[PDF] matlab complex number fft

Is FFT a discrete set of real numbers?

All the FFT implementations we have come across result in complex values (with real and imaginary parts), even if the input to the algorithm was a discrete set of real numbers (integers). Is it not possible to represent frequency domain in terms of real numbers only? The FFT is fundamentally a change of basis.

What is FFT amplitude & phase?

The FFT provides you with amplitude and phase. The amplitude is encoded as the magnitude of the complex number ( sqrt (x^2+y^2)) while the phase is encoded as the angle ( atan2 (y,x) ). To have a strictly real result from the FFT, the incoming signal must have even symmetry (i.e. x [n]=conj (x [N-n]) ).

How to enforce symmetricity between FFT and IFFT?

The order of operations is not preserved between FFT and IFFT and so round-off creeps in, whereas on the CPU everything cancels out perfectly. You can enforce symmetricity in the IFFT using the 'symmetric' option. Sign in to comment. The gpuArray implementation of the fft family of functions always returns complex results.

What is the FFT coefficient for a given frequency?

If your FFT coefficient for a given frequency f is x + i y, you can look at x as the coefficient of a cosine at that frequency, while the y is the coefficient of the sine.