Z transform

Basics : 

What is the Z transform?
The Z transform has a real and imaginary part like Fourier transform. A plot of imaginary part versus the real part is called a Z plane or complex Z plane. Read more

Application of z transform : 
1.Pole-zero description of discrete-time system 2. Analysis of linear discrete signal 3. Use to analysis digital filter Read more 

Advantages: 1. Z transform is used for the digital signal
2. Discrete-time signals and linear time-invariant (LTI) systems can be completely characterized using Z transform
Disadvantages: 1. Z transform cannot apply in continuous signal Read more

ROC :


Z transform ROC :

The ROC stands for the region of convergence of X(Z) is set for all the values of Z for which X(Z)  attains finite values. Every time when we find Z transform we must indicate its ROC. Read more

Z Transform example :
Find Z transform of  F[K] =Cos(ak) u[k] Read more

Properties and theorems of Z transform :

Properties of Z transform :
1. Linearity 2. Time shifting 3. Scaling 4. Time reversal Read more

            Z                                 Z
If  x(n) ↔ X (Z)  Then x (n-k) ↔ Z -k  X (Z)  Read more


If  x1(n) * x2(n) ↔ X1(Z)  * X2(Z)   Read more

Z transform stability :
A necessary and sufficient condition for the system to be BIBO stable is given as,

n=∞
∑   |h(n)| <  ∞   Read more
n=-∞

IZT :

Inverse Z transform :
Mathematically it can be represented as : 
x(n) = z-1 X(Z)
x(n) = Z-1 X(Z) Read more

Z transform partial fraction expansion
The equation in partial expansion form as follows :  X(Z) / Z =  A1 /  Z - P1  + A2 / Z - P2  + .............+   AN / Z - PN  Read more


Inverse z transform partial fraction expansion examples : 
Determine IZT of the following :
X(Z) = 1- 1/2 Z-1 / 1- 1/4 Z-2  Read more 


Inverse Z transform using long division method
While carrying out the long division method, always convert the given expression in the simplest form. Read more