To interpolate a uniformly sampled spectrum , by the factor , we may take the length inverse DFT, append zeros to the time-domain data, and take a length DFT. If is a power of two, then so is and we can use a Cooley-Tukey FFT for both steps (which is very fast):
This operation creates new bins between each pair of original bins in , thus increasing the number of spectral samples around the unit circle from to . An example for is shown in Fig.2.4 (compare to Fig.2.3).
X = fft(x,N); % FFT size N > length(x)
Zero-Padding to the Next Higher Power of 2
Proof of Aliasing Theorem