Question 5 (a) The impulse response of a discrete-time filter is given as, hin) 0.56n-1] +n-2)0.56 n -3]. i. Derive the filter's frequency response; 11. Roughly sketch the filter's magnitude response for 0 ii. Is it a low-pass or high-pass filter? Ω 2m; (b) A continuous-time signal se(t) is converted into a discrete-time signal as shown below. s(t) is a unit impulse train. s(t) x,) Conversion into x(1) __→ⓧ一ㄅㄧ-discrete-time sequence ー→ xu [n] The frequency spectrum of ap (t) is given as follows 400 -100π 0 100π -4007 400T i. Determine the sampling frequency being used; ii. Sketch the frequency spectra of zet) and xanl; iti. A low-pass filter can be used to reconstruct e(t) from ap(t). Specify the range of the cut-off frequency of this filter; iv. Draw an illustrative diagram to describe how ac(t) can be reconstructed from ap(t) by using a zero-order hold. From the frequency response point of view, explain why zero-order hold can not achieve perfect reconstruction. Question 5 (a) The impulse response of a discrete-time filter is given as, hin) 0.56n-1] +n-2)0.56 n -3]. i. Derive the filter's frequency response; 11. Roughly sketch the filter's magnitude response for 0 ii. Is it a low-pass or high-pass filter? Ω 2m; (b) A continuous-time signal se(t) is converted into a discrete-time signal as shown below. s(t) is a unit impulse train. s(t) x,) Conversion into x(1) __→ⓧ一ㄅㄧ-discrete-time sequence ー→ xu [n] The frequency spectrum of ap (t) is given as follows 400 -100π 0 100π -4007 400T i. Determine the sampling frequency being used; ii. Sketch the frequency spectra of zet) and xanl; iti. A low-pass filter can be used to reconstruct e(t) from ap(t). Specify the range of the cut-off frequency of this filter; iv. Draw an illustrative diagram to describe how ac(t) can be reconstructed from ap(t) by using a zero-order hold. From the frequency response point of view, explain why zero-order hold can not achieve perfect reconstruction.
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Engineering 2022-05-15 19:04:59