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The Z-Transform like other transforms (e.g. Fourier, Laplace) maps/transforms a signal from one domain to another. For instance the fourier transform of a signal will give us info. on the frequency spectrum of the signal in frequency domain. The Z-transform of the signal will give rise to the pole-zero plot which discusses issues such as stability, causality etc. of the system.
Z-transform is discrete version of the S-domain transform. There are some ways to transform S-domain transfer functions to Z-domain.
For example bilinear transformation where H(z)=H(s) when S=2.Fs.Z-1/Z+1.
z-transe is more general than fourier trans.u know some signal which are not absolutly sumable have z-transe you know it is a math tools and no pysical meaning(but fourier transe have)
Many real world systems behaviour is correctly described by sets of linear differential equations (or linear difference equations in the case of discrete-time systems). The solutions to these sets of equations take the form of a linear combination of e^-st. Laplace transform represents signals and system responses in terms of linear combinations of e^st and so makes it possible to convert a set of linear differential equations into a set of ordinary linear equations which can then be solved using
gaussian elimination or some such method. That is
the significance of the Laplace transform For Z transform it is the same as Laplace but for discrete
time systems. The Z transform can be viewed as the laplace transform in which the jw access has been mapped onto the unit circle.
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