1) find the z-transform, x(z), of x(n)= cos(1.75n-0.85)u(n) 2) Find the system t

Question

1) find the z-transform, x(z), of x(n)= cos(1.75n-0.85)u(n)

2) Find the system transfer function of a causal LSI system whose impulse response is given bystyle="font-family: arial;">style="font-size: 10pt;">for="multiplechoice1_0_4">

h[n]n = (-0.8)^n-1 sin[4(n-2)]u[n-2]style="font-family: arial;">

b) -style="font-family: arial; font-size: 11px;">0.4844z^-1/(z^2-1.0458+0.64)

for="multiplechoice2_0_4">

3) The transfer function (TF) of a system is given below. Find its impulse response inn domain. Hint: First multiply the TF by the z-transform of input or x(z)or the z-transform of unit impulse. Factor the denominator and then expand using partial fraction expansion. Then perform its inversion using z-transform tablesstyle="font-family: arial;">style="font-family: arial;">style="font-family: arial;">style="font-family: arial;">style="font-family: arial;">style="font-family: arial;">style="font-family: arial;">style="font-size: 10pt;">for="multiplechoice1_0_3">

H(z) = 0.5/(z^2-1.5z+0.56)style="font-family: arial;">

b) style="font-family: arial;">style="font-family: arial;">style="font-family: arial;">5(0.8)^n-1 u(n-1) -5(0.7)^n-1 u(n-1)

d)>style="font-family: arial;">5(0.8)^n-2 u(n-1) -5(0.7)^n-2 u(n-1)

4) The transfer function of a system is given by for="multiplechoice3_0_4">

H(z) = s/(z(z-0.1)for="multiplechoice3_0_4">

c)>14.027 (0.1)^n-1 u(n-1)-14.027(0.6703)^n-1 u(n-1)

for="multiplechoice4_0_4">

5) face="arial">Which of the following is the correct expansion of the signal

x[n] = (0.9)^n sin(2pi n) u[n-1]  Hint: After suitable algebraic manipulation, use the trig identity Sin(A+B) = Sin A Cos B + Cos A Sin B.

a) (0.9)^n-1[-0.4500 sin(2pi/3(n-1)) -0.7794 cos (2pi/3(n-1))] u(n-1)

b) (0.9)^n-1[-0.4500 sin(2pi/3(n-1)) +0.7794 cos (2pi/3(n-1))] u(n-1)

c) (0.9)^n-1[0.4500 sin(2pi/3(n-1)) +0.7794 cos (2pi/3(n-1))] u(n-1)

d) (0.9)^n-1[0.7794 sin(2pi/3(n-1)) +0.4500 cos (2pi/3(n-1))] u(n-1)

find the z-transform, x(z), of x(n)= cos(1.75n-0.85)u(n) Find the system transfer function of a causal LSI system whose impulse response is given by h[n]n = (-0.8)^n-1 sin[4(n-2)]u[n-2] The transfer function (TF) of a system is given below. Find its impulse response inn domain. Hint: First multiply the TF by the z-transform of input or x(z)or the z-transform of unit impulse. Factor the denominator and then expand using partial fraction expansion. Then perform its inversion using z-transform tables H(z) = 0.5/(z^2-1.5z+0.56) The transfer function of a system is given by H(z) = s/(z(z-0.1) Which of the following is the correct expansion of the signal x[n] = (0.9)^n sin(2pi n) u[n-1] Hint: After suitable algebraic manipulation, use the trig identity Sin(A+B) = Sin A Cos B + Cos A Sin B.

Explanation / Answer

d

b

c

d

a

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