Q4. (5 points). The generalized Fourier Transform of 1 is the impulse functionS). Use this conclusion...
Q4) Calculate the Fourier transform of the following time domain signals. Use the properties of the Fourier transform found in the "Properties of Fourier Transforms" table in textbook and the "Famous Fourier Transforms Table" in textbook instead of direct integration as much as possible to simplify your calculation wherever appropriate: 2-2
Problem 5: [9 Points) Find the inverse Fourier transform of the frequency functions, (a) c) x(a 2 -6 Problem 5: [9 Points) Find the inverse Fourier transform of the frequency functions, (a) c) x(a 2 -6
Question 31 1 pts Fourier transform is used for Periodic functions Constant functions Non-periodic functions Unbounded functions Question 32 1 pts Fourier transform of the impulse function is: Infinity 1 Zero None of the above
Consider signal ?(?)=cos(2??)cos(20??) a.(10 Points) Calculate the Fourier transform of ℎ(?)=?(?)cos(20??) using impulse functions. b.(10 Points) Specify the frequency response of a filter that returns an output signal proportional to the cos(2??)
5 = 10 marks ] Question 1 [3 2 (a) Use the Fourier transform, -) / Ф(Р) e'pr/h d3p 27TH and the inverse transform 1 b(FeipF/hd3r Ф(Р) 2тh to prove the Fourier Integral Theorem: 1 ') ei(F'-p)/h d3p' d*r. Ф(р) - 2тh (b) Explain why the Dirac-ô may be represented via - ih)/ 1 8(F- F') (c) Show that for arbitrary wave functions /a,b(f) that / -/ Фа (р)" фь (р) d'р, Va(r = where ba and da (and /,...
2c.- 25 Points: Compute the discrete Fourier transform (DFT) of the impulse response function given by the signal: h[n] = {h[0], h[1], h[2], h[3],0,0,0,0} = {+1, +1, +1, +1,0,0,0,0}
Question 33 1 pts Fourier transform of the impulse response of a system is: Same as Laplace transform of the Impulse response Same as step response Same as the frequency response None of the above Question 34 1 pts The total energy of a signal can be calculated in time domain or the frequency domain. This is a result of: None of the above Parseval's theorem Laplace theorem Fourier theorem
Q4. a) Use Z-transform method to determine the output time sequence y(n) for the following impulse response and excitation, h(n) = {2,-1,1,3}, x(n) = (-1)" u(n). b) For the DSP system shown, if x(t)=10 sin(300 ft), find x(n) and y(n). x(t) y(t) A/D h(n) =(n + 1)a"u[n] D/A f=1KHz
6) Answer the following questions: a) (5 points) Using the Fourier transform, find the value of the following integral S. sinc(Be)dt b) (5 points) Find the Amplitude and phase spectra of the following signal x(t) Ae=sin(5t), t20, t<0. 10. c) (5 points) Find the Fourier transform of v(t) 1
1. (a) You have seen that the Fourier transform of cos(wt) and sin(wt) func- tions results in even and odd combinations of delta functions in the frequency domain. Prove the opposite. That is, find the combination of delta functions in the time domain that give cosine and sine functions in the frequency domain. (b) Use the signum function to relate these two combinations of delta functions and use the convolution theorem to show that sin (wt) = cos (wt) *...