why z transform is used in dsp?

why z transform is used in dsp?
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. ... It can be considered as a discrete-time equivalent of the Laplace transform.
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How do you use Z transform?
To find the Z Transform of this shifted function, start with the definition of the transform : Since the first three elements (k=0, 1, 2) of the transform are zero, we can start the summation at k=3. In general, a time delay of n samples, results in multiplication by z-n in the z domain.
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What are the properties of Z transform?
Linearity. ...
Time Shifting. ...
Time Expansion (Scaling) ...
Convolution. ...
Time Difference. ...
Time Accumulation. ...
Time Reversal. ...
Scaling in Z- domain.
Full answer in: fourier.eng.hmc.edu
What is the significance of region of convergence in Z transform?
Region of convergence ( ROC ) is the region ( regions ) where the z - transform X( z )or H( z ) converges. ROC allows us to determine the inverse z – transform uniquely. First let's consider some examples. The unit sample δ(n)has z - transform 1 , hence ROC is all the z plane . Jul 5, 2009
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What is transformation in DSP?
The Bilinear transform is a mathematical relationship which can be used to convert the transfer function of a particular filter in the complex Laplace domain into the z-domain, and vice-versa.
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