Discrete signals can be generated by software or obtained from real world through ADC. Discrete signals are sampled from analog signals. So you get samples in fixed time intervals. Discrete signal is as sequence of numbers. The element number n of sequence is marked as x(n). The most common number rows:

Unit sample sequence

d[n] = 1, if n=0
d[n] = 0, otherwise

You can describe it in Matlab like

% Plot an unit impulse signal
n = -5:5;
x = 0*n;
index=find(n==0);
x(index)=1;
% plot
stem(n, x);
axis([-inf, inf, -0.2, 1.2]);
xlabel(’n');
ylabel(’x');
title(’Unit Impulse Signal delta[n]‘);

Unit Step Sequence

u[n] = 1, if n>=0
u[n] = 0, otherwise

You can describe it in Matlab like:

% Plot an unit impulse signal
n = -5:5;
x = 0*n;
index=find(n>=0);
x(index)=1;
% plot
stem(n, x);
axis([-inf, inf, -0.2, 1.2]);
xlabel(’n');
ylabel(’x');
title(’Unit Step Signal u[n]‘);

As you can see step is nothing more than set of impulses. And impulse
can be expressed as d[n]=u(n)-u(n-1); Thus any sequence of numbers can
be expressed asset of impulses like this:

For example sin() sequence can be written like this:

Matlab script would look like this:

% Plot a sinusoidal signal
n = 0:40;
omega=0.3;
x = sin(omega*n);
% plot
stem(n, x);
axis([-inf, inf, -1.2, 1.2]);
xlabel(’n');
ylabel(’x');
title(’sin[\omega n]‘);

And it would look like:

So it is nothing more than multiplication of queues.

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This entry was posted on Thursday, April 20th, 2006 at 10:46 pm and is filed under DSP Lessons. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.