Reference no: EM133051612

UEI303 Signals and Systems

Question 1. A system may or may not be:

i. Memoryless ii. Time invariant iii. Linear iv. Causal v. Stable

Determine which of these properties hold and which do not hold for

Justify your answers.

Question 2. Find the convolution of h(t) = δ(t +2) + 2δ(t + 1) and

Question 3. Consider the analog signal x(t) = 3cos(2000Πt) +5 sin(6000Πt) + 10cos(12000Πt)

(a) What is the Nyquist rate of x(t)? What is the discrete-time signal x[n] obtained after sampling at a rate of F; = 5000 samples/s?

(b) What is the analog signal y(t) after reconstruction with an ideal interpolation?

Question 4. Find the Fourier transforms of:

(a) x₁ (t) = sin(ω_ot) (b) x₂(t) = a{u(t +T₁) - u(t - T₁)}

Question 5. Given that x(t) has the Fourier transform X(jω), express the Fourier transforms of the signals listed below in terms of X(jω) using suitable properties of the Fourier transform.

(a) x₁ (t) = x(1 - t) + x(-1 - t) (b) x₂(t) = d2/dt² x(t -1) (c) x₃(t) = tx²(t) (d) x₄(t) = x*(-5t)