Inverse Z transform

版本 1.0.0 (3.6 KB) 作者: ARF
Function izt calculates the numerical inverse Z-transform of a rational function of z^-1 at specified points.
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Function izt calculates the numerical inverse Z-transform of a rational function of z^-1 at specified points using the partial fraction expansion method. It considers the region of convergence (ROC) of the Z-transform.
The Z-transform is assumed to have numerator and denominator coefficients p and q, respectively, arranged in increasing powers of z^-1. The ROC includes the point z0. 'nvec' is the array of input points, which can be a vector, matrix, or tensor. 'tol' specifies the computational error tolerance, with a default value set to 1e-6.
The Z-transform is defined as:
-1 -M
p(1) + p(2) * z + ... + p(M + 1) * z
X(z) = -----------------------------------------
-1 -N
q(1) + q(2) * z + ... + q(N + 1) * z
where M = numel(p) - 1 and N = numel(q) - 1.
Note: If X(z) includes positive powers of z in the numerator or denominator, it can be reformulated to the above structure by dividing the numerator and the denominator by the highest power of z.
Example: Suppose we want to calculate the inverse z transform of
-1 -2 -3
1+ 2z - z +z
X(z)= ---------------------------------, with ROC:1/6<|z|<1/2
-1 -2 -1
(1 - z + 1/4 z )(1 + 1/6 z )
at n = -3, 0, and 3. We have p = [1 2 -1 1] and q = conv([1 -1 1/4], [1 1/6]) = [1.0000 -0.8333 0.0833 0.0417]
To indicate the ROC we chose z0 = 1/4 which falls inside the ROC. We also set nvec = [-3 0 3]. Finally by executing
x = izt(p, q, z0, nvec)
we get
x =
214.5000 7.5625 0.0761
References:
A. V. Oppenheim and R. Schafer, Discrete-Time Signal Processing, Prentice Hall, 3rd Ed. 2010.
A. R. Forouzan, "Region of convergence of derivative of z transform," IET Electronics Letters, vol. 52, no. 8, pp. 617-619.

引用格式

A. R. Fororouzan (2024). Inverse Z transform (https://www.mathworks.com/matlabcentral/fileexchange/<...>), MATLAB Central File Exchange. Retrieved June 4, 2024.

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1.0.0