Reference no: EM13249513

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

a) 0.6600z^2 -0.8569z/(z^2+0.3565z+1)

b) 0.6600z^2 +0.8569z/(z^2-0.3565z+1)

c) 0.8569z^2-0.6600z/(z^2-0.3565z+1)

d) 0.6600z^2 +0.8569z/(z^2+0.3565z+1)

2) Find the system transfer function of a causal LSI system whose impulse response is given by

h[n] = (0.62)^n-1sin[6(n-2)]u[n-2]

a)-0.81181z^-2/(z^2-1.2482z+0.4225)

b) -0.81181z^-2/(z^21.2482z+0.4225)

c) -0.81181z^-1/(z^2-1.2482z+0.4225)

d) 0.81181z^-1/(z^2+1.2482z+0.4225)

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 tables.

H(z) = 0.1/(z^2-1.3z+0.36)

a) -0.2(0.9)^n-1 u(n-1)-0.2(0.4)^n-1 u(n-1)

b) 0.2(0.9)^n-1 u(n-2)+0.2(0.4)^n-2 u(n-2)

c) 0.2(0.9)^n-1 u(n-1)-0.2(0.4)^n-1u(n-1)

d)0.2(0.4)^n-1 u(n-1)-0.2(0.9)^n-1 u(n-1)

4) The transfer function of a system is given by

H(z) = s/z(z-0.1)

such a system we apply an input of the type x[n ]= e ?0.4n for n ?0. Find the response of the system in n domain.
a)14.027(0.1)^n-1 u(n-1) +14.027(0.6703)^n-1 u(n-1)
b) -14.027(0.1)^n-1 u(n-1) +14.027(0.6703)^n-1 u(n-1)

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

d) -14.027(0.1)^n u(n-1) +14.027(0.6703)^n-1 u(n-1)

5. Which of the following is the correct expansion of the signal

x[n] = (0.4)^n sin(pi/6 n) u[n-1]

a) (0.4)^n-1[0.3464 sin(pi/6(n-1)-0.2000 cos(pi/6(n-1))]u(n-1)

b) (0.4)^n-1[0.2000sin(pi/6(n-1))+0.3464 cos (pi/6(n-1))]u(n-1)

c) (0.4)^n-1[-0.3464 sin(pi/6(n-1)-0.2000 cos(pi/6(n-1))]u(n-1)

d) (0.4)^n-1[0.3464 sin(pi/6(n-1)+0.2000 cos(pi/6(n-1))]u(n-1)