Chapter 2

% Program 2_1

% Generation of the ensemble average

%

R = 50;

m = 0:R-1;

s = 2*m.*(0.9.^m); % Generate the uncorrupted signal

d = rand(R,1)-0.5; % Generate the random noise

x1 = s+d';

stem(m,d);

xlabel('Time index n');ylabel('Amplitude'); title('Noise');

pause

for n = 1:50;

d = rand(R,1)-0.5;

x = s + d';

x1 = x1 + x;

end

x1 = x1/50;

stem(m,x1);

xlabel('Time index n');ylabel('Amplitude'); title('Ensemble average');

% Program 2_2

% Generation of complex exponential sequence

%

a = input('Type in real exponent = ');

b = input('Type in imaginary exponent = ');

c = a + b*i;

K = input('Type in the gain constant = ');

N = input ('Type in length of sequence = ');

n = 1:N;

x = K*exp(c*n);%Generate the sequence

stem(n,real(x));%Plot the real part

xlabel('Time index n');ylabel('Amplitude');

title('Real part');

disp('PRESS RETURN for imaginary part');

pause

stem(n,imag(x));%Plot the imaginary part

xlabel('Time index n');ylabel('Amplitude');

title('Imaginary part');

% Program 2_3

% Generation of real exponential sequence

%

a = input('Type in argument = ');

K = input('Type in the gain constant = ');

N = input ('Type in length of sequence = ');

n = 0:N;

x = K*a.^n;

stem(n,x);

xlabel('Time index n');ylabel('Amplitude');

title(['\alpha = ',num2str(a)]);

% Program 2_4

% Signal Smoothing by a Moving-Average Filter

%

R = 50;

d = rand(R,1)-0.5;

m = 0:1:R-1;

s = 2*m.*(0.9.^m);

x = s + d';

plot(m,d,'r-',m,s,'b--',m,x,'g:')

xlabel('Time index n'); ylabel('Amplitude')

legend('d[n]','s[n]','x[n]');

pause

M = input('Number of input samples = ');

b = ones(M,1)/M;

y = filter(b,1,x);

plot(m,s,'r-',m,y,'b--')

legend('s[n]','y[n]');

xlabel ('Time index n');ylabel('Amplitude')

% Program 2_5

% Illustration of Median Filtering

%

N = input('Median Filter Length = ');

R = 50; a = rand(1,R)-0.4;

b = round(a); % Generate impulse noise

m = 0:R-1;

s = 2*m.*(0.9.^m); % Generate signal

x = s + b; % Impulse noise corrupted signal

y = medfilt1(x,3); % Median filtering

subplot(2,1,1)

stem(m,x);axis([0 50 -1 8]);

xlabel('n');ylabel('Amplitude');

title('Impulse Noise Corrupted Signal');

subplot(2,1,2)

stem(m,y);

xlabel('n');ylabel('Amplitude');

title('Output of Median Filter');

% Program 2_6

% Illustration of Convolution

%

a = input('Type in the first sequence = ');

b = input('Type in the second sequence = ');

c = conv(a, b);

M = length(c)-1;

n = 0:1:M;

disp('output sequence =');disp(c)

stem(n,c)

xlabel('Time index n'); ylabel('Amplitude');

% Program 2_7

% Computation of Cross-correlation Sequence

%

x = input('Type in the reference sequence = ');

y = input('Type in the second sequence = ');

% Compute the correlation sequence

n1 = length(y)-1; n2 = length(x)-1;

r = conv(x,fliplr(y));

k = (-n1):n2';

stem(k,r);

xlabel('Lag index'); ylabel('Amplitude');

v = axis;

axis([-n1 n2 v(3:end)]);

% Program 2_8

% Computation of Autocorrelation of a

% Noise Corrupted Sinusoidal Sequence

%

N = 96;

n = 1:N;

x = cos(pi*0.25*n); % Generate the sinusoidal sequence

d = rand(1,N) - 0.5; % Generate the noise sequence

y = x + d; % Generate the noise-corrupted sinusoidal sequence

r = conv(y, fliplr(y)); % Compute the correlation sequence

k = -28:28;

stem(k, r(68:124));

xlabel('Lag index'); ylabel('Amplitude');