# Fast Fourier Transform

An algorithm, or digital calculation routine, that efficiently calculates the discrete Fourier transform from the sampled time waveform. In other words it converts, or "transforms" a signal from the time domain into the frequency domain.

**Applications**

- Spectral Estimation (Periodograms)
- Fast Convolutions (Fast Frequency Domain FIR Filters)
- Transform Coding (Used In STC, IRIDUM Vocoders, MPEGS, AC-3)
- Speech Recognition and Speech "Pitch" Modifications
- Speech and Image Enhancement (Spectral Noise Subtraction)
- Adaptive System Identification and Noise Cancellation
- Numerical Computation (solving systems of equations, finite elements, etc)

### Historical Notes

**1965***Tukey and Cooley publish a paper introducing the "Fast Fourier Transform" algorithm.*

### Bins

The individual frequencies at which the amplitudes are calculated, commonly called lines.

### Line Spacing

The frequency difference between two adjacent bin centers or lines.

### Narrowband Analysis

Another way of saying FFT analysis.

### Windowing

An amplitude weighting of the time signal used with gated continuous signals to give them a slow onset and cut-off in order to reduce the generation of side lobes in their frequency spectrum.

**See also: **Blackman Window, Bohman Window, Cauchy Window, Discrete Fourier Transform, FFT Analyser, Fourier Transform, Hamming Window, Hanning Window, Kaiser Bessel Window, Leakage, Overlap Processing, Picket Fence Effect, Rectangular Window, Signals, Windowing.

**Subjects: ** Analysis Mechanical Engineering Noise & Vibration Physics Signal Processing

- Discrete-time Signal Processing, , US Imports & PHIPEs
- Fourier Transform and Its Applications, , McGraw-Hill Book Company Ltd
- Fast Fourier Transform and Its Applications, , Prentice-Hall

**Further reading:**

- Bruel & Kjaer - Technical Reviews These documents give detailed articles on measurement and signal processing theory.

**Weblinks:**