(a) Using Fourier transform, find the output y(t) for the input x(t) = etu(t) for the continuous-time LTI system described by: PIZ dy(t) + 2y(1) =x(t) dt
(a) Using Fourier transform, find the output y(t) for the input x(t) = etu(t) for the continuous-time LTI system described by: PIZ dy(t) + 2y(1) =x(t) dt
Introductory Circuit Analysis (13th Edition)
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Question
![(a)
Using Fourier transform, find the output y(t) for the input x(t) = etu(t) for the
continuous-time LTI system described by:
dy(t)
+ 2 y(t) = x(t)
plZ
dt
(b)
A causal discrete-time LTI system, having input x[n] and output y[n], has
impulse response h[n] given by:
SOve
A[n] = [2(})" - (})"]«[n])
Where u[n] represents the unit step function.
Using the Discrete-time Fourier Transform,
(i)
determine the frequency response of the system.
(ii)
express the dynamics of the system in terms of a differential equation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F792113aa-8952-4be0-b0a2-7328b30572ad%2F3dabd746-c3db-433d-9c93-25c1cb855591%2Fazgt4o7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a)
Using Fourier transform, find the output y(t) for the input x(t) = etu(t) for the
continuous-time LTI system described by:
dy(t)
+ 2 y(t) = x(t)
plZ
dt
(b)
A causal discrete-time LTI system, having input x[n] and output y[n], has
impulse response h[n] given by:
SOve
A[n] = [2(})" - (})"]«[n])
Where u[n] represents the unit step function.
Using the Discrete-time Fourier Transform,
(i)
determine the frequency response of the system.
(ii)
express the dynamics of the system in terms of a differential equation.
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