1. The impulse response of a causal system is: h(t) = A cos(wt) e-t/u(t) where u(t) is the Heaviside step function. The response is measured experimentally with a sampling interval of T. a. Write an expression for the sampled impulse response h[n]. b. Calculate the z transform of h[n] and write an expression for H[z]. Use the tables provided below as necessary. c. Does the system have an infinite impulse response (IIR) or finite impulse response (FIR)? Justify your answer.
1. The impulse response of a causal system is: h(t) = A cos(wt) e-t/u(t) where u(t) is the Heaviside step function. The response is measured experimentally with a sampling interval of T. a. Write an expression for the sampled impulse response h[n]. b. Calculate the z transform of h[n] and write an expression for H[z]. Use the tables provided below as necessary. c. Does the system have an infinite impulse response (IIR) or finite impulse response (FIR)? Justify your answer.
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![1. The impulse response of a causal system is:
h(t) = A cos(wt) e¯¹/¹u(t)
where u(t) is the Heaviside step function. The response is measured experimentally with a
sampling interval of T.
a. Write an expression for the sampled impulse response h[n].
b. Calculate the z transform of h[n] and write an expression for H[z]. Use the tables
provided below as necessary.
c.
Does the system have an infinite impulse response (IIR) or finite impulse response
(FIR)? Justify your answer.
d.
What is the DC gain of H[z]?
e. Write a difference equation that describes the output y[n] in terms of input x[n].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8be12032-d26f-4088-913e-abb4eb227e0d%2F8b759a16-0f55-4d1a-9dc0-5af0a6de57d6%2Fpfh716_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. The impulse response of a causal system is:
h(t) = A cos(wt) e¯¹/¹u(t)
where u(t) is the Heaviside step function. The response is measured experimentally with a
sampling interval of T.
a. Write an expression for the sampled impulse response h[n].
b. Calculate the z transform of h[n] and write an expression for H[z]. Use the tables
provided below as necessary.
c.
Does the system have an infinite impulse response (IIR) or finite impulse response
(FIR)? Justify your answer.
d.
What is the DC gain of H[z]?
e. Write a difference equation that describes the output y[n] in terms of input x[n].
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