67 relations: Abraham de Moivre, Advanced z-transform, Argument (complex analysis), Autoregressive–moving-average model, Bilinear transform, Causal system, Chirp Z-transform, Complex conjugate, Complex number, Contour integration, Convolution, Cross-correlation, Decimation (signal processing), Dirac delta function, Discrete Fourier transform, Discrete time and continuous time, Discrete-time Fourier transform, Eliahu I. Jury, Final value theorem, Finite impulse response, Formal power series, Fourier series, Fourier transform, Fraction (mathematics), Frequency domain, Frequency response, Fundamental theorem of algebra, Generating function, Generating function transformation, Geometric series, Geophysics, Heaviside step function, Hertz, Imaginary unit, Impulse response, Initial value theorem, John R. Ragazzini, Laplace transform, Laurent series, Linear time-invariant theory, Linearity, Lotfi A. Zadeh, Mathematics, Multiplication, Parseval's theorem, Partial fraction decomposition, Periodic summation, Pierre-Simon Laplace, Pole–zero plot, Probability-generating function, ..., Radian, Radius of convergence, Real number, Recurrence relation, Sequence, Signal processing, Starred transform, Time-scale calculus, Transfer function, Two-sided Laplace transform, Unit circle, Upsampling, Witold Hurewicz, Zak transform, Zero of a function, Zeros and poles, Zeta function regularization. Expand index (17 more) »

## 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.

New!!: Z-transform and Abraham de Moivre · See more »

## Advanced z-transform

In mathematics and signal processing, the advanced z-transform is an extension of the z-transform, to incorporate ideal delays that are not multiples of the sampling time.

New!!: Z-transform and Advanced z-transform · See more »

## Argument (complex analysis)

In mathematics, the argument is a multi-valued function operating on the nonzero complex numbers.

New!!: Z-transform and Argument (complex analysis) · See more »

## Autoregressive–moving-average model

In the statistical analysis of time series, autoregressive–moving-average (ARMA) models provide a parsimonious description of a (weakly) stationary stochastic process in terms of two polynomials, one for the autoregression and the second for the moving average.

New!!: Z-transform and Autoregressive–moving-average model · See more »

## Bilinear transform

The bilinear transform (also known as Tustin's method) is used in digital signal processing and discrete-time control theory to transform continuous-time system representations to discrete-time and vice versa.

New!!: Z-transform and Bilinear transform · See more »

## Causal system

In control theory, a causal system (also known as a physical or nonanticipative system) is a system where the output depends on past and current inputs but not future inputs—i.e., the output y(t_) depends on only the input x(t) for values of t \le t_.

New!!: Z-transform and Causal system · See more »

## Chirp Z-transform

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

New!!: Z-transform and Chirp Z-transform · See more »

## Christmas

Christmas is an annual festival commemorating the birth of Jesus Christ,Martindale, Cyril Charles.

New!!: Z-transform and Christmas · See more »

## Christmas and holiday season

The Christmas season, also called the festive season, or the holiday season (mainly in the U.S. and Canada; often simply called the holidays),, is an annually recurring period recognized in many Western and Western-influenced countries that is generally considered to run from late November to early January.

New!!: Z-transform and Christmas and holiday season · See more »

## Christmas Eve

Christmas Eve is the evening or entire day before Christmas Day, the festival commemorating the birth of Jesus.

New!!: Z-transform and Christmas Eve · See more »

## Christmas traditions

Christmas traditions vary from country to country.

New!!: Z-transform and Christmas traditions · 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.

New!!: Z-transform and Complex conjugate · 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.

New!!: Z-transform and Complex number · 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.

New!!: Z-transform and Contour integration · 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.

New!!: Z-transform and Convolution · 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.

New!!: Z-transform and Cross-correlation · See more »

## Decimation (signal processing)

In digital signal processing, decimation is the process of reducing the sampling rate of a signal.

New!!: Z-transform and Decimation (signal processing) · See more »

## Dirac delta function

In mathematics, the Dirac delta function (function) is a generalized function or distribution introduced by the physicist Paul Dirac.

New!!: Z-transform and Dirac delta function · 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.

New!!: Z-transform and Discrete Fourier transform · See more »

## Discrete time and continuous time

In mathematics and in particular mathematical dynamics, discrete time and continuous time are two alternative frameworks within which to model variables that evolve over time.

New!!: Z-transform and Discrete time and continuous time · 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.

New!!: Z-transform and Discrete-time Fourier transform · See more »

## Eliahu I. Jury

Eliahu Ibraham Jury (born May 23, 1923) is an American engineer, born in Baghdad, Iraq.

