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

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.

Answer 1

[Star Strider]

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.

[mayur khedekar]

Thanks for the help and it helped me alot.

[Star Strider]

As always, my pleasure!

[Varun Gupta]

Hey, do you know how visualise the magnitude response of the SG filter using the fvtool? Thank you.

[Star Strider]

@Varun Gupta — I doubt that fvtool would work with the Savitzky-Golay filter, since it is not a ‘filter’ in the sense that fvtool defines filters. The closest you can likely get is to use the fft function or the Signal Analyzer app.

If you want to create a FIR filter that approximates its spectrum (once you calculated the spectrum), use the firls or related functions to design it.

.

[Varun Gupta]

I ran the signalVisualizer tool ---> (views) Spectrum, and feel much closer to what I wanted to see,

Its a graph against Power Spectrum (dB) and normalized frequency, I see that the graph is quite similar to how the frequency response of the SG filter should look like.

Are they idicating the same thing?

Thank you so much for the help.

[Star Strider]

‘Are they idicating the same thing?’

Probably.

My pleasure.