hw8 - EE 224, HW 8, due April 3. 1. It is often useful to...

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Unformatted text preview: EE 224, HW 8, due April 3. 1. It is often useful to represent operations on signals as convolutions. For each of the systemr outputs, find the corresponding impulse responses h(t), i.e. find h(t) so that {.W)} = {5605)} * {M0}- (a) W) = fioo$(’r)d7- (b) W) = [LIflTMT- (C) W) = W)- (d) W) = W - T)- Hint: Use the definition of the impulse response. 2. (a) Prove that, for T > 0, {rect(%)} * {mg-n = Tmé» (1) using the graphical (flip—shift—integrate) approach. (b) Find a different proof of (1) Hint: This problem is solved in handout # 13 for the special case of T = 1 s. Generalize the derivations in handout # 13 to arbitrary T > O. 3. Problem P—9.8 on p. 280 of the textbook. 4. Problem P—9.9 on p. 280 of the textbook. Hint: Use the fact that = tu(t) = r(t) (unit ramp signal). 5. Compute the convolution (ac * h) (t) Where 33(t) and h(t) are 93(t) ': u(t), h(t) = no: — 1) and plot the result. BB 224, HW 8, due April 3. 6. The derivative of a function $05) with respect to t may be written as the convolution: W) = (20* M) where 6’(t) is the doublet, described in handout # 10. If y(t) = (33*h) (if), use the. above identity to Show that (93’ * h’W) = Mi). 7. Problem 13—91? on p. 282 of the textbook. (7552;? i , , . . k _\ ...
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hw8 - EE 224, HW 8, due April 3. 1. It is often useful to...

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