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Generating function and Z-transform

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

Difference between Generating function and Z-transform

Generating function vs. Z-transform

In mathematics, a generating function is a way of encoding an infinite sequence of numbers (an) by treating them as the coefficients of a power series. 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 Generating function and Z-transform

Generating function and Z-transform have 14 things in common (in Unionpedia): Abraham de Moivre, Contour integration, Convolution, Discrete Fourier transform, Formal power series, Generating function transformation, Geometric series, Mathematics, Partial fraction decomposition, Pierre-Simon Laplace, Probability-generating function, Radius of convergence, Recurrence relation, Sequence.

Abraham de Moivre

Abraham de Moivre (26 May 166727 November 1754) was a French mathematician known for de Moivre's formula, a formula that links complex numbers and trigonometry, and for his work on the normal distribution and probability theory.

Abraham de Moivre and Generating function · Abraham de Moivre and Z-transform · See more »

Contour integration

In the mathematical field of complex analysis, contour integration is a method of evaluating certain integrals along paths in the complex plane.

Contour integration and Generating function · Contour integration 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 Generating function · Convolution and Z-transform · See more »

Discrete Fourier 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.

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Formal power series

In mathematics, a formal power series is a generalization of a polynomial, where the number of terms is allowed to be infinite; this implies giving up the possibility of replacing the variable in the polynomial with an arbitrary number.

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Generating function transformation

In mathematics, a transformation of a sequence's generating function provides a method of converting the generating function for one sequence into a generating function enumerating another.

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Geometric series

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

Generating function 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.

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Partial fraction decomposition

In algebra, the partial fraction decomposition or partial fraction expansion of a rational function (that is, a fraction such that the numerator and the denominator are both polynomials) is the operation that consists in expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator.

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Pierre-Simon Laplace

Pierre-Simon, marquis de Laplace (23 March 1749 – 5 March 1827) was a French scholar whose work was important to the development of mathematics, statistics, physics and astronomy.

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Probability-generating function

In probability theory, the probability generating function of a discrete random variable is a power series representation (the generating function) of the probability mass function of the random variable.

Generating function and Probability-generating function · Probability-generating function and Z-transform · See more »

Radius of convergence

In mathematics, the radius of convergence of a power series is the radius of the largest disk in which the series converges.

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Recurrence relation

In mathematics, a recurrence relation is an equation that recursively defines a sequence or multidimensional array of values, once one or more initial terms are given: each further term of the sequence or array is defined as a function of the preceding terms.

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Sequence

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

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The list above answers the following questions

Generating function and Z-transform Comparison

Generating function has 122 relations, while Z-transform has 67. As they have in common 14, the Jaccard index is 7.41% = 14 / (122 + 67).

References

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

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