This document discusses discrete time system analysis and the Z-transform. It introduces the Z-transform as the discrete-time counterpart of the Laplace transform, which is used to represent and analyze linear time-invariant discrete-time systems. The Z-transform is used to convert difference equations in the time domain to algebraic equations in the Z-domain, which can then be more easily solved and converted back to the time domain using the inverse Z-transform. The document also notes that the Z-transform generalizes the discrete-time Fourier transform and is well-suited for solving difference equations with initial conditions.

1. UNIT – II
DISCRETE TIME SYSTEM ANALYSIS
DISCRETE TIME SIGNAL
PROCESSING
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2. UNIT II DISCRETE TIME SYSTEM
ANALYSIS
 Z-transform and its properties - Inverse Z-transforms
- Difference equation - Analysis of linear time
invarient system in Z domain - Stability analysis,
frequency response - Linear and circular convolution.
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3. Z-transform
 A linear time-invariant discrete-time system is represented by
difference equations. The direct solution of higher order difference
equations is quite tedious and time consuming. So usually they are
solved by indirect methods.
 The Z-transform plays the same role for discrete-time systems as
that played by Laplace transform for continuous-time systems.
The Z-transform is the discrete-time counterpart of the Laplace
transform. It is the Laplace transform of the discretized version of
the continuous-time signal x(t).
 To solve the difference equations which are in time domain, they
are converted first into algebraic equations in z-domain using Z-
transform, the algebraic equations are manipulated in z-domain
and the result obtained is converted back into time domain using
inverse Z-transform.
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4.  The Z-transform has the advantage that it is a simple and
systematic method and the complete solution can be obtained
in one step and the initial conditions can be introduced in the
beginning of the process itself. The Z-transform plays an
important role in the analysis and representation of discrete-
time Linear Shift Invariant (LSI) systems.
 It is the generalization of the Discrete-Time Fourier
Transform (DTFT). The Z-transform may be one-sided
(unilateral) or two-sided (bilateral). It is the one-sided or
unilateral Z-transform that is more useful, because we mostly
deal with causal sequences. Further, it is eminently suited for
solving difference equations with initial conditions.
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10. ROC
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19. Thank You
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