Question

5. A system is known whose input-output relationship is determined by the following difference equation: y(n)--T(n-1) = x(n) +-x(n-1) Find the system function H(z) and plot the pole-zero plot

Answer 1

use z-transform directly, y[n] will be transformed Y(z) in the z plane. Typically, y is the output signal and z is input signal.

Also z transform rules are as below.

y[n-1] is transformed to Y(z)* z^-1

y[n-2] is transformed to Y(z)* z^-2

Using the same rule for above difference equation we get,

Pole is the z value for which denominator becomes zero.

Zero is the z value for which numerator of the transfer function becomes zero.

To find zero 27 To tind poe, 1-1 2 2 2 21召っ 7名

pole is plotted as cross and zero is plotted as a circle as shown below

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2. 0