Converting between zero padded and non zero padded FFT

2013 3 15
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I have a signal, x = [1 2 3 4]. I have the fft(x) which is
10.0000
-2.0000 + 2.0000i
-2.0000
-2.0000 - 2.0000i
I want to get the fft for y = [1 2 3 4 0 0 0 0] which is
10.0000
-0.4142 - 7.2426i
-2.0000 + 2.0000i
2.4142 - 1.2426i
-2.0000
2.4142 + 1.2426i
-2.0000 - 2.0000i
-0.4142 + 7.2426i
How can get the fft of y from the fft of x?

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Wayne King
Wayne King 2013-3-15

0 个投票

In this simple case, you have just decreased the separation between adjacent DFT bins by a factor of 2.
y = [1 2 3 4 0 0 0 0];
ydft = fft(y);
ydft = downsample(ydft,2);
% or ydft = ydft(1:2:end);
That will be the same as
xdft = fft(1:4);
but in general, the above won't work.

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John
John 2013-3-15
I'm just trying to compute the FFT of [1 2 3 4 0 0 0 0 0 0 etc.. 0 0 0 0 0] with a lot of zeros efficiently to save time.
Honglei Chen
Honglei Chen 2013-3-15
Hi John, like Wayne said, from y to x is possible but from x to y in general can't be done. Keep in mind that FFT assumes periodicity in both time and frequency domain so the two signals are indeed different in FFT's eye.

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Youssef Khmou
Youssef Khmou 2013-3-15

0 个投票

hi,
x and y are two different signals in terms of frequencies, you have to compute both ffts, i am not conscious if there are methods for derive ffts for padded signals

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