Practical Zero Padding
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
![$ L-1$](http://www.dsprelated.com/josimages_new/sasp2/img185.png)
![$ X$](http://www.dsprelated.com/josimages_new/sasp2/img119.png)
![$ N$](http://www.dsprelated.com/josimages_new/sasp2/img61.png)
![$ LN$](http://www.dsprelated.com/josimages_new/sasp2/img271.png)
![$ L=2$](http://www.dsprelated.com/josimages_new/sasp2/img272.png)
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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Zero-Padding to the Next Higher Power of 2
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Proof of Aliasing Theorem