Question

2. Causality A causal system is a system where the current output depends on past/current inputs but not 3.5 future inputs 6 10 Exercise 2 0.5 The system y[n] - x[n] + x[n +1] is not causal. Use the input signal x[n]=U[n] to show this, as follows: 2 8 10 yIn] 2 . Define the time (sample) interval to be 1 between -6 and 9, and label it as n. Define the signal x[n]=U[n] as an array with the values 0 for n<0 and 1 for n>-0 and label it as x. 10 · Figure 2 Exercise 2 Result . Define the signal x[nt1]-UIn+1 as an array of zeros for n<-1 and 1 for n>--1 and label it as x shift Define the output signal y[n] as x[n]tx[n+1] On the same window, plot the signals x[n], x[n+1] and y[n] using the commands (subplot) and (stem).You should have a plot identical to the one shown in Figure 2 : What is your comment about the system causality?

Answer 1

Files MATLAB Drive 1 n -6.9; 5 y x+x1; 6 subplot(3,1,1);stem(n,x);title('x (n)'); 7 subplot(3,1,2); 8 stem ( n , x1) ; title ( X ( n+1 ) י ) ; 9 subplot (3,1,3); 10 stem ( n. У); title(ly(n)' );

Show Data Cursor Figure 1: prob 0.8 0.6 0.4 0.2 -6 -4 2 2 10 0.8 0.6 0.4 0.2 -6 -4 2 10 y(n) 1.5 0.5 -6 -4 2 10
as y(n) is not zero for n<=0; hence not causal