1D Gaussian Filter using FFT

Question

SM 2011-5-18

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https://ww2.mathworks.cn/matlabcentral/answers/7662-1d-gaussian-filter-using-fft

Hi I am trying to filter data(not periodic) represented by tanh profile.

My steps are -

signal: tanh (x)

ffts = fft(signal)

g = 1D Gaussian Filter normalised by its area

fftg = FFT(g)

fs = ffts.*fftg

s = real(ifft(fs))

But this is not giving the correct output.

What am I doing wrong?

Thanks in advance

SM

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Answer 1

phani 2011-5-18

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https://ww2.mathworks.cn/matlabcentral/answers/7662-1d-gaussian-filter-using-fft#answer_10551

dear SM i can suggest you one one of the possible way. the convolution in the time domain is same as the multiplication in the frequency domain. so design a filter using fdatool and obtain the coefficients and do convolution of your signal and the filter coefficients. and compare the ffts of both i.e. FFT without filtering and FFT with filtering. i think that may work.

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SM 2011-5-18

Dear Phani

Thanks for your reply.

I do not want to use fdatool but use a simple gaussian profile like

g = sqrt(6/(pi*s^2))*exp(-6*x.^2/(s^2));

I tried convolution also in this way-

w = conv(S,g,'same');

I fo not get correct result. Do you think this is OK?

Regards

SM

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Answer 2

Honglei Chen 2011-5-18

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Hi SM,

From the code you posted here, my suspect is that you did not use enough points in your FFT to remove the aliasing. Note that ifft of product of fft is, in theory, the circular convolution so you have to use enough points to make it the same as linear convolution. Can you try to use 2*numel(g)-1 as number of FFT points in your snippet and see if it resolves the issue? The 'same' option in CONV merely returns the central part of the linear convolution, which is not the same as the circular convolution.

HTH,

Honglei