Question

Consider the system we discussed in the last lecture, i.e., the system for discrete time processing of continuous time signal. Suppose that the system works as follows: 1. The system receives a continuous time signal (1) as an input and sample it with the sampling period T, = 1/100 to generate the sample sequence [n] = *(nl). The continuous time signal r(t) has bandwidth 20x rad/sec. 2. The sample sequence in is led to a discrete time LT'I system with the frequency response for 9â¬[-*,7). (1) Si if2 ⬠(/4,/2) H( ) { o if 92<*/4 or 1921 ⬠(/2, ] The LTI system output is denoted by ylne. 3. The LT'I system output yin is fed to the reconstruction block, and (1) is generated as follows: 26) = E vIn] - sine (7%). (2) In the last lecture, we discussed that when the sampling rate is higher than the Nyquist rate, the above entire system is equivalent to a continuous time LTI system having () and (t) as the input and the output respectively. Find the frequency response G w) of the equivalent continuous time UTI system. (Hint: you can repeat the frequency domain analysis we did in the last lecture: (i) consider some hypothetical example of X (w). (ii) plot X (w), X:(jw), X(eft), Yel), Y Gw), and Y. (jw), and (iii) analyze the relation between X (w) and Y. (jw) to identify G w )) G6w) = 100 if we (256,504 10 if wl<25x or w > 50 G(jw) = 100 if |W⬠150x, 100x] o illal <50w or kul> 100 Si if we (25w, 50x] 10 if w< 25x or > 50x - 1/100 if we [25*, 50x] 10 if w<25 or > 50x

Answer 1

Step-by-step explanation:

The equivalent continuous-time LTI system has a frequency response G(jw) given by:

G(jw) = 100 if |w| < 150x, 100x]

o if |w| < 50x or |w| > 100x

1/100 if |w| [25x, 50x]

10 if w < 25x or w > 50x.