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Using the sliding-tape algorithm, find c[n] = x[n] *g[n] for the signal below x[n] 5 g[n] 1

Using the sliding-tape algorithm, find c[n] = x[n] *g[n] for the signal below x[n] 5 g[n] 1

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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**Title: Using the Sliding-Tape Algorithm** **Objective:** To find \( c[n] = x[n] * g[n] \) for the given signals using the sliding-tape algorithm. **Signals Description:** 1. **Signal \( x[n] \):** - The graph shows a discrete-time signal starting at \( n = 0 \) and ending at \( n = 5 \). - The amplitude is 5 at each step from \( n = 0 \) to \( n = 5 \), resembling a rectangular pulse. - At \( n = 5 \), the signal drops to 0. 2. **Signal \( g[n] \):** - This graph represents a discrete-time impulse response. - It includes several impulses spaced at unit intervals. - Significant impulses are highlighted at \( n = -4, -3, -2, -1, 0, 1 \). - The impulse at \( n = 0 \) has a magnitude of 1; the magnitudes for other impulses are not specified. **Task Explanation:** - **Sliding-Tape Algorithm:** - A method used to perform convolution. - Involves sliding one signal over another and calculating overlap. - **Convolution \( c[n] = x[n] * g[n] \):** - The convolution operation combines two signals to produce a third signal, representing how the shape of one is modified by the other. **Solution Steps:** 1. Identify the range over which \( x[n] \) and \( g[n] \) will overlap. 2. Multiply each overlapping element and sum these products to obtain \( c[n] \) for each \( n \). 3. The result, \( c[n] \), reflects the combined effect of signals \( x[n] \) and \( g[n] \). This explanation and the graphs will help illustrate how the sliding-tape algorithm is applied to find the convolution of two discrete-time signals.
Transcribed Image Text:**Title: Using the Sliding-Tape Algorithm** **Objective:** To find \( c[n] = x[n] * g[n] \) for the given signals using the sliding-tape algorithm. **Signals Description:** 1. **Signal \( x[n] \):** - The graph shows a discrete-time signal starting at \( n = 0 \) and ending at \( n = 5 \). - The amplitude is 5 at each step from \( n = 0 \) to \( n = 5 \), resembling a rectangular pulse. - At \( n = 5 \), the signal drops to 0. 2. **Signal \( g[n] \):** - This graph represents a discrete-time impulse response. - It includes several impulses spaced at unit intervals. - Significant impulses are highlighted at \( n = -4, -3, -2, -1, 0, 1 \). - The impulse at \( n = 0 \) has a magnitude of 1; the magnitudes for other impulses are not specified. **Task Explanation:** - **Sliding-Tape Algorithm:** - A method used to perform convolution. - Involves sliding one signal over another and calculating overlap. - **Convolution \( c[n] = x[n] * g[n] \):** - The convolution operation combines two signals to produce a third signal, representing how the shape of one is modified by the other. **Solution Steps:** 1. Identify the range over which \( x[n] \) and \( g[n] \) will overlap. 2. Multiply each overlapping element and sum these products to obtain \( c[n] \) for each \( n \). 3. The result, \( c[n] \), reflects the combined effect of signals \( x[n] \) and \( g[n] \). This explanation and the graphs will help illustrate how the sliding-tape algorithm is applied to find the convolution of two discrete-time signals.
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