Reference no: EM133124253

Question 1: If x[n] = (-0.5)nu[n], -∞ < n < ∞, find the following. Represent each discrete signal as a sequence of numbers or sketch each discrete signal.

(1) x[2n]

(2) x[n/2]

(3) x[n -3]

(4) The energy and power of x[n].

Question 2:
Consider the following two signals of finite length, compute the convolution and correlation of the two signals.
x₁[n] = (n + 1)(u[n] - u[n - 3])
x₂[n] = (n + 2)(u[n] - u[n - 5])

Question 3:
Given a discrete system, if the input x[n] = (0.3)ⁿ u[n] and the impulse response h[n] = (0.8)ⁿ u[n], find the output y[n] using the z-transform method.

Question 4:
Let the following equation describe a discrete-time system:

y[n] = 0.8y[n - 1] + 0.5x[n] + 0.5x[n - 1] and n ≥ 0
(1) Compute the frequency response, H(e^jΩ).
(2) Compute the response of the system when the input is: x[n] = cos(0.5Πn + Π) for n ≥ 0.

Question 5:
Let the sequences x[n]={1, 3, 5} and h[n]= {2, 4}. Each has length of N₁ =3 and N₂ = 2, respectively. Append zeros to x[n] and h[n] to make the length of both equal to N₁ + N₂ -1. Computer the linear convolution of the sequences using the Discrete Fourier Transform (DFT) method.