Consider a linear, time-invariant, continuous-time system.a) Since the impulse response of the system is given as ℎ (?) = ? (?) - ? (? - ?), calculate the frequency response of the system (??).b) Write the Fourier series representation by finding the fundamental frequency of the input signal ? (?) = cos (4000??).c) Show that the output signal of the system (?) can be obtained by using the Fourier series coefficients of the input signal (?) and the frequency response of the system ? (??).d) What is the fundamental frequency of the ? (?) sign? Explain why.e) Write the Fourier series representation of the sign ? (?). Consider a linear, time-invariant, continuous-time system.a) Since the impulse response of the system is given as h (t) = & (t) - 8(t - T), calculate the frequency response of the system (jw).b) Write the Fourier series representation by finding the fundamentalfrequency of the input signal x (t) = cos (4000nt).c) Show that the output signal of the system (t) can be obtained byusing the Fourier series coefficients of the input signal (t) and thefrequency response of the system H (jw).d) What is the fundamental frequency of the y (t) sign? Explain why.e) Write the Fourier series representation of the sign y (t).

Since the given input is a periodic signal, output is also a same periodic signal with modified…

Answered: Consider a linear, time-invariant,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Consider a linear, time-invariant, continuous-time system.
a) Since the impulse response of the system is given as ℎ (?) = ? (?) - ? (? - ?), calculate the frequency response of the system (??).
b) Write the Fourier series representation by finding the fundamental frequency of the input signal ? (?) = cos (4000??).
c) Show that the output signal of the system (?) can be obtained by using the Fourier series coefficients of the input signal (?) and the frequency response of the system ? (??).
d) What is the fundamental frequency of the ? (?) sign? Explain why.
e) Write the Fourier series representation of the sign ? (?).

Consider a linear, time-invariant, continuous-time system.
a) Since the impulse response of the system is given as h (t) = & (t) - 8
(t - T), calculate the frequency response of the system (jw).
b) Write the Fourier series representation by finding the fundamental
frequency of the input signal x (t) = cos (4000nt).
c) Show that the output signal of the system (t) can be obtained by
using the Fourier series coefficients of the input signal (t) and the
frequency response of the system H (jw).
d) What is the fundamental frequency of the y (t) sign? Explain why.
e) Write the Fourier series representation of the sign y (t).

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