Question 1:

The Fourier transform of a signal is given by X(ω) = 1 + e^j2ω - 3e^-j2ω. Determine the signal in the time domain.

Question 2:

Determine the difference equation for the system whose frequency response is

H(w) = (1 + e^-jω)/1 - 0.75e^-jω

Question 3:

Calculate the convolution x₁[n]*x₂[n] where x₁[n] = {1, 0, 0, -1} (x₁ [0] = 1) and x₂[n] = {1, 2, 0, 2, 1} (x₂[0] = 0)

Question 4:

An LTI system is given by:

                                     y[n] = x[n] - 2x [n - 1] + x[n - 2]

(a) Determine its impulse response.

(b) Determine the frequency response.

(c) What is the output if the input is

                                    x[n] = cos(Π.n/2) + cos(Πn)

Question 5:

The impulse response of an LTI system is given by

h[n] = δ[n] - 2 cosω₀δ[n - 1] + δ[n - 2]

(a) Determine the frequency response of the system for ω_o = Π/4.

(b) Determine the output for the input signal

x[n] = cos(Πn/4) + cos(Πn)