Upsampling and plotting a frequency domain signal

Question

I want to upsample by 5 a signal in frequency domain, and then plot (stem) it. I figured how to upsample,

Fk=(1/5)*upsample(ak_new,5);

now this creates a vector that is 5 times bigger than the original one, and I need to take the inverse Fourier series of this signal

Fn=(Fk*(exp((1i*2*pi/N*n'*n))));

where n is a sample vector (-1000:1000) , as you can see, I can't make the transformation since n is not the same size as Fk anymore. How can I solve this?

Answer 1

You need to plot your upsampled signal in frequency domain, on a similarly "upsampled" frequency vector.

If your initial frequency vector was -1000, -999, -998 ... , now it should be -1000, -999.8, -999.6 .

Here is a simple example:

Fs = 2000;              % Sampling frequency                    
T = 1/Fs;               % Sampling period       
L = 2000;               % Length of signal
t = (0:L-1)*T;          % Time vector

S = sin(2*pi*400*t);    % Signal

Y = fft(S);
ak_new = fftshift(abs(Y/L));        % Initial signal in frequency domain
Fk = upsample(ak_new,5);            % Upsampled signal

f   = (Fs/L)*(-L/2:  1  :L/2-1);    % Initial frequency vector
fup = (Fs/L)*(-L/2:(1/5):L/2-1/5);  % Upsampled frequency vector

subplot(2, 1, 1);
stem(f, ak_new);
title('Before upsampling');

subplot(2, 1, 2);
stem(fup, Fk);
title('After upsampling');