New!!: Z-transform and Eliahu I. Jury · See more »

## Final value theorem

In mathematical analysis, the final value theorem (FVT) is one of several similar theorems used to relate frequency domain expressions to the time domain behavior as time approaches infinity.

New!!: Z-transform and Final value theorem · See more »

## Finite impulse response

In signal processing, a finite impulse response (FIR) filter is a filter whose impulse response (or response to any finite length input) is of finite duration, because it settles to zero in finite time.

New!!: Z-transform and Finite impulse response · See more »

## 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.

New!!: Z-transform and Formal power series · See more »

## Fourier series

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

New!!: Z-transform and Fourier series · 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.

New!!: Z-transform and Fourier transform · See more »

## Fraction (mathematics)

A fraction (from Latin fractus, "broken") represents a part of a whole or, more generally, any number of equal parts.

New!!: Z-transform and Fraction (mathematics) · 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.

New!!: Z-transform and Frequency domain · See more »

## Frequency response

Frequency response is the quantitative measure of the output spectrum of a system or device in response to a stimulus, and is used to characterize the dynamics of the system.

New!!: Z-transform and Frequency response · See more »

## Fundamental theorem of algebra

The fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root.

New!!: Z-transform and Fundamental theorem of algebra · See more »

## Generating function

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.

New!!: Z-transform and Generating function · See more »

## 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.

New!!: Z-transform and Generating function transformation · See more »

## Geometric series

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

New!!: Z-transform and Geometric series · See more »

## Geophysics

Geophysics is a subject of natural science concerned with the physical processes and physical properties of the Earth and its surrounding space environment, and the use of quantitative methods for their analysis.

New!!: Z-transform and Geophysics · See more »

## Heaviside step function

The Heaviside step function, or the unit step function, usually denoted by or (but sometimes, or), is a discontinuous function named after Oliver Heaviside (1850–1925), whose value is zero for negative argument and one for positive argument.

New!!: Z-transform and Heaviside step function · See more »

## Hertz

The hertz (symbol: Hz) is the derived unit of frequency in the International System of Units (SI) and is defined as one cycle per second.

New!!: Z-transform and Hertz · See more »

## Imaginary unit

The imaginary unit or unit imaginary number is a solution to the quadratic equation.

New!!: Z-transform and Imaginary unit · See more »

## Impulse response

In signal processing, the impulse response, or impulse response function (IRF), of a dynamic system is its output when presented with a brief input signal, called an impulse.

New!!: Z-transform and Impulse response · See more »

## Initial value theorem

In mathematical analysis, the initial value theorem is a theorem used to relate frequency domain expressions to the time domain behavior as time approaches zero.

New!!: Z-transform and Initial value theorem · See more »

## John R. Ragazzini

John Ralph Ragazzini (January 3, 1912 – November 22, 1988) was an American electrical engineer and a professor of Electrical Engineering.

New!!: Z-transform and John R. Ragazzini · See more »

## Laplace transform

In mathematics, the Laplace transform is an integral transform named after its discoverer Pierre-Simon Laplace.

New!!: Z-transform and Laplace transform · See more »

## Laurent series

In mathematics, the Laurent series of a complex function f(z) is a representation of that function as a power series which includes terms of negative degree.

New!!: Z-transform and Laurent series · See more »

## Linear time-invariant theory

Linear time-invariant theory, commonly known as LTI system theory, comes from applied mathematics and has direct applications in NMR spectroscopy, seismology, circuits, signal processing, control theory, and other technical areas.

New!!: Z-transform and Linear time-invariant theory · See more »

## Linearity

Linearity is the property of a mathematical relationship or function which means that it can be graphically represented as a straight line.

New!!: Z-transform and Linearity · See more »

## Lotfi A. Zadeh

Lotfi Aliasker Zadeh (Lütfəli Rəhim oğlu Ələsgərzadə; لطفی علیعسگرزاده; February 4, 1921 – September 6, 2017) was a mathematician, computer scientist, electrical engineer, artificial intelligence researcher and professor emeritus of computer science at the University of California, Berkeley.

New!!: Z-transform and Lotfi A. Zadeh · See more »

## Mathematics

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

New!!: Z-transform and Mathematics · See more »

## Multiplication

Multiplication (often denoted by the cross symbol "×", by a point "⋅", by juxtaposition, or, on computers, by an asterisk "∗") is one of the four elementary mathematical operations of arithmetic; with the others being addition, subtraction and division.

New!!: Z-transform and Multiplication · See more »

## New Year

New Year is the time or day at which a new calendar year begins and the calendar's year count increments by one.

