Fft of a complex signal

1. What is the FFT of a complex number?
2. Can a Fourier transform be complex?
3. How do you calculate FFT of a signal?
4. What is complex conjugate of FFT?

What is the FFT of a complex number?

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])).

Can a Fourier transform be complex?

The complex Fourier transform is important in itself, but also as a stepping stone to more powerful complex techniques, such as the Laplace and z-transforms. These complex transforms are the foundation of theoretical DSP.

How do you calculate FFT of a signal?

The FFT operates by decomposing an N point time domain signal into N time domain signals each composed of a single point. The second step is to calculate the N frequency spectra corresponding to these N time domain signals. Lastly, the N spectra are synthesized into a single frequency spectrum. separate stages.

What is complex conjugate of FFT?

The complex conjugate of FFT(A) results from negating the imaginary part of FFT(A). The values of the elements in the power spectrum array are proportional to the magnitude squared of each frequency component making up the time-domain signal.