**BASIC OPERATIONS ON SIGNALS:**

When we perform an operation signal it may undergoes several manipulation which may include amplitude of the signal or independent variable. Some basic operation are performed on signals. They are:

**Time-shifting:**

Time shifting of a signal x(n) may be defined as delay or advance of a signal in time, which is represented with the function.

y(n)=x(n+k)

When k is positive, then y(n) is shifted to right then the signal is delayed, when y(n) is shifted to left then the signal is advanced.

clc;

close all;

clear all;

t=0:.01:1;

x1=sin(2*pi*4*t);

%shifting of a signal 1

figure;

subplot(2,2,1);

plot(t,x1);

xlabel(‘time t’);

ylabel(‘amplitude’);

title(‘input signal’);

subplot(2,2,2);

plot(t+2,x1);

xlabel(‘t+2’);

ylabel(‘amplitude’);

title(‘right shifted signal’);

subplot(2,2,3);

plot(t-2,x1);

xlabel(‘t-2’);

ylabel(‘amplitude’);

title(‘left shifted signal’);

**Time reversal:**

Time reversal of a signal x(t) is defined as folding of a signal at t=0,it is very useful in convolution.

Y(t)=y(-t)

clc;

close all;

clear all;

t=0:.01:1;

x1=sin(2*pi*4*t);

h=length(x1);

nx=0:h-1;

subplot(2,2,1);

plot(nx,x1);

xlabel(‘nx’);

ylabel(‘amplitude’);

title(‘input signal’)

y=fliplr(x1);

nf=-fliplr(nx);

subplot(2,2,2);

plot(nf,y);

xlabel(‘nf’);

ylabel(‘amplitude’);

title(‘folded signal’);

**Addition:**

Addition of signal may be defined as adding of two continuous signals x_{1}(t) and x_{2}(t) at every time instant.

c(t) = x (t) + y (t)

clc;

close all;

clear all;

t=0:.01:1;

x1=sin(2*pi*4*t);

x2=sin(2*pi*8*t);

subplot(2,2,1);

plot(t,x1);

xlabel(‘time’);

ylabel(‘amplitude’);

title(‘input signal 1’);

subplot(2,2,2);

plot(t,x2);

xlabel(‘time’);

ylabel(‘amplitude’);

title(‘input signal 2’);

y1=x1+x2;

subplot(2,2,3);

plot(t,y1);

xlabel(‘time’);

ylabel(‘amplitude’);

title(‘addition of two signals’);

**Multiplication:**

Multiplcation of signal may be defined as multiplying of two continuous signals x_{1}(t) and x_{2}(t) at every time instant.

C(t)=x(t) y(t)

clc;

close all;

clear all;

t=0:.01:1;

x1=sin(2*pi*4*t);

x2=sin(2*pi*8*t);

subplot(2,2,1);

plot(t,x1);

xlabel(‘time’);

ylabel(‘amplitude’);

title(‘input signal 1’);

subplot(2,2,2);

plot(t,x2);

xlabel(‘time’);

ylabel(‘amplitude’);

title(‘input signal 2’);

y2=x1.*x2;

subplot(2,2,3);

plot(t,y2);

xlabel(‘time’);

ylabel(‘amplitude’);

title(‘multiplication of two signals’);

**Scaling:**

Scaling is defined as time expansion are compression of a given signal. Mathematically is represented as

Y(t)=x(at)

clc;

close all;

clear all;

t=0:.01:1;

x1=sin(2*pi*4*t);

A=2;

y=A*x1;

figure;

subplot(2,2,1);

plot(t,x1);

xlabel(‘time’);

ylabel(‘amplitude’);

title(‘input signal’)

subplot(2,2,2);

plot(t,y);

xlabel(‘time’);

ylabel(‘amplitude’);

title(‘amplified input signal’);