Complex and Real Planes of Discrete Fourier Transforms

A Fourier transform converts signals from the time domain to the frequency domain. In the Fourier domain, it is possible to analyze the signals in the real, absolute, or imaginary planes. In any communication channel some noise is added to the signal. The white noise contains all the frequencies with a uniform power spectrum.

Notice that the sinc signal is the rect in the absolute Fourier plane, and rect as a signal gives sinc as the absolute Fourier plane.

The variables and represent the time and frequency index. The Fourier planes are shifted by half of the signal sample size.