Frequency domain is a term used to describe the analysis of mathematical functions or signals with respect to frequency. The Mathematical concept of a function expresses dependence between two quantities one of which is given (the independent variable, argument of the function In the fields of communications, Signal processing, and in Electrical engineering more generally a signal is any time-varying or spatial-varying quantity
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. Time domain is a term used to describe the analysis of mathematical functions or physical signals with respect to Time. A frequency-domain representation can also include information on the phase shift that must be applied to each sinusoid in order to be able to recombine the frequency components to recover the original time signal. 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
The frequency domain relates to the Fourier transform or Fourier series by decomposing a function into an infinite or finite number of frequencies. This article specifically discusses Fourier transformation of functions on the Real line; for other kinds of Fourier transformation see Fourier analysis and In Mathematics, a Fourier series decomposes a periodic function into a sum of simple oscillating functions Infinity (symbolically represented with ∞) comes from the Latin infinitas or "unboundedness In Mathematics, a set is called finite if there is a Bijection between the set and some set of the form {1 2. Frequency is a measure of the number of occurrences of a repeating event per unit Time. This is based on the concept of Fourier series that any waveform can be expressed as a sum of sinusoids (sometimes infinitely many. waveformogg|right|a sine square and sawtooth wave at 440 hz]] Waveform means the shape and form of a signal such as a Wave moving in a solid liquid or gaseous )
A spectrum analyzer is the tool commonly used to visualize real-world signals in the frequency domain. A spectrum analyzer or spectral analyzer is a device used to examine the spectral composition of some electrical, acoustic, or optical
Contents |
Magnitude and phase
In using the Laplace, Z-, or Fourier transforms, the frequency spectrum is complex, describing the magnitude and phase of a signal, or of the response of a system, as a function of frequency. 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 soluble algebraic In Mathematics and Signal processing, the Z-transform converts a discrete Time-domain signal which is a Sequence of real This article specifically discusses Fourier transformation of functions on the Real line; for other kinds of Fourier transformation see Fourier analysis and 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 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 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 or spectral density. Familiar concepts associated with a Frequency are colors musical notes radio/TV channels and even the regular rotation of the earth In Statistical signal processing and Physics, the spectral density, power spectral density ( PSD) or energy spectral density ( A spectrum analyzer is a device that displays the spectrum. A spectrum analyzer or spectral analyzer is a device used to examine the spectral composition of some electrical, acoustic, or optical
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. In Statistical signal processing and Physics, the spectral density, power spectral density ( PSD) or energy spectral density ( In the mathematical sciences, a stationary process (or strict(ly stationary process or strong(ly stationary process) is a Stochastic 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 is often thought of as converting time-domain sound waveforms to frequency-domain spectra. The ear is the sense organ that detects Sounds The Vertebrate ear shows a common biology from Fish to Humans with variations waveformogg|right|a sine square and sawtooth wave at 440 hz]] Waveform means the shape and form of a signal such as a Wave moving in a solid liquid or gaseous 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.
See also
References
Time domain is a term used to describe the analysis of mathematical functions or physical signals with respect to Time. A wavelet is a mathematical function used to divide a given function or continuous-time signal into different frequency components and study each component with a resolution The short-time Fourier transform ( STFT) or alternatively short-term Fourier transform, is a Fourier-related transform used to determine the sinusoidal This article specifically discusses Fourier transformation of functions on the Real line; for other kinds of Fourier transformation see Fourier analysis andDapyx Software network: MP3 Explorer | Ebook Manager | Zenithic