All Topics  
Frequency domain

 

 
   Email Print
   Bookmark   Link
 

 

Frequency domain
 
 
  Topics Frequency domain Topic Home

In electronics
Electronics

Electronics refers to the flow of charge through nonmetal electrical conductor , whereas electrical refers to the flow of charge through metal electrical conductor....
 and control systems engineering, frequency domain is a term used to describe the analysis of mathematical functions or signals with respect to frequency
Frequency

Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency....
, rather than time.

Speaking non-technically, a time-domain graph shows how a signal changes over time, whereas a frequency-domain graph shows how much of the signal lies within each given frequency band over a range of frequencies. A frequency-domain representation can also include information on the phase
Phase (waves)

The phase of an oscillation or wave is the fraction of a complete cycle corresponding to an offset in the displacement from a specified reference point at time t = 0....
 shift that must be applied to each sinusoid in order to be able to recombine the frequency components to recover the original time signal.

A given function or signal can be converted between the time and frequency domains with a pair of mathematical operator
Operator

In mathematics, an operator is a function which operates on another function. Often, an "operator" is a function which acts on functions to produce other functions ; or it may be a generalization of such a function, as in linear algebra, where some of the terminology reflects the origin of the subject in operations on the functions which ar...
s called a transform
Transform (mathematics)

In mathematics a transform is an operator applied to a Function so that under the transform certain operations are simplified. For example, in arithmetic when finding the logarithm of numbers, the process of finding the logarithm of the product is reduced to the simpler process of adding the logarithms of each factor....
.






Discussion
Ask a question about 'Frequency domain'
Start a new discussion about 'Frequency domain'
Answer questions from other users
Full Discussion Forum



Encyclopedia


In electronics
Electronics

Electronics refers to the flow of charge through nonmetal electrical conductor , whereas electrical refers to the flow of charge through metal electrical conductor....
 and control systems engineering, frequency domain is a term used to describe the analysis of mathematical functions or signals with respect to frequency
Frequency

Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency....
, rather than time.

Speaking non-technically, a time-domain graph shows how a signal changes over time, whereas a frequency-domain graph shows how much of the signal lies within each given frequency band over a range of frequencies. A frequency-domain representation can also include information on the phase
Phase (waves)

The phase of an oscillation or wave is the fraction of a complete cycle corresponding to an offset in the displacement from a specified reference point at time t = 0....
 shift that must be applied to each sinusoid in order to be able to recombine the frequency components to recover the original time signal.

A given function or signal can be converted between the time and frequency domains with a pair of mathematical operator
Operator

In mathematics, an operator is a function which operates on another function. Often, an "operator" is a function which acts on functions to produce other functions ; or it may be a generalization of such a function, as in linear algebra, where some of the terminology reflects the origin of the subject in operations on the functions which ar...
s called a transform
Transform (mathematics)

In mathematics a transform is an operator applied to a Function so that under the transform certain operations are simplified. For example, in arithmetic when finding the logarithm of numbers, the process of finding the logarithm of the product is reduced to the simpler process of adding the logarithms of each factor....
. An example is the Fourier transform
Fourier transform

In mathematics, Fourier analysis is a subject area which grew out of the study of Fourier series. The subject began with trying to understand when it was possible to represent general functions by sums of simpler trigonometric functions....
, which decomposes a function into the sum of a (potentially infinite) number of sine wave
Sine wave

The sine wave or sinusoid is a function that occurs often in mathematics, physics, signal processing, hearing , electrical engineering, and many other fields....
 frequency components. The 'spectrum' of frequency components is the frequency domain representation of the signal. The inverse Fourier transform converts the frequency domain function back to a time function.

A spectrum analyzer
Spectrum analyzer

A spectrum analyzer or spectral analyzer is a device used to examine the spectral composition of some electricity, acoustics, or optics waveform....
 is the tool commonly used to visualize real-world signals in the frequency domain.

