%% ------------------------------------------------------------------------

%%            Output Info about this m-file

fprintf('\n***********************************************************\n');

fprintf('        <DSP using MATLAB> Problem 2.3.1 \n\n');

time_stamp = datestr(now, 31);

[wkd1, wkd2] = weekday(today, 'long');

fprintf('      Now is %20s, and it is %7s  \n\n', time_stamp, wkd2);

%% ------------------------------------------------------------------------

%%

%% {...,-2,-1,0,1,2,...}

%%            *

%% Plot 5 periods

self_length = 5;

periods = 5;

n = [-2:(2+(periods-1) * self_length)];x = [-2,-1,0,1,2];

xtilde = x' * ones(1,periods); xtilde = (xtilde(:))';

figure('NumberTitle', 'off', 'Name', 'Problem 2.3.1');

set(gcf,'Color','white');

stem(n,xtilde); title('Sequence in Problem 2.3.1');

xlabel('n'); ylabel('xtilde(n)');grid on;

%% ------------------------------------------------------------------------

%%            Output Info about this m-file

fprintf('\n***********************************************************\n');

fprintf('        <DSP using MATLAB> Problem 2.3.2 \n\n');

time_stamp = datestr(now, 31);

[wkd1, wkd2] = weekday(today, 'long');

fprintf('      Now is %20s, and it is %7s  \n\n', time_stamp, wkd2);

%% ------------------------------------------------------------------------

%%

%% exp(0.1n)[ u(n) - u(n-20)]     0-20 valid

%%

%% Plot 3 periods    [0;3*20-1]  [0,59]

n = [0:20];   % We can get self_periods=21 from here

x = exp(0.1*n) .* (stepseq(0,0,20) - stepseq(20,0,20));

%x = (stepseq(0,0,20) - stepseq(20,0,20));

figure('NumberTitle', 'off', 'Name', 'Problem 2.3.2 x(n)');

set(gcf,'Color','white');

stem(n,x); title('x(n) Sequence');

xlabel('n'); ylabel('x(n)');grid on;

self_length = 21;

periods = 3;

n1 = [0:20 + (periods-1) * self_length];

xtilde = x' * ones(1,periods); xtilde = (xtilde(:))';

figure('NumberTitle', 'off', 'Name', 'Problem 2.3.2');

set(gcf,'Color','white');

stem(n1,xtilde); title('Sequence in Problem 2.3.2');

xlabel('n'); ylabel('xtilde(n)');grid on;

%% ------------------------------------------------------------------------

%%            Output Info about this m-file

fprintf('\n***********************************************************\n');

fprintf('        <DSP using MATLAB> Problem 2.3.3 \n\n');

time_stamp = datestr(now, 31);

[wkd1, wkd2] = weekday(today, 'long');

fprintf('      Now is %20s, and it is %7s  \n\n', time_stamp, wkd2);

%% ------------------------------------------------------------------------

%%

%% sin(0.1*pi*n)[ u(n) - u(n-10)]     0-10 valid

%%

%% Plot 4 periods     

n = [0:10];   % We can get self_periods=11 from here

x = sin(0.1*pi*n) .* (stepseq(0,0,10) - stepseq(10,0,10));

figure('NumberTitle', 'off', 'Name', 'Problem 2.3.3 x(n)');

set(gcf,'Color','white');

stem(n,x); title('x(n) Sequence');

xlabel('n'); ylabel('x(n)');grid on;

self_length = 11;

periods = 4;

n1 = [0:10 + (periods-1) * self_length];

xtilde = x' * ones(1,periods); xtilde = (xtilde(:))';

figure('NumberTitle', 'off', 'Name', 'Problem 2.3.3');

set(gcf,'Color','white');

stem(n1,xtilde); title('Sequence in Problem 2.3.3');

xlabel('n'); ylabel('xtilde(n)');grid on;

%% ------------------------------------------------------------------------

%%            Output Info about this m-file

fprintf('\n***********************************************************\n');

fprintf('        <DSP using MATLAB> Problem 2.3.4 \n\n');

time_stamp = datestr(now, 31);

[wkd1, wkd2] = weekday(today, 'long');

fprintf('      Now is %20s, and it is %7s  \n\n', time_stamp, wkd2);

%% ------------------------------------------------------------------------

%%

%% {...,1,2,3,...} + {...,1,2,3,4,...}     n=[0:24]

%%      *                 *

%%  what is the periods

self_length1 = 3;

periods1 = 8;

n1 = [0:(2+(periods1-1) * self_length1)];

x1 = [1, 2, 3];

xtilde1 = x1' * ones(1,periods1); xtilde1 = (xtilde1(:))';

figure('NumberTitle', 'off', 'Name', 'Problem 2.3.4 Period Seq 1');

set(gcf,'Color','white');

stem(n1,xtilde1); title('Sequence {...,1,2,3,...}');

xlabel('n'); ylabel('xtilde1(n)');grid on;

self_length2 = 4;

periods2 = 6;

n2 = [0:(3+(periods2-1) * self_length2)];

x2 = [1, 2, 3, 4];

xtilde2 = x2' * ones(1,periods2); xtilde2 = (xtilde2(:))';

figure('NumberTitle', 'off', 'Name', 'Problem 2.3.4 Period Seq 2');

set(gcf,'Color','white');

stem(n2,xtilde2); title('Sequence {...,1,2,3,4,...}');

xlabel('n'); ylabel('xtilde2(n)');grid on;

x = xtilde1 + xtilde2

%[x,n] = sigadd(xtilde1,24,xtilde2,24);

figure('NumberTitle', 'off', 'Name', 'Problem 2.3.4');

set(gcf,'Color','white');

stem(x); title('Sequence {...,1,2,3,...} + {...,1,2,3,4,...}');

xlabel('n'); ylabel('x(n)');grid on;