Directly implementing the discrete Fourier transform (DFT) on *N* data samples requires approximately *N* complex operations and is a time-consuming process. The fast Fourier transform (FFT) is a fast algorithm for calculating
the DFT. The following equation defines the DFT.

The following measurements comprise the basic functions for FFT-based signal analysis:

You can use the basic functions as the building blocks for creating additional measurement functions, such as the frequency response, impulse response, coherence, amplitude spectrum, and phase spectrum.

The FFT and the power spectrum are useful for measuring the frequency content of stationary or transient signals. The FFT produces the average frequency content of a signal over the total acquisition. Therefore, use the FFT for stationary signal analysis or in cases where you need only the average energy at each frequency line.

An FFT is equivalent to a set of parallel filters of bandwidth Δ*f* centered at each frequency increment from DC to (*F*_{s}/2) - (*F*_{s}/*N*). Therefore, frequency lines also are known as frequency bins or FFT bins.