New!!: Z-transform and New Year · See more »

## New Year's Day

New Year's Day, also called simply New Year's or New Year, is observed on January 1, the first day of the year on the modern Gregorian calendar as well as the Julian calendar.

New!!: Z-transform and New Year's Day · See more »

## New Year's Eve

In the Gregorian calendar, New Year's Eve (also known as Old Year's Day or Saint Sylvester's Day in many countries), the last day of the year, is on 31 December which is the seventh day of Christmastide.

New!!: Z-transform and New Year's Eve · 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.

New!!: Z-transform and Parseval's theorem · See more »

## 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.

New!!: Z-transform and Partial fraction decomposition · 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.

New!!: Z-transform and Periodic summation · See more »

## 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.

New!!: Z-transform and Pierre-Simon Laplace · See more »

## Pole–zero plot

In mathematics, signal processing and control theory, a pole–zero plot is a graphical representation of a rational transfer function in the complex plane which helps to convey certain properties of the system such as.

New!!: Z-transform and Pole–zero plot · See more »

## 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.

New!!: Z-transform and Probability-generating function · See more »

## Radian

The radian (SI symbol rad) is the SI unit for measuring angles, and is the standard unit of angular measure used in many areas of mathematics.

New!!: Z-transform and Radian · 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.

New!!: Z-transform and Radius of convergence · See more »

## Real number

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

New!!: Z-transform and Real number · See more »

## 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.

New!!: Z-transform and Recurrence relation · See more »

## Sequence

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

New!!: Z-transform and Sequence · See more »

## Signal processing

Signal processing concerns the analysis, synthesis, and modification of signals, which are broadly defined as functions conveying "information about the behavior or attributes of some phenomenon", such as sound, images, and biological measurements.

New!!: Z-transform and Signal processing · See more »

## Starred transform

In applied mathematics, the starred transform, or star transform, is a discrete-time variation of the Laplace transform, so-named because of the asterisk or "star" in the customary notation of the sampled signals.

New!!: Z-transform and Starred transform · See more »

## Time-scale calculus

In mathematics, time-scale calculus is a unification of the theory of difference equations with that of differential equations, unifying integral and differential calculus with the calculus of finite differences, offering a formalism for studying hybrid discrete–continuous dynamical systems.

New!!: Z-transform and Time-scale calculus · See more »

## Transfer function

In engineering, a transfer function (also known as system function or network function) of an electronic or control system component is a mathematical function giving the corresponding output value for each possible value of the input to the device.

New!!: Z-transform and Transfer function · See more »

## Two-sided Laplace transform

In mathematics, the two-sided Laplace transform or bilateral Laplace transform is an integral transform equivalent to probability's moment generating function.

New!!: Z-transform and Two-sided Laplace transform · See more »

## Unit circle

In mathematics, a unit circle is a circle with a radius of one.

New!!: Z-transform and Unit circle · See more »

## Upsampling

In digital signal processing, upsampling can refer to the entire process of increasing the sampling rate of a signal, or it can refer to just one step of the process, the other step being interpolation.

New!!: Z-transform and Upsampling · See more »

## Witold Hurewicz

Witold Hurewicz (June 29, 1904 – September 6, 1956) was a Jewish-Polish mathematician.

New!!: Z-transform and Witold Hurewicz · 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.

New!!: Z-transform and Zak transform · See more »

## Zero of a function

In mathematics, a zero, also sometimes called a root, of a real-, complex- or generally vector-valued function f is a member x of the domain of f such that f(x) vanishes at x; that is, x is a solution of the equation f(x).

New!!: Z-transform and Zero of a function · See more »

## Zeros and poles

In mathematics, a zero of a function is a value such that.

New!!: Z-transform and Zeros and poles · See more »

## Zeta function regularization

In mathematics and theoretical physics, zeta function regularization is a type of regularization or summability method that assigns finite values to divergent sums or products, and in particular can be used to define determinants and traces of some self-adjoint operators.

New!!: Z-transform and Zeta function regularization · See more »

## 2018

2018 has been designated as the third International Year of the Reef by the International Coral Reef Initiative.

New!!: Z-transform and 2018 · See more »

## 2019

2019 (MMXIX) will be a common year starting on Tuesday of the Gregorian calendar, the 2019th year of the Common Era (CE) and Anno Domini (AD) designations, the 19th year of the 3rd millennium, the 19th year of the 21st century, and the 10th and last year of the 2010s decade.

New!!: Z-transform and 2019 · See more »

## Redirects here:

Bilateral Z-transform, Bilateral z-transform, Laurent transform, Z Transform, Z transform, Z-domain, Z-transformation.

## References

[1] https://en.wikipedia.org/wiki/Z-transform