You have a following analog filter, which is realized using a discrete filter:Xa (t) -> A/D ->x(n) h(n) ->y(n) D/A ->ya (t) The sampling rate in the A/D and D/A is 120 samples/sec, and the impulse response is h(n)=(0.5)n u(n). what is the digital frequency in x(n) if xa (t)=3cos(20πt)? Find H(z), the z-transform of h(n). Find |H(Ω)|, the magnitude response of the filter, where Ω=2π F: digital frequency Draw the pole-zero plot of the filter. Hint: H(z)=N(z)/D(z), where N(z) and D(z) are the functions of z) Find the output Ya (t)=Xa (t)* h(n). (* : convolution, when Xa (t)=3u(t).) Find the steady-state output Yss (t) when Xa (t)=3u(t). To prevent aliasing, a prefilter would be required to process Xa (t) before it passes to the A/D converter. What type of filter should be used, and what would be the largest cutoff frequency that would work for the given configuration?

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Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

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You have a following analog filter, which is realized using a discrete filter:

X_a(t) -> A/D ->x(n) h(n) ->y(n) D/A ->y_a(t)

The sampling rate in the A/D and D/A is 120 samples/sec, and the impulse response is h(n)=(0.5)ⁿu(n).

^whatis the digital frequency in x(n) if x_a(t)=3cos(20πt)?
Find H(z), the z-transform of h(n).
Find |H(Ω)|, the magnitude response of the filter, where Ω=2π F: digital frequency
Draw the pole-zero plot of the filter. Hint: H(z)=N(z)/D(z), where N(z) and D(z) are the functions of z)
Find the output Y_a(t)=X_a(t)^*h(n). (^*: convolution, when X_a(t)=3u(t).)
Find the steady-state output Y_ss(t) when X_a(t)=3u(t).
To prevent aliasing, a prefilter would be required to process X_a(t) before it passes to the A/D converter. What type of filter should be used, and what would be the largest cutoff frequency that would work for the given configuration?

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