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):

(3.45) |

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).

In matlab, we can specify zero-padding by simply providing the optional FFT-size argument:

X = fft(x,N); % FFT size N > length(x)

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University