low pass filtering for smoothing

Question

I am using the following code in Matlab, from some source (sadly I cant remember).
The code is used for smoothing signals using a low pas filter.

 function y = fftSmooth(resp,srateCorrectedSmoothedWindow)
    L      = length(resp);
    window = zeros(1,L);
    window(floor((L-srateCorrectedSmoothedWindow+1)/2)...
    :floor((L+srateCorrectedSmoothedWindow)/2))=1;

    % zero phase low pass filtering
    tmp = ifft(fft(resp).*fft(window)/srateCorrectedSmoothedWindow);      
    y=-1*ifft(fft(-1*tmp).*fft(window)/srateCorrectedSmoothedWindow);

I have removed some unnecessary parts to shorten the code.

My question: how exactly is the filter designed (the last two lines)? Shouldn't it be in the time domain?

Answer 1

The code apparently originate from BreathMetrics (Matlab toolbox for analyzing respiratory recordings): breathmetrics/fftsmooth.m. It is descripted in Automated analysis of breathing waveforms using BreathMetrics: A respiratory signal processing toolbox, Chemical Senses, 2018. A draft is here.

Below, the function is visualyy decomposed into frequency/time steps. As @Jdip wrote, that is a filter implementation in the frequency domain.

%%% function y = fftSmooth(resp,srateCorrectedSmoothedWindow)

%Set inputs
lResp = 2048;
resp = randn(1,lResp)+10*exp(-(((1:lResp)-lResp/2)/(0.01*lResp)).^2);
srateCorrectedSmoothedWindow = 16;

    L      = length(resp);
    window = zeros(1,L);
    window(floor((L-srateCorrectedSmoothedWindow+1)/2)...
    :floor((L+srateCorrectedSmoothedWindow)/2))=1;

    % zero phase low pass filtering
    tmp = ifft(fft(resp).*fft(window)/srateCorrectedSmoothedWindow);      
    y=-1*ifft(fft(-1*tmp).*fft(window)/srateCorrectedSmoothedWindow);
  
    figure(1);clf
    subplot(2,1,2)
plot([resp;y]')  
axis tight;legend('Time Signal','Time Signal filtered')
    subplot(2,1,1)
yyaxis left
plot(abs(fft(resp)))
yyaxis right
plot(abs(fft(window)))
axis tight;legend('Spectrum','Window')