It’s a communication problem, thanks! Question2: Find the Fourier Transform of w(t) by: (a) Evaluating the...
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...
The Fourier transform of f(t), F(W) is as follows: F(W) = F[f(t)] vendºsce-iat de Find the Fourier transform of f(t): 0 < \t] =1 = 1t| 10 t = 0,|t| > 1 (1) f(t) = {i (2) f(t) = {2 (t2 0 < t < 1 lo |t| > 1
2) (Fourier Transforms Using Properties) - Given that the Fourier Transform of x(t) e Find the Fourier Transform of the following signals (using properties of the Fourier Transform). Sketch each signal, and sketch its Fourier Transform magnitude and phase spectra, in addition to finding and expression for X(f): (a) x(t) = e-21,-I ! (b) x(t)-t e 21 1 (c) x(t)-sinc(rt ) * sinc(2π1) (convolution) [NOTE: X(f) is noLI i (1 + ㎡fy for part (c)] 2) (Fourier Transforms Using Properties)...
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 .
f(t)=(9t+20t2)2(7-20)t H(t) Find the Fourier transform of: . Your answer should be expressed as a function of w using the correct syntax Fourier transform is F(w)Skipped f(t)=(9t+20t2)2(7-20)t H(t) Find the Fourier transform of: . Your answer should be expressed as a function of w using the correct syntax Fourier transform is F(w)Skipped
The Fourier transform W(f) of a time domain signal w(t) is given by: W(f) = 5.87 exp[ -( 0.047 f )2 ] Find the imaginary part of the Fourier transform of the shifted signal w(t - 0.50) at the frequency 3.24 Hz. The correct answer is 3.93
Question 4 (2 marks) Attempt 1 Find the Fourier transform of. cos(19)e7t j(t)= Your answer should be expressed as a function of w using the 2Tt correct syntax. Fourier transform Skipped is F(w) = Question 4 (2 marks) Attempt 1 Find the Fourier transform of. cos(19)e7t j(t)= Your answer should be expressed as a function of w using the 2Tt correct syntax. Fourier transform Skipped is F(w) =
W (t) = (a) Find W (f) using the Duality Property of the Fourier Transform and the Table.
Question Question 5 (2 marks) Attempt 1 Find the Fourier transform of: f(t) ˊ-e-10t Your answer should be expressed as a function of w using the correct syntax. Fourier transform is F(w) = π(164t2)2 Question Question 5 (2 marks) Attempt 1 Find the Fourier transform of: f(t) ˊ-e-10t Your answer should be expressed as a function of w using the correct syntax. Fourier transform is F(w) = π(164t2)2
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) =...