Signal x. ( t ) = sin ( 167t ) + 10 cos ( 24rt) is...

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Signal x. ( t ) = sin ( 167t ) + 10 cos ( 24rt) is sampled at a rate of f, to obtain the discrete - time signal x [n]. For each of the following sampling rates in kHz : (i) determine the spectrum X (e) of x [ n]; (ii) plot its magnitude as a function of a in rad / sam ; and (iii) explain whether x. (t) can be recovered from x [n]. ( a ) fs = 30, (b) fs = 20, (c) fs = 15. Hint cos ant sin wot T [8 (w-wo) +8 (W+ wo) ] jn [8 (w + wo) -8 (w - wo)] Signal x. ( t ) = sin ( 167t ) + 10 cos ( 24rt) is sampled at a rate of f, to obtain the discrete - time signal x [n]. For each of the following sampling rates in kHz : (i) determine the spectrum X (e) of x [ n]; (ii) plot its magnitude as a function of a in rad / sam ; and (iii) explain whether x. (t) can be recovered from x [n]. ( a ) fs = 30, (b) fs = 20, (c) fs = 15. Hint cos ant sin wot T [8 (w-wo) +8 (W+ wo) ] jn [8 (w + wo) -8 (w - wo)]

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