'''Frequency domain''' is a term used to describe the analysis of mathematical functions with respect to frequency

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 also includes information on the phase shift that must be applied to each

frequency in order to be able to recombine the

frequency components to recover the original

time signal

The

frequency domain relates to the Fourier series by decomposing a signal into an infinite or finite

number of

frequencies## Common transforms

The Z-transform and Laplace transform are two transforms that transform a signal in the

time domain into the complex

frequency domain

- The Laplace transform is used for continuous signals in Cartesian coordinates with $s=a\; +\; jb$
- The Z-transform is used for discrete signals in circular coordinates with $z\; =\; r\; cdot\; e^\{jomega\}$

The

other well known transform is the

Fourier transform and the Discrete-time Fourier transform These two transforms are subsets of the Laplace transform and Z-Transform respectively

- Evaluating the Laplace transform on the imaginary axis (or $s=jb$) is equivalent to the Fourier transform
- Evaluating the Z-transform on the unit circle (or $z=e^\{jomega\}$) is equivalent to the discrete Fourier transform

The

result of transforming a

time domain signal into the

frequency domain is commonly called the frequency spectrum of the signal That is, it shows the spectral content of the signal

## Magnitude and phase

In using the Laplace Z-, or Fourier transforms the

frequency spectrum is complex and describes the

frequency magnitude and phase 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 power spectrum A spectrum analyser is a device that displays the power spectrum

A

biological system that operates in the

frequency domain is the auditory system in which the basilar membrane of the inner ear is able to perform a power

spectrum decomposition of incoming sound waves The

result is that we are able to hear a collection of different frequencies played together as a collection of separate notes rather than simply a complicated noise

## See also

- Frequency spectrum
- Power spectrum
- Spectrum analyzer