Question

Using the basic developed MATLAB signal functions, generate the following sequences and then plot the signal samples using the stem function. x_1[n] = 3 delta[n + 2] + 2 delta[n] - delta[n - 3] + 5 delta[n - 7], for -5 lessthanorequalto n lessthanorequalto 15. X_2[n] = 10u[n] - 5u[n - 5] - 10u[n - 10] + 5u[n - 15]. Generate the periodic sequence and plot the samples (using the stem function) of cap x[n] = {..., -2, -1, 0, 1, 2, ..., } over 5 periods. Let x[n] = {2, 4, -3, 1, -5, 4, 7}. Generate and plot the samples (using the stem function) of x[n] = x[n + 3]x[n - 2] + x[1 - n]x[n + 1]. Using the evenodd function, decompose the sequence x[n] = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} into its even and odd components. Plot these components using the stem function.

Answer 1

clc;
clear all;
n=-5:1:15; % Define n Range
figure;
x1=3*(n==-2) + (2*(n==0)) - (n==3) + 5*(n==7); % First Plot
stem(n,x1);
title('Figure 1 Impulse Plot Vs Time');
xlabel('Time');
ylabel('Amplitude');
grid on;
%--------------------------------------------------------------------------
figure;
n=-1:1:30; % Define n Range
x2=(10*(n>=0)) - 5*(n>=5) - 10*(n>10) + 5*(n>=15); % Second Plot
stem(n,x2);
title('Figure 2 Step Functions Plot Vs Time');
xlabel('Time');
ylabel('Amplitude');
grid on;
%--------------------------------------------------------------------------
n=0:24;
x3=(-2*(mod(n,5)==0)) - 1*(mod(n,5)==1) - 0*(mod(n,5)==2) + 1*(mod(n,5)==3) + 2*(mod(n,5)==4); % Second Plot
n=-12:1:12;
figure;
stem(n,x3);
title('Figure 3 Plot Vs Time');
grid on;
xlabel('Time');
ylabel('Amplitude');
%--------------------------------------------------------------------------
x_val_1=zeros(10,1);
x_val=[2;4;-3;1;-5;4;7];
x_val=[x_val_1;x_val;x_val_1];
x_rev=x_val(numel(x_val):-1:1); % Time Reversal
x4=circshift(x_val,-3,1).*circshift(x_val,2,1) +circshift(x_rev,1,1) .* circshift(x_rev,1,1) ;
figure;
n=-13:1:13;
stem(n,x4);
title('Figure 4 Plot Vs Time');
grid on;
xlabel('Time');
ylabel('Amplitude');
%--------------------------------------------------------------------------
x_val_1=zeros(9,1);
x_val=[0:9]';
x_n=[x_val_1;x_val];
x_n_rev=x_n(numel(x_n):-1:1); % Time Reversal
x_even=[x_n+x_n_rev]./2;
x_odd=[x_n-x_n_rev]./2;
n=-9:1:9;
figure;
stem(n,x_even);
title('Figure 5 Even Signal Plot Vs Time');
grid on;
xlabel('Time');
ylabel('Even Signal');
figure;
stem(n,x_odd);
title('Figure 6 Odd Signal Plot Vs Time');
grid on;
xlabel('Time');
ylabel('Odd Signal');

Figure 1 Impulse Plot Vs Time Time

Figure 2 Step Functions Plot Vs Time 10 20 25 30 Time

Figure 3 Plot Vs Time 1.5 0.5 0.5. 15 10 Time

Figure 4 Plot Vs Time 60 50 40 兰 30 . . . 20t 15 10 Time

Figure 5 Even Signal Plot Vs Time 4.5 4 3.5 2.5 2 0.5 0 2 8 Time

Figure 6 Odd Signal Plot Vs Time び) -3 8 6-2246810 Time