Shown in Figure P6.22(a) is the frequency response H(jw) of a continuous-time filter

Chapter 6, Problem 6.22

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Shown in Figure P6.22(a) is the frequency response H(jw) of a continuous-time filter referred to as a lowpass differentiator. For each of the input signals x(t) below, determine the filtered output signal y(t). (a) x(t) = cos(21Tt + 0) (b) x(t) = cos(41Tt+O) (c) x(t) is a half-wave rectified sine wave of period, as sketched in Figure P6.22(b). IH (jw}l { sin21Tt, m:::; t:::; (m+ ~) x(t) = 0, (m + ~) :::; t :::; m for any integer m

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