# Frequency domain In physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency, rather than time.

- Frequency domain

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## Fourier transform

Mathematical transform that decomposes functions depending on space or time into functions depending on spatial frequency or temporal frequency.         The term Fourier transform refers to both the frequency domain representation and the mathematical operation that associates the frequency domain representation to a function of space or time.

## Control engineering

Control engineering or control systems engineering  A system can be mechanical, electrical, fluid, chemical, financial or biological, and its mathematical modelling, analysis and controller design uses control theory in one or many of the time, frequency and complex-s domains, depending on the nature of the design problem.

## Time domain

Time domain refers to the analysis of mathematical functions, physical signals or time series of economic or environmental data, with respect to time. The use of the contrasting terms time domain and frequency domain developed in U.S. communication engineering in the late 1940s, with the terms appearing together without definition by 1950.

## Frequency response

Quantitative measure of the magnitude and phase of the output as a function of input frequency. The frequency response characterizes systems in the frequency domain, just as the impulse response characterizes systems in the time domain.

## Fourier series

Sum that represents a periodic function as a sum of sine and cosine waves.         This transform thus can generate frequency domain representations of non-periodic functions as well as periodic functions, allowing a waveform to be converted between its time domain representation and its frequency domain representation.

## Digital signal processing

Use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations. Nonlinear signal processing is closely related to nonlinear system identification and can be implemented in the time, frequency, and spatio-temporal domains.

## Discrete Fourier transform

Complex-valued function of frequency.    The DFT is therefore said to be a frequency domain representation of the original input sequence.

## Z-transform   In mathematics and signal processing, the Z-transform converts a discrete-time signal, which is a sequence of real or complex numbers, into a complex frequency-domain (z-domain or z-plane) representation.

## Wavelet transform

Representation of a square-integrable function by a certain orthonormal series generated by a wavelet.   But smooth, periodic signals are better compressed using other methods, particularly traditional harmonic analysis in the frequency domain with Fourier-related transforms.

## Data compression

Process of encoding information using fewer bits than the original representation.   To determine what information in an audio signal is perceptually irrelevant, most lossy compression algorithms use transforms such as the modified discrete cosine transform (MDCT) to convert time domain sampled waveforms into a transform domain, typically the frequency domain.

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