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3) Consider a casual LTI system S whose input x[n] and output y[n] related by the difference equation 2y[n] – y[n – 1] + y[n – 3] = x[n] – 5x[n – 4]. a) Verify that S may be considered a cascade connection of two casual LTI systems S, and S2 with the following input-output relationship: Sa: 2yı[n] = x1[n] - 5x1[n – 4], %3D S2: Y2[n] = }ya[n – 1] -y,[n – 3] + xz[n]. b) Draw a block diagram representation of S1. Draw a block diagram representation of S2. c)

3) Consider a casual LTI system S whose input x[n] and output y[n] related by the difference equation 2y[n] – y[n – 1] + y[n – 3] = x[n] – 5x[n – 4]. a) Verify that S may be considered a cascade connection of two casual LTI systems S, and S2 with the following input-output relationship: Sa: 2yı[n] = x1[n] - 5x1[n – 4], %3D S2: Y2[n] = }ya[n – 1] -y,[n – 3] + xz[n]. b) Draw a block diagram representation of S1. Draw a block diagram representation of S2. c)

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
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3) Consider a casual LTI system S whose input x[n] and output y[n] related by the difference equation 2y[n] – y[n – 1] + y[n – 3] = x[n] – 5x[n – 4]. a) Verify that S may be considered a cascade connection of two casual LTI systems S, and S2 with the following input-output relationship: Sz: 2y,[n] = x,[n] – 5x1[n – 4], S2: Ya[n] = y2[n – 1] -y½[n – 3] + x,[n]. b) Draw a block diagram representation of S1. c) Draw a block diagram representation of S2. d) Draw a block diagram representation of S as a cascade connection of the block diagram representation of S, followed by the block diagram representation of S2. e) Draw a block diagram representation of S as a cascade connection of the block diagram representation of S, followed by the block diagram representation of S1.
Transcribed Image Text:3) Consider a casual LTI system S whose input x[n] and output y[n] related by the difference equation 2y[n] – y[n – 1] + y[n – 3] = x[n] – 5x[n – 4]. a) Verify that S may be considered a cascade connection of two casual LTI systems S, and S2 with the following input-output relationship: Sz: 2y,[n] = x,[n] – 5x1[n – 4], S2: Ya[n] = y2[n – 1] -y½[n – 3] + x,[n]. b) Draw a block diagram representation of S1. c) Draw a block diagram representation of S2. d) Draw a block diagram representation of S as a cascade connection of the block diagram representation of S, followed by the block diagram representation of S2. e) Draw a block diagram representation of S as a cascade connection of the block diagram representation of S, followed by the block diagram representation of S1.
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