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Converting between zero padded and non zero padded FFT

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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?

Respuesta aceptada

Wayne King
Wayne King el 15 de Mzo. de 2013
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.
  2 comentarios
John
John el 15 de Mzo. de 2013
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 el 15 de Mzo. de 2013
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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Más respuestas (1)

Youssef  Khmou
Youssef Khmou el 15 de Mzo. de 2013
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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