O Consider discrete time LTI systems with the following impulse responses: System 1: h₁[n] = (-2/3)"u[n = 2] - System 2: h2[n] = 2"u[3 n] System 3: h3[n] = 2" un — 3] - System 4: ha[n] = u[n − 1] - u[n - 8] - System 5: h[n] = d[n + 2] − d[n = 8]. - (a) For each of the preceding systems, state whether it is (i) causal (ii) stable. Justify your answers.

02: For the pole-zero plot shown in figure Q2, answer the following a- Find the time response (y(t)) for a unit-step input. b- Find the time response (y(t)) for a unit-impulse input. Im K=1 Re Figure Q2

Nowadays switching power supplies are commonly used because they offer better efficiency and smaller size compared to a linear power supply, because high switching frequency allows for smaller transformers. One place to find a SMPS (switching mode power supply) is a phone charger. Switching power supplies cause high frequency noise on switching transients. The noise on the output is filtered in various ways but savings may be considered on the output filter (extra inductors and capacitors = extra costs), which means the output will have some amount of noise left getting to the device via the USB cable. Estimate the frequency where the phone charger starts to act as an antenna when the USB cable length is 1.9 meters. Submit your answer in MHz without the unit, rounded to one decimal place. Hint: Either "rule of thumb" can be used.

(c) A linear time (shift) invariant system is shown in Figure Q1(c) with q[n], p[n] and r[n] represent the impulse response, the input signal and the output signal of the system respectively. The following difference equation defines the system: r[n] = 4p[n] + 3p[n 1] - 3p[n - 2] + 2p[n-3] (i) (ii) Find and draw the impulse response q[n] of the system. Compute and draw the output response r[n] of the system given the input signal p[n] = [1 2 3 1]. (iii) Discuss and show that the output response of the system r[n] can also be obtained using the circular convolution operation between p[n] and q[n]. p[n]. q[n] Figure Q1(c) ►r[n]