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Discrete Fourier transform and Z-transform

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Discrete Fourier transform and Z-transform

Discrete Fourier transform vs. Z-transform

In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency. 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 representation.

Similarities between Discrete Fourier transform and Z-transform

Discrete Fourier transform and Z-transform have 16 things in common (in Unionpedia): Chirp Z-transform, Complex conjugate, Complex number, Convolution, Cross-correlation, Discrete-time Fourier transform, Fourier series, Fourier transform, Frequency domain, Geometric series, Mathematics, Parseval's theorem, Periodic summation, Real number, Sequence, Zak transform.

Chirp Z-transform

The Chirp Z-transform (CZT) is a generalization of the discrete Fourier transform.

Chirp Z-transform and Discrete Fourier transform · Chirp Z-transform and Z-transform · See more »

Complex conjugate

In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign.

Complex conjugate and Discrete Fourier transform · Complex conjugate and Z-transform · See more »

Complex number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.

Complex number and Discrete Fourier transform · Complex number and Z-transform · See more »

Convolution

In mathematics (and, in particular, functional analysis) convolution is a mathematical operation on two functions (f and g) to produce a third function, that is typically viewed as a modified version of one of the original functions, giving the integral of the pointwise multiplication of the two functions as a function of the amount that one of the original functions is translated.

Convolution and Discrete Fourier transform · Convolution and Z-transform · See more »

Cross-correlation

In signal processing, cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other.

Cross-correlation and Discrete Fourier transform · Cross-correlation and Z-transform · See more »

Discrete-time Fourier transform

In mathematics, the discrete-time Fourier transform (DTFT) is a form of Fourier analysis that is applicable to the uniformly-spaced samples of a continuous function.

Discrete Fourier transform and Discrete-time Fourier transform · Discrete-time Fourier transform and Z-transform · See more »

Fourier series

In mathematics, a Fourier series is a way to represent a function as the sum of simple sine waves.

Discrete Fourier transform and Fourier series · Fourier series and Z-transform · See more »

Fourier transform

The Fourier transform (FT) decomposes a function of time (a signal) into the frequencies that make it up, in a way similar to how a musical chord can be expressed as the frequencies (or pitches) of its constituent notes.

Discrete Fourier transform and Fourier transform · Fourier transform and Z-transform · See more »

Frequency domain

In 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.

Discrete Fourier transform and Frequency domain · Frequency domain and Z-transform · See more »

Geometric series

In mathematics, a geometric series is a series with a constant ratio between successive terms.

Discrete Fourier transform and Geometric series · Geometric series and Z-transform · See more »

Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

Discrete Fourier transform and Mathematics · Mathematics and Z-transform · See more »

Parseval's theorem

In mathematics, Parseval's theorem usually refers to the result that the Fourier transform is unitary; loosely, that the sum (or integral) of the square of a function is equal to the sum (or integral) of the square of its transform.

Discrete Fourier transform and Parseval's theorem · Parseval's theorem and Z-transform · See more »

Periodic summation

In signal processing, any periodic function, s_P(t) with period P, can be represented by a summation of an infinite number of instances of an aperiodic function, s(t), that are offset by integer multiples of P. This representation is called periodic summation: When s_P(t) is alternatively represented as a complex Fourier series, the Fourier coefficients are proportional to the values (or "samples") of the continuous Fourier transform, S(f) \ \stackrel \ \mathcal\, at intervals of 1/P.

Discrete Fourier transform and Periodic summation · Periodic summation and Z-transform · See more »

Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

Discrete Fourier transform and Real number · Real number and Z-transform · See more »

Sequence

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed.

Discrete Fourier transform and Sequence · Sequence and Z-transform · See more »

Zak transform

In mathematics, the Zak transform is a certain operation which takes as input a function of one variable and produces as output a function of two variables.

Discrete Fourier transform and Zak transform · Z-transform and Zak transform · See more »

The list above answers the following questions

Discrete Fourier transform and Z-transform Comparison

Discrete Fourier transform has 151 relations, while Z-transform has 67. As they have in common 16, the Jaccard index is 7.34% = 16 / (151 + 67).

References

This article shows the relationship between Discrete Fourier transform and Z-transform. To access each article from which the information was extracted, please visit:

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