1/Ts;
Fn = Fs/2;
FTy = fft(y)/L;
FTsgf = fft(sgf)/L;
Fv = linspace(0, 1, fix(L/2)+1)*Fn;
Iv = 1:numel(Fv);
figure
subplot(3,1,1)
plot(Fv, abs(FTy(Iv))*2)
grid
title('Fourier Transform: y')
subplot(3,1,2)
plot(Fv, abs(FTsgf(Iv))*2)
grid
title('Fourier Transform: Savitzky-Golay Filter of y')
subplot(3,1,3)
plot(Fv, abs(FTsgf(Iv)./FTy(Iv))*2)
grid
title('Savitzky-Golay Transfer Function')

This nicely demonstratres the lowpass filter characteristic.

Experiment with other signals to get different (but likely similar) resultls.

Related Solutions

MATLAB: Low pass filter VS high pass filter

Calculate the Fourier transform of the filter from the signals.

t = ...;                                                    % Time Vector
s = ...;                                                    % Original Signal Vector
s_filtered = ...;                                           % Filtered Signal Vector
Ts = mean(diff(t));                                         % Sampling Interval (Assumes Constant Intervals)
Fs = 1/Ts;                                                  % Sampling Frequency
Fn = Fs/2;                                                  % Nyquist Frequency
L = numel(t);                                               % Signal Length
FTs = fft(s)/L                                              % Fourier Transform of Original Signal
FTs_filt = fft(s_filtered)/L;                               % Fourier Transform of Filtered Signal
Fv = linspace(0, 1, fix(L/2)+1)*Fn;                         % Frequency Vector (One-Sided Fourier Transform)
Iv = 1:numel(Fv);                                           % Index Vector (One-Sided Fourier Transform)
H = FTs_filt ./ FTs;                                        % Complex Transfer Function
figure
subplot(2,1,1)
plot(Fv, abs(H(Iv)))
ylabel('Amplitude')
grid
subplot(2,1,2)
plot(Fv, angle(H(Iv)))
xlabel('Frequency')
ylabel('Phase')
grid
sgtitle('Bode Plot of Filter')

That should reveal the filter characteristics, as well as reasonably accurate aspects of its design (e.g. passband and stopband frequencies).

MATLAB: FFT and smoothing of signal

Now I understand what you want to do. This is most easily done with the Signal Processing Toolbox sgolayfilt function to create the Savitzky-Golay filtered spectrum.

The Code â€”

D = load('Isma_gp TENS_LOW.mat');  
sig = D.TENS_LOW_42;
sig = sig - mean(sig);                                      % Remove d-c Offset
L = length(sig);
Fs = 1/0.0117;                                              % Sampling Frequency
Fn = Fs/2;                                                  % Nyquist Frequency
FTsig = fft(sig)/L;
Fv = linspace(0, 1, fix(length(FTsig)/2)+1)*Fn;             % Frequency Vector
Iv = 1:length(Fv);                                          % Index Vector
FTsiga = double(abs(FTsig(Iv))*2);                          % Truncate, Magnitude, Convert To Double
sgf_sm = sgolayfilt(FTsiga, 5, 501);                        % Create â€˜sgolayfiltâ€™ Filtered FFT
figure(1)
plot(Fv, FTsiga)
hold on
plot(Fv, sgf_sm, '-r', 'LineWidth',2)
hold off
axis([0  1    ylim])
grid
xlabel('Frequency')
ylabel('Amplitude')
legend('Original Spectrum', 'Savitzky-Golay Filtered Spectrum')

Experiment with the sgolayfilt parameters to get the result you want.

Best Answer

Related Solutions

MATLAB: Low pass filter VS high pass filter

MATLAB: FFT and smoothing of signal

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