- Digital Signal Process Urgent Need Answer 1 (145.07 KiB) Viewed 42 times
- Q3 - Fourier Transforms for Circuit Analysis This question is concerned with the analysis of circuits in the frequency domain Answer all parts of this question Use of mathematical software, such as MATLAB, is permitted, but the answers expected will be numbers or mathematical expressions. , , Enter all numbers rounded to 3 significant figures unless otherwise advised. Q3(i) Fourier Transform Properties a) 1 T Which of the following integrals represents the Fourier transform * *(t)exp(-jks?t) dt ( -2 (exp(-16) L- (r)exple - )dt - ſtde (t)exp(-jut)dt b) Match the Fourier transform property to the example ) shown below. du F/ Symmetry: F(e) Frequency convolution: expG36) exp150) de FO) 2SC_they + #P(0)5w) (w+2). (115) ° (نما)* قات 2 Time integration: L*)d- Frequency differentiation: () () Submit Unanswered Q3(ii) Fourier transform of a system A first-order low-pass filter with input (t) and output y(t) and cut-off frequency 1000 rads- has impulse response: h(t) = 1000 exp(-1000€) no(t) where tto(t) is the unit step or Heaviside function c) Give an expression for the transfer function of the low-pass filter (s) Submit part 1 mark Unanswered d) Give the system function of the low pass filter Hju). Submit part I mark Q3(iii) Step response of a system a e) The Fourier transform of the unit-step function is given by the following transform pair: uo(t) 18W) + 1 المال Determine the response yı(t) of the filter h(t) when the input r(t) = 3uo(t). Hint use the Fourier transforms of h(t) and (t) and the convolution property to find Yi(jw) then inverse Fourier transform the result. Show steps (You will lose 1 mark.) Answer: Q3(iv) Delayed response f) Give the response of the system is initially at rest and then subject to a delayed input x1(t - 6).