Concept explainers
(a)
Find the Fourier transform of
(a)
Answer to Problem 23P
The Fourier transform of
Explanation of Solution
Given data:
Formula used:
Consider the general form of Fourier transform of
Consider the scaling property of the Fourier transform.
Calculation:
Find
Conclusion:
Thus, the Fourier transform of
(b)
Find the Fourier transform of
(b)
Answer to Problem 23P
The Fourier transform of
Explanation of Solution
Formula used:
Consider the Time shift property of the Fourier transform.
Consider the scaling property of the Fourier transform.
Calculation:
Find
Conclusion:
Thus, the Fourier transform of
(c)
Find the Fourier transform of
(c)
Answer to Problem 23P
The Fourier transform of
Explanation of Solution
Formula used:
Consider the Modulation property of the Fourier transform.
Calculation:
Find
Conclusion:
Thus, the Fourier transform of
(d)
Find the Fourier transform of
(d)
Answer to Problem 23P
The Fourier transform of
Explanation of Solution
Formula used:
Consider the Time differentiation property of the Fourier transform.
Calculation:
Find
Conclusion:
Thus, the Fourier transform of
(e)
Find the Fourier transform of
(e)
Answer to Problem 23P
The Fourier transform of
Explanation of Solution
Formula used:
Consider the Time integration property of the Fourier transform.
Calculation
Find
Conclusion:
Thus, the Fourier transform of
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Chapter 18 Solutions
Fundamentals of Electric Circuits
- The Fourier transform of the function f(t) = e²u(-t+2) is: Select one: O F(w) = O F(w): O F(w) = O F(w) = e²(2-ju) 2-ju e²-to 2-jw e²(2-ju) 2+jw e²(2+) 2-jwarrow_forwardUse identities plus known transform pairs to find the inverse Fourier transforms of the following functions. 1. f (ω) = cos (2ω) 2. f (ω) = 1/25+(w-1)2arrow_forwardFind the Fourier transform of the following signal shown in Figure (2), using differentia property. j(t) th Figure (2) 3 tarrow_forward
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- Prove the fourier transforms relationship for the following below: d/dt[x(t)] -----> j2πfX(f)arrow_forwardFind the inverse transforms of the following functions: F₁(0) = 100 jo+100 F₂(0) = F3(0) = 500 (jo+100) (jo+500) 500 jo (jo+10) jo+100) Find the Fourier transforms fi(t) = 2u(t) - 2 f₂(t) = 2 sgn(t) - 2u(t) f3(t) = - sgn(t) - 1 f(t) = 10sin[2(t-5)] f(t) = 3ej4t sgn(t) 10,000 F₁(00) jo (jo+100)(jo+1000) F₂(0) = -10 0² jo (jo+20) (jo+40) of the following waveforms: fi(t) = ¹(e²te-1²t) + 10(e²t+e-2t) f₂(t) = ¹0(sin 5t)arrow_forwardFind fourier transform of the following equation. 1.f(t)=sin3wt Check whether the following system are causal or non causal. 1.x(t)+x(t-3) 2.x(t+1)+x(t-2) 3.3x(n+4)arrow_forward
- The question asks "to find the Fourier Transform". You only need to answer question b. Thanks!! Only barrow_forwardFind the inverse Fourier transform of 4T A(w). (a) sinc (2t) (b) sinc²(t) (c) sinc (t/2) (d) sinc²(t/4) O () Moving to another question will save this response. 2Type here to search Coparrow_forwardFind the Fourier Transform of the following. A. (t) = 4e2t+2u(t-1)arrow_forward
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