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Consider the first-order discrete-time system given by the difference equation: ynayn-1]+x[n] The impulse response is the output of this system when the input is set to the unit pulse, so that a[n] - [n]. Similarly, the step response is the output of this system when the input is set to the unit step sequence, such that a[n] = u[n]. Calculate the impulse response and step response for the system given Assume the system is causal so that for n <0 both a[n] =0 and y[n] = 0. -

Consider the first-order discrete-time system given by the difference equation: ynayn-1]+x[n] The impulse response is the output of this system when the input is set to the unit pulse, so that a[n] - [n]. Similarly, the step response is the output of this system when the input is set to the unit step sequence, such that a[n] = u[n]. Calculate the impulse response and step response for the system given Assume the system is causal so that for n <0 both a[n] =0 and y[n] = 0. -

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Consider the first-order discrete-time system given by the difference equation: y[n] = -ay[n-1]+xn] The impulse response is the output of this system when the input is set to the unit pulse, so that a[n] = [n]. Similarly, the step response is the output of this system when the input is set to the unit step sequence, such that a[n] = u[n]. Calculate the impulse response and step response for the system given Assume the system is causal so that for n < 0 both x[n] = 0 and y[n] = 0. HINTS. There are a variety of approaches to solving for the step response and impulse response. Perhaps the easiest approach is to calculate the step response first, and then note the relationship between the step response and the impulse response. These are: 72 u[n] = Σ 6[m], _and_§[n] = u[n] — u[n — 1] m=-00 - The particular solution then for the step response is easier to determine than the particular solution for the impulse response.
Transcribed Image Text:Consider the first-order discrete-time system given by the difference equation: y[n] = -ay[n-1]+xn] The impulse response is the output of this system when the input is set to the unit pulse, so that a[n] = [n]. Similarly, the step response is the output of this system when the input is set to the unit step sequence, such that a[n] = u[n]. Calculate the impulse response and step response for the system given Assume the system is causal so that for n < 0 both x[n] = 0 and y[n] = 0. HINTS. There are a variety of approaches to solving for the step response and impulse response. Perhaps the easiest approach is to calculate the step response first, and then note the relationship between the step response and the impulse response. These are: 72 u[n] = Σ 6[m], _and_§[n] = u[n] — u[n — 1] m=-00 - The particular solution then for the step response is easier to determine than the particular solution for the impulse response.
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