I have followed the link below to simulate two different zero-padding methods (zero-centered and casual) <https://ccrma.stanford.edu/~jos/mdft/Zero_Padding.html> Sample code ``` close all; clear all; x = [3 2 1 1 2]; n = length(x); fft_len = 64; zeropadd = fft_len - n; y = [x(1:(n-1)/2+1) zeros(1,zeropadd) x((n-1)/2+2:end)]; x_zeropad = [x zeros(1,zeropadd)]; y_fft = fft(y); x_fft = fft(x, fft_len); x_zp_fft = fft(x_zeropad); subplot(311) stem(y_fft) xlabel 'n', ylabel 'fft(y)' subplot(312) stem(x_fft) xlabel 'n', ylabel 'fft(x)' subplot(313) stem(x_zp_fft) xlabel 'n', ylabel 'fft(x_zp)' ``` Output is [![enter image description here][1]][1] [1]: https://i.sstatic.net/0pFyt.png My question is why is the spectrum of `fft(y)` is different from `fft(x)` and `fft(x_zp)`