Fft real/imaginary

1. What is the real and imaginary part of FFT?
2. Is the FFT of a real signal real?
3. What is the imaginary part of a Fourier transform mean?
4. Why does FFT return complex numbers?

What is the real and imaginary part of FFT?

The real portion of an FFT result is how much each frequency component resembles a cosine wave, the imaginary component, how much each component resembles a sine wave.

Is the FFT of a real signal real?

Most real-world signals are real-valued. Therefore, you can use the real fast Fourier transform (FFT) for most applications. You also can use the complex FFT by setting the imaginary part of the signal to zero.

What is the imaginary part of a Fourier transform mean?

If you consider the input as current, the transfer function or Fourier transform as impedance then the output is potential. If Fourier transform is impedance, then the real part of FT is resistive part of the impedance and imaginary part is the reactive part of the impedance.

Why does FFT return complex numbers?

It's because processing periodic signals involves trigonometry all the time, and there is a simple way to move from sines and cosines to more simple complex numbers algebra: Euler's formula. So most of the time signals are just converted to their complex exponential form.