Q3 Fourier Transforms For Circuit Analysis This Question Is Concerned With The Analysis Of Circuits In The Frequency D 1 (81.48 KiB) Viewed 55 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) which of the following integrals represents the Fourler transform? x() exp(-1)dt 0 x(1) exp(-jordt 1 X(T) expit -T) dr x(1) exp(-jk. t)dt Submit part 1 mark Unanswered b) Match the Fourler transform property to the example Fja) shown below. 1 FW) X - 76) ( 'Guts)+(+15) Judit f(t)dt 2x jw +5 O O O O O Area under F(6): f(0) Frquency shift: exp(6) (1) Frequency differentiation: (-)" f(t) /n Frequency convolution: exp(-51) exp(-15) O O O O 0 O Submit part 1 mark Unanswered Q3(ii) Fourier transform of a system A first-order low-pass filter with Input x(t) and output yr) and cut-off frequency 10 rads has impulse response: t) ) : h(t) = 10 exp(-101) (1) where wo(t) is the unit step or Heavis de function. . c) Glve an expression for the transfer function of the low-pass filter H(s). c) Submit part 1 mark Unanswered d) Glve the system function of the low-pass filter (jw). Submit part 1 mark Unanswered Q3(iii) Step response of a system el The Fourier transform of the unit-step function is given by the following transform pair: 1 1 Molt) x) + je Determine the response y. (1) of the filter h(r) when the input x (t) = 54.(t). Hint use the Fourier transforms of h(t) and X (t) and the convolution property to find Y6w) then Inverse Fourier transform the result. h) Show steps You will lose e1 mark) mark Answer: Submit part 4 marks Unanswered
Unanswered Q3(iv) Delayed response f) Give the response of the system is initially at rest and then subject to a delayed input x (1 - 1). Submit part 2 marks Unanswered Submit all parts 10 marks
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