Before going towards actual programming part, let us recall the definition of the discrete time signal.

“In discrete time signal, the value of the signal is specified only at a specific time. So signal represented at “discrete interval of time” is called as a discrete time signal.”

### MATLAB Program:

clc;

clear all;

close all;

x=[0:15];

for i=1:16

y(i)=1;

end

subplot(2,3,1)

stem(x,y)

title('Discrete time Step Function')

xlabel('Samples')

ylabel('Step function')

for i=1:16

y(i)=x(i);

end

subplot(2,3,2)

stem(x,y)

title('Discrete time Ramp Function')

xlabel('Samples')

ylabel('Ramp signal')

y=[zeros(1,4),1,zeros(1,11)];

subplot(2,3,3)

stem(x,y)

title('Discrete time Impulse Function')

xlabel('Samples')

ylabel('Impulse function')

for i=1:16

y(i)=exp(-0.22*i);

end

subplot(2,3,4)

stem(x,y)

title('Discrete time Exponential Function')

xlabel('Samples')

ylabel('Exponential function')

z=[1:35]

for i=1:35

y(i)=sin(2*pi*0.1*i)

end

subplot(2,3,5)

stem(z,y)

title('Discrete time Sine Function')

xlabel('Samples')

ylabel('Sine function')

z=[1:35]

for i=1:35

y(i)=cos(2*pi*0.1*i)

end

subplot(2,3,6)

stem(z,y)

title('Discrete time Cosine Function')

xlabel('Samples')

ylabel('Cosine function')

### Explanation:

- Representation of discrete time step function:

x=[0:15];

for i=1:16

y(i)=1;

end

subplot(2,3,1)

stem(x,y)

title('Discrete time Step Function')

xlabel('Samples')

ylabel('Step function')

For representing discrete time step function, let us consider x-axis represents a number of samples and y-axis represents corresponding values of the signal. Here we use two matrix x and y. x=[0:15] represents matrix ‘x’ contains 16 elements from 0 to 15. Then we used one for loop from 1:16 (16 times) in which we define matrix y, which stores ‘1’ entire the matrix. Then we give command subplot(2,3,1). Here we used subplot command because we want all the basic signals on a single display. (2,3,1) represents there are 2 rows and 3 columns of graphs (it means 2*3=6 graphs are possible) 1 indicates that we want this graph at first position.

As we know for continuous signal plotting we use plot command but for a discrete time signal, we have to use stem command.

- Similarly, for discrete time ramp signal, we use y(i)=x(i) keeping all the program same.
- For impulse function we use y=[zeros(1,4),1,zeros(1,11)] that means first 4 elements of the matrix are ‘0(zeros)’ 5th element is ‘1’ and from 6th to 16th it is again ‘0’. Thus y becomes 16 element matrix. Thus we can plot a graph of impulse function using Matlab.
- For exponential signal, we have used exp(-0.22*i). Here negative sign indicates that the nature of the exponential signal is decreasing. But if you remove the negative sign it will become a simple increasing exponential signal.
- Similarly, we can plot discrete time sine and cosine functions using MATLAB

## MATLAB Program

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