GENERATION OF SIGNALS AND SEQUENCES

GENERATION OF SIGNALS AND SEQUENCES:

If we defines amplitude of the signal at every instant of time is called continuous time signal, else if we define at some instant of time is called discrete time signal. If the signal repeats at regular intervals is called as periodic signal. Else it is called as aperiodic. Let us consider some example of periodic and aperiodic signals.

Periodic: ramp, sinc, unit step and ramp.

Aperiodic: sawtooth, square, triangular sinusoidal.

Ramp signal:

The ramp function is a singular real function.it is applied in engineering. Easily computable because of the mean of the experimental variable and its definite quantity. Ramp function is defined as:

               r(t)= t   when   t≥0

0 Otherwise

clc;

clear all;

close all;

t=0:0.001:0.1;

y1=t;

figure;

subplot(2,2,1);

plot(t,y1);

xlabel(‘time’);

ylabel(‘amplitude’);

title(‘ramp signal’);

%generation of ramp sequence

subplot(2,2,2);

stem(t,y1);

xlabel(‘n’);

ylabel(‘amplitude’);

title(‘ramp sequence’);

Unit step:

Unit step function is considered as a fundamental function in engineering and strongly recommended which the reader becomes very familiar.

u(t) =0 if t<0

         1 if t>0

          ½ if t=0

clc;

clear all;

close all;

t=-12:1:12;

y=(t>=0);

subplot(2,2,1);

plot(t,y);

xlabel(‘time’);

ylabel(‘amplitude’);

title(‘unit step signal’);

%generation of unit step sequence

subplot(2,2,2);

stem(t,y);

xlabel(‘n’);

ylabel(‘amplitude’);

title(‘unit step sequence’);

Unit impulse:

Unit impulse function is most useful function in study of linear system.

S(t) =1 when t=0

         0 otherwise

clc;

clear all;

close all;

%generation of unit impulse signal

t1=-1:0.01:1

y1=(t1==0);

subplot(2,2,1);

plot(t1,y1);

xlabel(‘time’);

ylabel(‘amplitude’);

title(‘unit impulse signal’);

%generation of impulse sequence

subplot(2,2,2);

stem(t1,y1);

xlabel(‘n’);

ylabel(‘amplitude’);

title(‘unit impulse sequence’);