An integrator has as its frequency response H(jw) = _;_ + 7T 8(w ), )W where the impulse
Chapter 6, Problem 6.31(choose chapter or problem)
An integrator has as its frequency response H(jw) = _;_ + 7T 8(w ), )W where the impulse at w = 0 is a result of the fact that the integration of a constant input from t = -oo results in an infinite output. Thus, if we avoid inputs that are constant, or equivalently, only examine H(jw) for w > 0, we see that 20logiH(Jw)l = -20log(w), -7T the form 1 H(jw) = jw(1 + jw/10) + 7T o(w ). Sketch the Bode plot for the system for w > 0.001. (b) Sketch the Bode plot for a differentiator. (c) Do the same for systems with the following frequency responses: (i) H(jw) = I+J:::noo (ii) H(jw) = (1 +(jw)/16:(jw)211QO)
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