This document contains 5 problems related to digital signal processing. Problem 1 involves designing a 25-tap finite impulse response (FIR) filter to approximate an ideal bandpass frequency response and plotting the filter's magnitude and phase response. Problem 2 repeats this for a bandstop filter. Problem 3 converts an analog filter to a digital infinite impulse response (IIR) filter using impulse invariance. Problem 4 does the same conversion using bilinear transformation. Problem 5 compares the two conversion methods and discusses their restrictions.

1. Helwan University
Faculty of Engineering
Department of Electronics, Communications & Computer
ELC 9421 Digital Signal Processing - Spring 2017
Sheet Seven
‫ن‬ ‫ا‬ ‫و‬ ‫ل‬ ‫ح‬ ‫ب‬ ‫ة‬ ‫س‬ ‫د‬ ‫ن‬ ‫ه‬ ‫ل‬ ‫ا‬ ‫ة‬ ‫ي‬ ‫ل‬ ‫ك‬–‫ن‬ ‫ا‬ ‫و‬ ‫ل‬ ‫ح‬ ‫ة‬ ‫ع‬ ‫م‬ ‫ا‬ ‫ج‬ Page 1 of 1
1) Design an FIR filter phase, digital filter approximating the ideal frequency
response
H(w) = {
1, |w| ≤ π/6
0, π/6 ≤ |w| ≤ π
a) Determine the coefficients of a 25-tap filter based on the window method
with a rectangular window.
b) Determine and plot the magnitude and phase response of the filter.
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2) Repeat problem (1) for a Band-Stop filter having the ideal response
H(w) = {
1, |w| ≤ π/6
0, π/6 ≤ |w| ≤ π/3
1, π/3 ≤ |w| ≤ π
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3) Consider a continuous time system with system function
𝐻(𝑠) =
𝑠 + 0.1
(𝑠 + 0.1)2 + 9
Find the digital IIR filter by means of the impulse invariance method. Find the
poles & zeros of such filter.
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4) convert the analog filter with system function
𝐻(𝑠) =
𝑠 + 0.1
(𝑠 + 0.1)2 + 16
Into a digital filter by means of the bilinear transformation (𝑇 = 1/2). Find the
poles and zeros of that filter. Plot |𝐻 (𝑗𝑤)|
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5) Compare between the transformation in problem (3) & (4). Mention the
restrictions of using the two methods.
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Best Wishes,
Prof. Elsayed. M. Saad
Dr. Amr E. Mohamed