Problem 4 There are three causal systems with the following difference equations labeled (1), (2), and (3): 4y[n]+2y[n 1] = 3x[n]−13x[n−1]+4x[n-2] (1) 3y[n]-4y[n-1]+y[n−2] = 2x[n] + x[n−1] (2) 15y[n]+2y[n-1]−y[n−2] = 30x[n]+15x[n-1] (3) a. Find the expression for the transfer function of the all three systems, H₁(z), H₂(z), H₂(z) and plot their pole-zero graphs, and determine whether each of them is BIBO stable or not. b. Two of these Filters are then connected in cascade, so that the cascaded system is BIBO stable. Select the two systems that will result in a BIBO stable system when connected in cascade. Find the expression for this system's transfer function, and then plot its pole-zero graph. c. Find the difference equation of the cascaded system.
Problem 4 There are three causal systems with the following difference equations labeled (1), (2), and (3): 4y[n]+2y[n 1] = 3x[n]−13x[n−1]+4x[n-2] (1) 3y[n]-4y[n-1]+y[n−2] = 2x[n] + x[n−1] (2) 15y[n]+2y[n-1]−y[n−2] = 30x[n]+15x[n-1] (3) a. Find the expression for the transfer function of the all three systems, H₁(z), H₂(z), H₂(z) and plot their pole-zero graphs, and determine whether each of them is BIBO stable or not. b. Two of these Filters are then connected in cascade, so that the cascaded system is BIBO stable. Select the two systems that will result in a BIBO stable system when connected in cascade. Find the expression for this system's transfer function, and then plot its pole-zero graph. c. Find the difference equation of the cascaded system.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Problem 4
There are three causal systems with the following difference equations labeled (1), (2),
and (3):
4y[n]+2y[n 1] = 3x[n]-13x[n-1]+4x[n-2] (1)
3y[n]-4y[n-1]+y[n-2] = 2x[n] + x[n-1] (2)
15y[n]+2y[n 1]-y[n-2] = 30x[n]+15x[n-1] (3)
a. Find the expression for the transfer function of the all three systems, H,(z), H₂(z),
H₂(z) and plot their pole-zero graphs, and determine whether each of them is BIBO
stable or not.
b. Two of these Filters are then connected in cascade, so that the cascaded system is
BIBO stable. Select the two systems that will result in a BIBO stable system when
connected in cascade. Find the expression for this system's transfer function, and then
plot its pole-zero graph.
c. Find the difference equation of the cascaded system.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb369eb62-11fd-4878-881a-f7bb242e6acd%2F91335eda-de76-48c3-9512-ecfbbe538a10%2Fwwsx7g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 4
There are three causal systems with the following difference equations labeled (1), (2),
and (3):
4y[n]+2y[n 1] = 3x[n]-13x[n-1]+4x[n-2] (1)
3y[n]-4y[n-1]+y[n-2] = 2x[n] + x[n-1] (2)
15y[n]+2y[n 1]-y[n-2] = 30x[n]+15x[n-1] (3)
a. Find the expression for the transfer function of the all three systems, H,(z), H₂(z),
H₂(z) and plot their pole-zero graphs, and determine whether each of them is BIBO
stable or not.
b. Two of these Filters are then connected in cascade, so that the cascaded system is
BIBO stable. Select the two systems that will result in a BIBO stable system when
connected in cascade. Find the expression for this system's transfer function, and then
plot its pole-zero graph.
c. Find the difference equation of the cascaded system.
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