Frequency Domain and Fourier Transform

Frequency domain analysis is also called spectrum analysis or spectral analysis. Fourier transform is used to convert signals from time or space domain to the frequency domain. Signal information is converted to a magnitude and phase component of each frequency. The Fourier transform is converted to the magnitude of each frequency component squared, forming a power spectrum. This power spectrum is studied to determine which frequencies are present in the input signal and which are missing. The phase information can also be obtained from the Fourier transform. The cepstrum is a commonly used frequency domain transformation which converts a signal to the frequency domain through Fourier transform. It takes the Fourier transform (FT) of the logarithm of the estimated spectrum of a signal. The name cepstrum is devised by reversing the first four letters of the word spectrum. A very important property of the cepstral domain is that the convolution of two signals can be expressed as the addition of their cepstra.

x₁ * x₂ → x’₁ + x’₂