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

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.

Answer 1

[Matt J]

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.

[Matt J]

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.

[Tarek Hajj Shehadi]

Thank you for the clarification, all is understood.