. Consider the discrete-time Fourier analysis of continuous-time signal system as shown below in figure: Sc(1) Anti-aliasing...

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Consider the discrete-time Fourier analysis of continuous-time signal system as shown below in figure: Sc(1) Anti-aliasing lowpass filter Haa(jn) Continuous-to- discrete-time conversion w[n] sc(t) = Ao cos(ot+00) + A₁ cos(2₁t+0₁), -00 <t<+00 where Ao 1, A₁ = 0.75, and 0o = 0₁ = 0. v[n] x[n] = Ao cos(won + 0o) + A1 cos(win +0₁), -∞0 <n<+oo where wo2oT and ₁ = 22₁T v[n] = Ao w[n] cos(won +0o) + A1 w[n] cos(win +0₁) DFT Assuming an ideal anti-aliasing filter Haa(j). The sampling rate for the C/D converter is 10 kHz, and the rectangular window w[n] is of length 32. a) Plot the magnitude spectrum of the window sequence (3 marks) b) What is the magnitude peak at 0 (2 marks) V[k] c) Plot the magnitude spectrum of the DFT of the window sequence for 20 = (27/6)x10 and 22₁ = (27/3)x10+ (4 marks) d) What are magnitude peaks at 27/6 and 27/3 (2 marks) e) How the magnitude spectrum peak and width are affected as the frequencies decrease (4 marks) Consider the discrete-time Fourier analysis of continuous-time signal system as shown below in figure: Sc(1) Anti-aliasing lowpass filter Haa(jn) Continuous-to- discrete-time conversion w[n] sc(t) = Ao cos(ot+00) + A₁ cos(2₁t+0₁), -00 <t<+00 where Ao 1, A₁ = 0.75, and 0o = 0₁ = 0. v[n] x[n] = Ao cos(won + 0o) + A1 cos(win +0₁), -∞0 <n<+oo where wo2oT and ₁ = 22₁T v[n] = Ao w[n] cos(won +0o) + A1 w[n] cos(win +0₁) DFT Assuming an ideal anti-aliasing filter Haa(j). The sampling rate for the C/D converter is 10 kHz, and the rectangular window w[n] is of length 32. a) Plot the magnitude spectrum of the window sequence (3 marks) b) What is the magnitude peak at 0 (2 marks) V[k] c) Plot the magnitude spectrum of the DFT of the window sequence for 20 = (27/6)x10 and 22₁ = (27/3)x10+ (4 marks) d) What are magnitude peaks at 27/6 and 27/3 (2 marks) e) How the magnitude spectrum peak and width are affected as the frequencies decrease (4 marks)

Answer rating: 100% (QA)

Answer to question A The magnitude peak at 0 is 125This is because the window sequence wn is a rectangular windowwhich has a constant magnitude of 1 f... View the full answer