If f(t) = ejwot. What is the Fourier Transform of f(2t - 1). Useful Formula: Fourier...
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) = )
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) = ) Using the convolution property of Fourier Transform to find the following convolution: sinc(t) * sinc (4t) [Hint: sinc(t) or rect(w/2)] TC .
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) = )
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) = )
الناز Wo e 2 If f(t) = 2jwot, What is the Fourier Transform of f(2t - 1). 786-w)e О 203 (+20)e+ 70 (+w) en 2006-..). المال
Question 1 (10 points) Determine Fourier Transform of f(t) = u(t – 2) + 6(t – 6)? e-12w + e-jow (ies + 70(w))er2we=you Giv - 70()e=12W +e=you Gius + 78(w))e=124 +e-sou Question 2 (10 points) Using the convolution property of Fourier Transform to find the following convolution: sinc(t) * sinc (4t) [Hint: sinc(t) én rect(w/2)] π sinc (2t) 2 TT 8 sinc(t)sinc(2t) TT sinc(4t) TT sinc(t)
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)
What is the Fourier Transform of f(t) = e =2* u(t)? 2 + jw 1 1 2-jw 1 1+2jw 1 1 iw - 2
Given that f (t) e-au(t to), where a 0, determine the Fourier transform F() of f(t). 7.1 (b) Given that where a > 0, determine the Fourier transform G (w) of g(0) by using the symmetry property and the result of part (a). Confirm the result of part (b) by calculating g) from G(w), using the inverse Fourier transform integral