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In x(n) 12 H₁(z) x(n) ↓2 the input signal is upsampled by I = 2, then filtered by H₁(2), and then downsampled by D = 2. Provide an argument that shows whether or not it is possible to find H₂(z) in H₂(z) y(n) y(n) so that the two systems are equivalent. If you argue that it is possible to find such an H₂(2), express this H₂(z) in terms of H₁(z).

In x(n) 12 H₁(z) x(n) ↓2 the input signal is upsampled by I = 2, then filtered by H₁(2), and then downsampled by D = 2. Provide an argument that shows whether or not it is possible to find H₂(z) in H₂(z) y(n) y(n) so that the two systems are equivalent. If you argue that it is possible to find such an H₂(2), express this H₂(z) in terms of H₁(z).

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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In x(n) 12 H₁(z) x(n) ↓2 the input signal is upsampled by I = 2, then filtered by H₁(2), and then downsampled by D = 2. Provide an argument that shows whether or not it is possible to find H₂(z) in H₂(z) y(n) y (n) so that the two systems are equivalent. If you argue that it is possible to find such an H₂(z), express this H₂(z) in terms of H₁(z).
Transcribed Image Text:In x(n) 12 H₁(z) x(n) ↓2 the input signal is upsampled by I = 2, then filtered by H₁(2), and then downsampled by D = 2. Provide an argument that shows whether or not it is possible to find H₂(z) in H₂(z) y(n) y (n) so that the two systems are equivalent. If you argue that it is possible to find such an H₂(z), express this H₂(z) in terms of H₁(z).
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