1 the response of a lti system to a step input xt ut

Question

1. The response of a LTI system to a step input, x(t) = U(t) is:

y(t) = (1 - e^-2t) U(t)

What is the response to an input of x)t) = 4U(t) - 4U(t-1) ?

2. Use properties to find the response of a system to an input as specified:

x(t) = 2U(t-10)

h(t) = sin(2t)U(t)

3. Determine the poles and zeros for the following transfer function and plot them on the s-plane:

H(s) = [4s+1]/[s² + 4s +13]

4. Find the Transfer Function of:

C1 = C2 = 100 μf , R1 = R2 = 1 kΩ

5. Draw the Bode Plot (magnitude and phase) of the Transfer Function below. Use log-linear paper and an asymptote for each term.

(a) H(s) = [250(s + 20)] / [s (s+5)(s+10)]

(b) H(s) = 16/[(s+1)(s+8)]

(c) H(s) = [1000(s+1)]/(s+20)²

Answer 1

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