How does the command: real(ifft(​fftshift(Y​))*N) operate?

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Tarek Hajj Shehadi
Tarek Hajj Shehadi 2021-4-19
评论： Tarek Hajj Shehadi 2021-4-20
Hello, I am interested in knowing how this form of the inverse FFT command which is
real(ifft(fftshift(Y))*N)
works and its complexity for a vector Y of N sample points, because I have seen some basic ifft commands as seen here but this one seems to involve ifft and fft together.

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Matt J
Matt J 2021-4-20
编辑：Matt J 2021-4-20
All of those oeprations are O(N) except for the IFFT which is O(Nlog(N)). So the chain of operations is O(Nlog(N)) overall.It would be slightly more efficient to re-implement it as,
N*real(ifft(fftshift(Y)))
since then the multiplication with N only needs to operate on real numbers.
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Matt J
Matt J 2021-4-20
but this one seems to involve ifft and fft together.
No, it doesn't. But the FFT is also O(log(N)), so including an FFT step wouldn't increase the complexity either.

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