Question Solved1 Answer Question 2: (a) Determine whether the discrete time system which has an output y[n] = 2 * x[n] over the interval (<=n<= 10 is linear or not by determining the response y1 [n] to the input signal x][n] = sin( (2pi /10) n ) and the response yz[n] to the input signal x2[n] = cos((2pi/10) n ). Determine the response yž[n] to the input signal x3[n] = x1[n] + x2[n] and compare it with y4[n] = yi[n] + y2[n] . Plot (using stem) in one graph all the input signals and their corresponding out- put signals. Use the disp command to output whether the system has ‘outputs consistent with a linear system ’or ‘not linear”. (b) Design an experiment to test whether the systems: (i) y[n]=x[n] (ii) y[n] = 2x[n] + 58[n] 14 are linear and time-invariant. Use the input data x[n] = [0,1]. Next, using a larger set of values, for your choice of the input data, repeat the experiment and analyze and interpret the results obtained with this new data set. Do the new results validate or invalidate the original results obtained with x[n] = [0,1] as choice of input data? Explain how a choice of data used may impact the results obtained.

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Transcribed Image Text: Question 2: (a) Determine whether the discrete time system which has an output y[n] = 2 * x[n] over the interval (<=n<= 10 is linear or not by determining the response y1 [n] to the input signal x][n] = sin( (2*pi /10) * n ) and the response yz[n] to the input signal x2[n] = cos((2*pi/10) * n ). Determine the response yž[n] to the input signal x3[n] = x1[n] + x2[n] and compare it with y4[n] = yi[n] + y2[n] . Plot (using stem) in one graph all the input signals and their corresponding out- put signals. Use the disp command to output whether the system has ‘outputs consistent with a linear system ’or ‘not linear”. (b) Design an experiment to test whether the systems: (i) y[n]=x[n] (ii) y[n] = 2x[n] + 58[n] 14 are linear and time-invariant. Use the input data x[n] = [0,1]. Next, using a larger set of values, for your choice of the input data, repeat the experiment and analyze and interpret the results obtained with this new data set. Do the new results validate or invalidate the original results obtained with x[n] = [0,1] as choice of input data? Explain how a choice of data used may impact the results obtained.

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%%MATLAB CODE FOR PART Aclose allclear allclear variablesclcn=0:10;x1=sin((2*pi/10).*n);x2=cos((2*pi/10).*n);x3=x1+x2;y1=2.*x1;y2=2.*x2;y3=2.*x3;y4=y1+y2;stem(n,x3);hold onstem(n,y3,'-r');hold onstem(n,y1+y2,'-g');hold onstem(n,y4,'-c');if y3==y4disp('output consistent with a linear system')elsedisp('output consistent with a non-linear system')end%%MATLAB code for part b%part 1close allclear allclear variablesclcn=0:10;for i=1:length(n)xx1(i)=0;xx2(i)=1;endxx3=xx1+xx2;yy3=xx3.^2;yy1=xx1.^2;yy2=xx2.^2;yy4=yy1+yy2;stem(n,yy3,'-r');hold onstem(n,yy4,'-c');if yy3==yy4disp('output consistent with a linear system')elsedisp('output consistent with a non-linear system')end%%My choice of data:x1=1:11%%x2=11:21for i=1:length(n)x1(i)=i;x2(i)=i+10;endx3=x1+x2;y1=x1.^2;y2=x2.^2;y3=x3.^2;y4=y1+y2;figurestem(n,y3);hold onstem(n,y4,'-r');if y3==y4disp('output consistent with a linear system')elsedisp('output consistent with a non-linear system')endfi ... See the full answer

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