The signal is an electric or electromagnetic current carrying data, that can be transmitted or received. Mathematically represented as a function of an independent variable e.g. density, depth, etc. Therefore, a signal is a physical quantity that varies with time, space or any other independent variable by which information can be conveyed
- Periodic Sequence: A discrete-time signal x(n) is said to be periodic with period N if only if x(N+n)=x(n) for all n
- Aperiodic Sequence: If the above periodic sequence equation does not satisfy even for one value of n, then the discrete-time signal is aperiodic as shown in the figure below
Example 1:
% Periodic and aperiodic sequences
clear all
n=0:1:50;
n1=0:1:50;
% sine wave with frequency w=0.2*pi
x1=sin(.2*pi*n);
% sine wave with frequency w=0.4*pi
x2=sin(.4*pi*n);
% sum of x1 and x2
x3=sin(.2*pi*n)+sin(.4*pi*n);
% aperiodic sequence
x4=sin(.5*n1);
% Periodic Sequence
subplot(2,2,1);
s1=stem(n,x1);
s1.Color='green';
xlabel('n'),ylabel('x1(n)')
axis([0 50 -1 1])
% Periodic Sequence
subplot(2,2,2);
s2=stem(n,x2);
s2.Color='green';
xlabel('n'),ylabel('x2(n)')
axis([0 50 -1 1])
% Aperiodic Sequence
subplot(2,2,3);
s3=stem(n,x3);
s3.Color='green';
xlabel('n'),ylabel('x3(n)')
axis([0 50 -2 2])
% Aperiodic Sequence
subplot(2,2,4);
s4=stem(n1,x4);
s4.Color='green';
xlabel('n'),ylabel('x4(n)')
axis([0 50 -1 1])
Output:
