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The output of a system can be calculated in either the time-domain (as a convolution process between the input signal and the system impulse response) or in the frequency-domain (as a multiplication process between the Fourier transform of the input signal and the frequency response of the system) i.e.: x (t) y(t)= x(t)* h(t) h(t) X(ƒ) H(ƒ) Y(ƒ)=X(ƒ)H(ƒ) For the following two systems and input signals, calculate and sketch (where appropriate) the following: i. ii. iii. iv. The Fourier transform of the input signal, x(t). The Frequency response of the system, H(f). The Fourier transform of the output signal, y(t). Calculate the single-sided bandwidth of the output signal.

The output of a system can be calculated in either the time-domain (as a convolution process between the input signal and the system impulse response) or in the frequency-domain (as a multiplication process between the Fourier transform of the input signal and the frequency response of the system) i.e.: x (t) y(t)= x(t)* h(t) h(t) X(ƒ) H(ƒ) Y(ƒ)=X(ƒ)H(ƒ) For the following two systems and input signals, calculate and sketch (where appropriate) the following: i. ii. iii. iv. The Fourier transform of the input signal, x(t). The Frequency response of the system, H(f). The Fourier transform of the output signal, y(t). Calculate the single-sided bandwidth of the output signal.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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The output of a system can be calculated in either the time-domain (as a convolution process between the input signal and the system impulse response) or in the frequency-domain (as a multiplication process between the Fourier transform of the input signal and the frequency response of the system) i.e.: x(t) h(1) X(f) H(f) Y(ƒ)= X(ƒ)H(f) For the following two systems and input signals, calculate and sketch (where appropriate) the following: i. ii. iii. iv. a. The Fourier transform of the input signal, x(t). The Frequency response of the system, H(f). The Fourier transform of the output signal, y(t). Calculate the single-sided bandwidth of the output signal. | y(t) = x(t)* h(t) System 1: Assume the input x(1) to the system is mathematically given as: -5x105 ≤t≤5x10-5 elsewhere x(t) = 10,0001100001 (t)= [10,000, 0, And the frequency response of the system H() is mathematically given as: H(f)= II 20,000 (f)={ 1, 0, -10,000 ≤ f≤ 10,000 elsewhere
Transcribed Image Text:The output of a system can be calculated in either the time-domain (as a convolution process between the input signal and the system impulse response) or in the frequency-domain (as a multiplication process between the Fourier transform of the input signal and the frequency response of the system) i.e.: x(t) h(1) X(f) H(f) Y(ƒ)= X(ƒ)H(f) For the following two systems and input signals, calculate and sketch (where appropriate) the following: i. ii. iii. iv. a. The Fourier transform of the input signal, x(t). The Frequency response of the system, H(f). The Fourier transform of the output signal, y(t). Calculate the single-sided bandwidth of the output signal. | y(t) = x(t)* h(t) System 1: Assume the input x(1) to the system is mathematically given as: -5x105 ≤t≤5x10-5 elsewhere x(t) = 10,0001100001 (t)= [10,000, 0, And the frequency response of the system H() is mathematically given as: H(f)= II 20,000 (f)={ 1, 0, -10,000 ≤ f≤ 10,000 elsewhere
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