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This is just a question out of my curiosity, normally we do not do this I have a x(n)=[1 2 3]

y(n) = fft[1 2 3 0] =  6 + 0i  -2 - 2i   2 + 0i  -2 + 2i %zero padding
y'(n) = fft([1 2 3]) = 6 + 0i  -1.5 + 0.87i  -1.5 - 0.87i

I used Matlab to generate these results. My question is there way to obtain y'(n) from y(n)?

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  • $\begingroup$ You mean other than taking the inverse fft, removing the zeros and then doing another fft? $\endgroup$
    – Aaron
    Dec 10, 2013 at 19:41
  • $\begingroup$ yes, some kind of direct calculation $\endgroup$
    – user7226
    Dec 10, 2013 at 19:43

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Yes. Zero padding allows interpolation in the frequency domain. You can get the same result directly in the frequency domain using circular sin(x)/x interpolation. See for example http://en.wikipedia.org/wiki/Whittaker%E2%80%93Shannon_interpolation_formula

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