For every integer n, evaluate the output y[n] of the convolution: y[n] = h[n] * x[n] where x[n] (0.5)"u[n], h[n] = u[3-n]. =
For every integer n, evaluate the output y[n] of the convolution: y[n] = h[n] * x[n] where x[n] (0.5)"u[n], h[n] = u[3-n]. =
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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![For every integer \( n \), evaluate the output \( y[n] \) of the convolution:
\[
y[n] = h[n] * x[n]
\]
where \( x[n] = (0.5)^n u[n] \), \( h[n] = u[3-n] \).
**Explanation:**
- \( x[n] \) is a discrete-time signal defined as \( (0.5)^n \) multiplied by the unit step function \( u[n] \).
- \( h[n] \) is also defined using a unit step function but with a shift, \( u[3-n] \), which effectively defines a reversed step starting at \( n = 3 \).
- The operation \( y[n] = h[n] * x[n] \) represents the convolution of \( h[n] \) and \( x[n] \), a fundamental concept in signals and systems, used to analyze systems' responses to inputs.
Note: Convolution is a mathematical operation used to determine the output (response) of a linear time-invariant (LTI) system for a given input. The unit step function, \( u[n] \), is often used in signal processing to represent signals that "turn on" at a certain point.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F039207b8-632a-4dc4-a3c4-fd77b3c684b4%2F02eb0792-6600-4842-bba1-927cc22266b7%2Fnnqinqa_processed.png&w=3840&q=75)
Transcribed Image Text:For every integer \( n \), evaluate the output \( y[n] \) of the convolution:
\[
y[n] = h[n] * x[n]
\]
where \( x[n] = (0.5)^n u[n] \), \( h[n] = u[3-n] \).
**Explanation:**
- \( x[n] \) is a discrete-time signal defined as \( (0.5)^n \) multiplied by the unit step function \( u[n] \).
- \( h[n] \) is also defined using a unit step function but with a shift, \( u[3-n] \), which effectively defines a reversed step starting at \( n = 3 \).
- The operation \( y[n] = h[n] * x[n] \) represents the convolution of \( h[n] \) and \( x[n] \), a fundamental concept in signals and systems, used to analyze systems' responses to inputs.
Note: Convolution is a mathematical operation used to determine the output (response) of a linear time-invariant (LTI) system for a given input. The unit step function, \( u[n] \), is often used in signal processing to represent signals that "turn on" at a certain point.
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