# z-transform

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## z-transform

[′zē ′tranz‚fȯrm]
(mathematics)
The z-transform of a sequence whose general term is ƒn is the sum of a series whose general term is ƒn z -n , where z is a complex variable; n runs over the positive integers for a one-sided transform, over all the integers for a two-sided transform.
References in periodicals archive ?
Then taking the one-side Z-transform of system (10), see more in [9], one gets the following equation in Z-domain
The CZT algorithm is a digital signal processing algorithm which is applicable to the general case calculating limited width of the z-transform along the spiral curve.
The filters [[LAMBDA].sup.(a).sub.n] (s, [xi]) can be mapped onto a rational Z-transform [M.sup.(a).sub.n] (z, [xi]) with real pole [absolute value of [xi]] < 1 using the following modified bilinear transformation [20]:
If Chirp z-transform (CZT) [20, 21] is applied to carry out the two consecutive mappings (since they are linear mappings), the proposed algorithm will not require interpolations and its reconstructed image would be free of truncation errors.
Define [A.sub.i]([n.sup.+]) = P{[[X.sub.i]]([n.sup.+]) = 1 | N([0.sup.+]) = i} with z-transform [a.sub.i](u) = [[summation].sup.[infinity].sub.n=0]([n.sup.+])[u.sup.n], [absolute value of u] < 1; thus the following expression of [a.sub.i](u) holds.
The Z-transform method [1, 2, 37] was applied to handle the linear time-invariant discretee-time systems (LTI discrete-time systems) and difference equations in Z-domain.
The mathematical background of the running example is the following: In Signal Processing, "the Z-transform for discrete-time signals is the counterpart of the Laplace transform for continuoustime signals, and they each have a similar relationship to the corresponding Fourier transform.
Generally, there are three common methods to derive the current expression at the loaded place: directly deducing by the volt-ampere characteristic [5], basing on the piecewise linear recursive convolution (PLRC) technique [6-8], using Z-transform approach [9-12].
Then the z-transform of the MFROH combined with the system (5) and for very small T is
Beginning with deterministic signals and filters then moving to stochastic ones, he explores such topics as discrete time signals and systems, the Z-transform, discrete filter design techniques, stochastic processes, and adaptive filters.
The design of these filters is based on the z-transform.Once the energy for each channel is computed, the values of each channel are subjected to the proposed support vector machine algorithm with respect to the class to rank the importance of the channel.
Following the well-known approach developed by Stephenson and Mitalas (Stephenson and Mitalas 1971), based on the use of the Z-transform (ZT) (Jury 1964), let us consider a thermal system, like a wall, in which u([tau]) is the input signal and y([tau]) is the correlated output signal.
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