**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

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 :

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 x

_{1}(n) * x_{2}(n) ↔ X_{1}(Z) * X_{2}(Z) Read more
Z transform stability :

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

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

The equation in partial expansion form as follows : X(Z) / Z = A

_{1}/ Z - P_{1}+ A_{2}/ Z - P_{2}+ .............+ A_{N}/ Z - P_{N }Read more
X(Z) = 1- 1/2 Z

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

^{-1}/ 1- 1/4 Z^{-2 }Read moreInverse Z transform using long division method

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