Converting between zero padded and non zero padded FFT

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?

Answer 1

[Wayne King]

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.

[John]

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]

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.

Answer 2

[Youssef Khmou]

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