Pass band ripple : ≤ 1 dB

Pass band edge : 4KHz

Stop band attenuation: 40dB

Stop edge : 8KHz

Sampling Rate : 24KHz

Use bilinear transformation.

Mumbai University > EXTC > Sem 6 > Discrete Time Signal Processing

Marks : 10

Year : DEC 2015

Bilinear method:

(1)calculate $Ω_p , Ω_s, \\ Ω_p= \dfrac 2T \tan⁡(\dfrac {w_p}2) \\ Ω_p= \dfrac 2{1/2400} \tan⁡(\dfrac {π/3}2) \\ Ω_p=27712.8 $

(2)calculate Filter order N

$N=\dfrac {\log⁡[\dfrac {10^{A_s/10}-1}{10^{A_s/10}-1}]} {\log⁡[\dfrac {Ω_s}{Ω_p} ]} \\ N=9.61 \\ Let N = 10$

(3)Calculate Analog filter $Ω_c$

$Ω_c = \dfrac {Ω_p}{(10^{A_{p/10}}-1)^{1/2N}} =29649.7 \space rad/sec$

(4)calculate digital Filter $W_c$

$Ω_c= \dfrac 2T \tan⁡(\dfrac {W_c}2) \\ \dfrac {Ω_c T}2= \tan⁡(\dfrac {W_c}2) \\ W_C=2 \tan^{-1}⁡(\dfrac {Ω_c T}2) \\ W_C=1.106 \text {radian}$