
we need help ? a. Find the Fourier transform of: X(t) = 2e- u(t)* 8(t -...
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Determine Fourier Transform of f(t) = u(t – 2) + 8(t – 6)? e-j2w te-j6w -j2w e-jów (x + 70(w))e=120 (a + 78(w)ezw +e-jou Gas - 78(a)e2 te-jow
Find the inverse Fourier Transform of H(jω) shown below:
6(3+j2w) H(W) = (1 + iw)(4 + jw)(2 + jw) Answer: h(t) = (2e-+ 3e-2t – 5e-4t)u(t)
Determine Fourier Transform of f(t) = u(t - 2) + 8(t - 6) Useful Formula: Fourier Transform: F[f(t)] = F(w) sof(t)e-jw dt Inverse Fourier Transform: F-1[F(w)] = f (t) = 24., F(w)ejwidw Time Transformation property of Fourier Transform: f(at – to). FC)e=itoch Laplace Transform: L[f(t)] = F(s) = $© f(t)e-st dt Shifting property: L[f(t – to)u(t – to)] = e-toSF(s) e [tuce) = 1 and c [u(e) = )
Bonus Question: Determine the Fourier Transform using the Fourier Transform integral for x(t) and then answer (b). (a) x(t) = 8(t) -e-tu(t) (b) Plot the magnitude of the Fourier Spectrum. Useful Formula: Fourier Transform: F[f(t)] = F(w) sof(t)e-jw dt Inverse Fourier Transform: F-1[F(w)] = f (t) = 24., F(w)ejwidw Time Transformation property of Fourier Transform: f(at – to). FC)e=itoch Laplace Transform: L[f(t)] = F(s) = $© f(t)e-st dt Shifting property: L[f(t – to)u(t – to)] = e-toSF(s) e [tuce) =...
Determine Laplace Transform of 8(t) = u(t – 2)u(t – 3) [hint: {[u(t)] :)] = :) Useful Formula: Fourier Transform: F[f(t)] = F(w) sof(t)e-jw dt Inverse Fourier Transform: F-1[F(w)] = f (t) = 24., F(w)ejwidw Time Transformation property of Fourier Transform: f(at – to). FC)e=itoch Laplace Transform: L[f(t)] = F(s) = $© f(t)e-st dt Shifting property: L[f(t – to)u(t – to)] = e-toSF(s) e [tuce) = 1 and c [u(e) = )
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What is the Inverse Fourier transform of Your answer should be expressed as a function of t using the correct syntax. Inverse FT. is f(t) = Skipped F(u)-(15ru2 +4ιτω4)sgn(a)? Find the Inverse Fourier transform of: F(u)--8πΗ(w+5)-H(w-5) e- Your answer should be expressed as a function of t using the correct syntax. Inverse F.T. is ft)Skipped 8iu Find the Inverse Fourier transform of: F(w) 16 πυ) sgn(w)e-20 Your answer should be expressed as a function of t using...
1. Use the Fourier Transform to solve the following problem with W1 21 (a) Find the Fourier Transform of u by applying F to the equation and initial condition; denote this function U(w, t). (b) Find u u(z, t) by taking the inverse transform of the U(w, t) you found in part (a).
1. Use the Fourier Transform to solve the following problem with W1 21 (a) Find the Fourier Transform of u by applying F to the equation and...
Determine the system response y(t) for h(t)=u(t)+u(t-2) and x(t)=u(t). [Hint: use Laplace Transform multiplication: L[x(t)h(t)) = x(s)H(s). Useful Formula: Fourier Transform: F[f(t)] = F(w) sof(t)e-jw dt Inverse Fourier Transform: F-1[F(w)] = f (t) = 24., F(w)ejwidw Time Transformation property of Fourier Transform: f(at – to). FC)e=itoch Laplace Transform: L[f(t)] = F(s) = $© f(t)e-st dt Shifting property: L[f(t – to)u(t – to)] = e-toSF(s) e [tuce) = 1 and c [u(e) = )
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Determine the Fourier Transform using the Fourier Transform integral for x(t) and then answer (b). (a) x(t) = (t)-e-fu(t) (b) Plot the magnitude of the Fourier Spectrum. 0 o Paragraph BIU ... AJ </>
Question 13 (2 marks) Attempt 1 ,2/144-aw Find the Inverse Fourier transform of: Te-v F(u)--3 Your answer should be expressed as a function of t using the correct syntax. Inverse F.T. is f(t)- Skipped a Screen Shot 2019-05-17 at 2.07.40 AM Search Question 14 (2 marks) Attempt 1 Find the inverse Fourier transform of: F(w-5 π w sgn(w) e-Tw Your answer should be expressed as a function of t using the correct syntax. Inverse F.T. is f(t)- Skipped Question 15...