Magnitude and phase


In using the Laplace
Laplace transform

In mathematics, the Laplace transform is one of the best known and most widely used integral transforms. It is commonly used to produce an easily solvable algebraic equation from an ordinary differential equation....
, Z-
Z-transform

In mathematics and signal processing, the Z-transform converts a discrete_mathematics time-domain signal, which is a sequence of real number or complex numbers, into a complex frequency-domain representation....
, or Fourier
Fourier transform

In mathematics, Fourier analysis is a subject area which grew out of the study of Fourier series. The subject began with trying to understand when it was possible to represent general functions by sums of simpler trigonometric functions....
 transforms, the frequency spectrum is complex, describing the magnitude
Magnitude (mathematics)

The magnitude of a mathematical object is its size: a property by which it can be larger or smaller than other objects of the same kind; in technical terms, an ordering of the class of objects to which it belongs....
 and phase
Phase (waves)

The phase of an oscillation or wave is the fraction of a complete cycle corresponding to an offset in the displacement from a specified reference point at time t = 0....
 of a signal, or of the response of a system, as a function of frequency. In many applications, phase information is not important. By discarding the phase information it is possible to simplify the information in a frequency domain representation to generate a frequency spectrum
Frequency spectrum

Familiar concepts associated with a frequency are colors, musical notes, radio/TV channels, and even the regular rotation of the earth. A source of light can have many colors mixed together and in different amounts ....
 or spectral density
Spectral density

In statistical signal processing and physics, the spectral density, power spectral density , or energy spectral density , is a positive real function of a frequency variable associated with a stationary stochastic process, or a deterministic function of time, which has dimensions of power per Hz, or energy per Hz....
. A spectrum analyzer
Spectrum analyzer

A spectrum analyzer or spectral analyzer is a device used to examine the spectral composition of some electricity, acoustics, or optics waveform....
 is a device that displays the spectrum.

The power spectral density is a frequency-domain description that can be applied to a large class of signals that are neither periodic nor square-integrable; to have a power spectral density a signal needs only to be the output of a wide-sense stationary random process.

Partial frequency-domain example

Due to popular simplifications of the hearing process and titles such as Plomp's "The Ear as a Frequency Analyzer," the inner ear
Ear

The ear is the sense organ that detects sounds. The vertebrate ear shows a common biology from fish to humans, with variations in structure according to order and species....
 is often thought of as converting time-domain sound waveform
Waveform

Waveform means the shape and form of a signal such as a wave moving in a solid, liquid or gaseous medium.In many cases the medium in which the wave is being propagated does not permit a direct visual image of the form....
s to frequency-domain spectra. The frequency domain is not actually a very accurate or useful model for hearing, but a time/frequency space or time/place space can be a useful description.

Different frequency domains

Although "the" frequency domain is spoken of in the singular, there are actually several different frequency domains, each defined by a different mathematical transform, which are used to analyze signals. These are the most common transforms used and the fields in which they are used:
  • Fourier series
    Fourier series

    In mathematics, a Fourier series decomposes a periodic function into a sum of simple oscillating functions, namely sine wave . The study of Fourier series is a branch of Fourier analysis....
     - repetitive signals, oscillating
    Oscillation

    Oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. Familiar examples include a swinging pendulum and Alternating current power....
     systems
  • Fourier transform
    Fourier transform

    In mathematics, Fourier analysis is a subject area which grew out of the study of Fourier series. The subject began with trying to understand when it was possible to represent general functions by sums of simpler trigonometric functions....
     - nonrepetitive signals
  • Laplace transform
    Laplace transform

    In mathematics, the Laplace transform is one of the best known and most widely used integral transforms. It is commonly used to produce an easily solvable algebraic equation from an ordinary differential equation....
     - electronic circuits and control system
    Control system

    A control system is a device or set of devices to manage, command, direct or regulate the behavior of other devices or systems.There are two common classes of control systems, with many variations and combinations: logic gate, and feedback or linear controls....
    s
  • Z transform - discrete signals, digital signal processing
    Digital signal processing

    Digital signal processing is concerned with the representation of the signal s by a sequence of numbers or symbols and the processing of these signals....
  • wavelet transform - digital image processing
    Digital image processing

    Digital image processing is the use of computer algorithms to perform on digital images. As a subfield of digital signal processing, digital image processing has many advantages over analog image processing; it allows a much wider range of algorithms to be applied to the input data, and can avoid problems such as the build-up of noise and si...
    , signal compression
    Signal compression

    In telecommunication, the term signal compression has the following meanings:In analog systems, reduction of the dynamic range of a Signalling by controlling it as a function of the inverse relationship of its instantaneous value relative to a specified reference level....


See also

  • Wavelet
    Wavelet

    A wavelet is a mathematical function used to divide a given function or continuous signal into different scale components. Usually one can assign a frequency range to each scale component....
  • Short-time Fourier transform
    Short-time Fourier transform

    The short-time Fourier transform , or alternatively short-term Fourier transform, is a List of Fourier-related transforms used to determine the sinusoidal frequency and phase content of local sections of a signal as it changes over time....