ex020100.m

DSP2 using matlab v4

% Chapter 02: Example 02.01: Signal Synthesis

%

figure(1); clf

% a) x(n) = 2*delta(n+2) - delta(n-4), -5<=n<=5

n = [-5:5];

x = 2*impseq(-2,-5,5)-impseq(4,-5,5);

subplot(2,2,1); stem(n,x); title('Sequence in Example 2.1a')

xlabel('n'); ylabel('x(n)'); axis([-5,5,-2,3])

%

% b) x(n) = n[u(n)-u(n-10)]+10*exp(-0.3(n-10))(u(n-10)-u(n-20)); 0<=n<=20

n = [0:20];

x1 = n.*(stepseq(0,0,20)-stepseq(10,0,20));

x2 = 10*exp(-0.3*(n-10)).*(stepseq(10,0,20)-stepseq(20,0,20));

x = x1+x2;

subplot(2,2,2);stem(n,x);

title('Sequence in Example 2.1b')

xlabel('n');ylabel('x(n)');axis([0,20,-1,11])

%

% c) x(n) = cos(0.04*pi*n) + 0.2*w(n); 0<=n<=50, w(n): Gaussian (0,1)

n = [0:50];

x = cos(0.04*pi*n)+0.2*randn(size(n));

subplot(2,2,3);stem(n,x);title('Sequence in Example 2.1c')

xlabel('n');ylabel('x(n)');axis([0,50,-1.4,1.4])

%

% d) x(n) = {...,5,4,3,2,1,5,4,3,2,1,...}; -10<=n<=9

n=[-10:9];

x=[5,4,3,2,1];

xtilde=x' * ones(1,4);

xtilde=(xtilde(:))';

subplot(2,2,4);stem(n,xtilde);title('Sequence in Example 2.1d')

xlabel('n');ylabel('xtilde(n)');axis([-10,9,-1,6])