frequency domain interpolation changes the signal spectrum

Question

I am working on some experimental data related to a sine-sweep excitation.

I first reconstructed the signal using the amplitude and frequency information I get from the data file:

% finz: frequency
% ginz: amplitude
R = 4; % sweep rate
tz = 60/R*log2(finz/finz(1)); % time
u_swt = sin(2*pi*((60*finz(1)/(R*log(2.))*(2.^(R/60*tz)-1))));
time_sign = ginz.*u_swt;
freq_sign = fft(time_sign);

This is what I obtain: enter image description here

I then tried to interpolate the frequency data before computing the time signal to obtain a 'nicer' signal (having more samples it should be easier to reconstruct it):

ginz = interp(ginz,200);
finz = interp(finz,200);

But now the spectrum is changed: enter image description here

Why the frequency spectrum is so different? Am I doing something wrong in the interpolation? Should I not interpolate the data?

MadDave MadDave · Accepted Answer · 2014-12-09T17:53:58

The details of the signal you are working with are not clear to me. For instance, can you please provide typical examples of finz and ginz? Also, it is not clear what you are hoping to achieve through interpolation, so it is hard to advise on its use.

However, if you interpolate a time series you should expect its spectrum to change as it increases the sampling frequency. The frequency of an interpolated signal will become smaller relative to the new sampling frequency. Therefore, the signal spectrum will be (not being very technical here) pushed towards zero. I have provided a script below which creates white Gaussian noise, and plots the spectrum for different levels of interpolation. In the first subfigure with no interpolation, the spectrum is uniformly occupied (by design - white noise). In subsequent subfigures, with increasing interpolation the occupied spectrum becomes smaller and smaller. Hope this helps.

% white Gaussian noise (WGN)
WGN = randn(1,1000);
% DFT of WGN
DFT_WGN = abs(fft(WGN));
% one-sided spectrum
DFT_WGN = DFT_WGN(1:length(WGN)/2);

% interpolated WGN by factor of 2 (q = 2)
WGN_interp_2 = interp(WGN,2);
% DFT of interpolated WGN
DFT_WGN_interp_2 = abs(fft(WGN_interp_2));
% one-sided spectrum
DFT_WGN_interp_2 = DFT_WGN_interp_2(1:length(DFT_WGN_interp_2 )/2);

% interpolated WGN by factor of 10 (q = 10)
WGN_interp_10 = interp(WGN,10);
% DFT of interpolated WGN
DFT_WGN_interp_10 = abs(fft(WGN_interp_10));
% one-sided spectrum
DFT_WGN_interp_10 = DFT_WGN_interp_10(1:length(DFT_WGN_interp_10 )/2);

figure
subplot(3,1,1)
plot(DFT_WGN)
ylabel('DFT')
subplot(3,1,2)
plot(DFT_WGN_interp_2)
ylabel('DFT (q:2)')
subplot(3,1,3)
plot(DFT_WGN_interp_10)
ylabel('DFT (q:10)')

Effect of interpolation on WGN

frequency domain interpolation changes the signal spectrum

1 Answers