Suppose that System #1 is a seven-point running average filter, n<0 { 1/7 n = 0, 1, 2, 3, 4, 5, 6 n> 6 h₁ [n] = And System #2 is described by the difference equation y₂[n] = y₁[n] — yı[n − 1] We can find the impulse response of the overall system, by first finding the impulse response of the first system and then use that response as the input to the second system. a) Determine the filter coefficients of System #1, and also for System #2. b) When the input signal x[n] is an impulse, 8[n], determine the signal y₁ [n] and make a plot. c) Determine the impulse response of the overall cascade system, i.e. find y[n] when x[n] = 8[n]. Take advantage of the fact that you already know the output of System #1, y₁ [n], when its input is an impulse.

Introductory Circuit Analysis (13th Edition)
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Exercise 2: The following diagram depicts a cascade connection of two linear time-
invariant systems, i.e. the output of the first system is the input to the second system,
and the overall output is the output of the second system.
x[n]
yı[n]
LTI
System #1
h₁[n]
LTI
System #2
h₂[n]
y[n]
Transcribed Image Text:Exercise 2: The following diagram depicts a cascade connection of two linear time- invariant systems, i.e. the output of the first system is the input to the second system, and the overall output is the output of the second system. x[n] yı[n] LTI System #1 h₁[n] LTI System #2 h₂[n] y[n]
Suppose that System #1 is a seven-point running average filter,
n<0
{
1/7 n = 0, 1, 2, 3, 4, 5, 6
n> 6
h₁ [n] =
And System #2 is described by the difference equation
y₂[n] = y₁[n] — yı[n − 1]
We can find the impulse response of the overall system, by first finding the impulse
response of the first system and then use that response as the input to the second
system.
a) Determine the filter coefficients of System #1, and also for System #2.
b) When the input signal x[n] is an impulse, 8[n], determine the signal
y₁ [n] and make a plot.
c) Determine the impulse response of the overall cascade system, i.e. find y[n] when
x[n] = 8[n]. Take advantage of the fact that you already know the output of System
#1, y₁ [n], when its input is an impulse.
Transcribed Image Text:Suppose that System #1 is a seven-point running average filter, n<0 { 1/7 n = 0, 1, 2, 3, 4, 5, 6 n> 6 h₁ [n] = And System #2 is described by the difference equation y₂[n] = y₁[n] — yı[n − 1] We can find the impulse response of the overall system, by first finding the impulse response of the first system and then use that response as the input to the second system. a) Determine the filter coefficients of System #1, and also for System #2. b) When the input signal x[n] is an impulse, 8[n], determine the signal y₁ [n] and make a plot. c) Determine the impulse response of the overall cascade system, i.e. find y[n] when x[n] = 8[n]. Take advantage of the fact that you already know the output of System #1, y₁ [n], when its input is an impulse.
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