### Z transform

Basics :

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

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

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

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

n=∞
∑   |h(n)| <  ∞   Read more
n=-∞

IZT :

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

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

Determine IZT of the following :
X(Z) = 1- 1/2 Z-1 / 1- 1/4 Z-2

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