# Understanding of discrete signals

Discrete signals can be generated by software or obtained from the real-world through ADC. Discrete signals are sampled from analog signals. So you get samples in fixed time intervals. The discrete signal is a sequence of numbers. The element number n of the 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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