How To Generate Periodic and Aperiodic Sequence in MATLAB?
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:
Matlab
% 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: