Determine the following

(i) The system transfer function H(z)

(ii) impulse response of the system h[n]

(iii) Step response of the system s[n].

Mumbai University > EXTC > Sem 4 > Signals and Systems

Marks : 10

Year : MAY 2015

(i) To determine the system transfer function H(z)

The given difference equation is

$y[n] =\dfrac 34 y[n - 1] – \dfrac18 y[n - 2] + x[n]$

Taking Z-transform of the difference equation

$Y(z) = \dfrac34 z^{-1} Y(z) - \dfrac18 z^{-2} Y(z) + X(z) \\ ∴[1 - \dfrac34 z^{-1} + \dfrac18 …