I'm having a rough time doing the following question from a HW. Given a sequence of your choice, what happens to the DFT if we add a 0 between every sample? I.e. if we have x[n] = [A,B,C], we turn it into x[n] = [A,0,B,0,C,0].
My initial thought was that the sampling frequency would double, similar to when we zero pad at the end of the signal. To do some analysis, I used the following MATLAB code.
Fs = 300; % Sampling frequency T = 1/Fs; % Sampling period L = 1500; % Length of signal t = (0:L-1)*T; % Time vector S = 0.7*sin(2*pi*50*t); %Signal - sine 50 Hz z = zeros(1,3000); z(1:2:end) = S; %Zero interp z_fft = fft(z); z_abs = abs(z_fft/(L*2)); P = z_abs(1:L*2/2+1); P(2:end-1) = 2*P(2:end-1); f = Fs*(0:(L*2/2))/(L*2); plot(f,P);
So I got confused, what is the result of adding the 0 between every sample? Does that doubles the frequency of my signal? What about that peak on f = 125Hz? Or am I making something wrong on my simulation?
Thanks for your time!