Generation of Different Types of Signals in Matlab

In this article it is shown how to generate various important signals in Matlab. The different types of signal includes Unit Impulse, Unit Step, square, rectangle. sawtooth and others. In the study of communication system these signals appear frequently and thus knowledge about how to generate them in Matlab is important. For more see matlab tutorials and matlab software download.

Here we show the generation of following signals-

1. Unit Impulse signal
2. Unit Step signal
3. Signum signal
4. Square wave signal
5. Rectangular wave signal

1. Unit Impulse (Delta Function):

The dirac delta function (continuous and discrete)is defined as-
\[\delta(t)=\begin{cases}1 & t = 0\\0 & otherwise\end{cases}\]
or,

\[\delta(n)=\begin{cases}1 & n = 0\\0 & otherwise\end{cases}\]
To generate a unit Impulse the following matlab statement can be used-

>> Imp=[1 zeros(1,N-1)]

Let the number of zeros be N=8, then

>> Imp=[1 zeros(1,7)];

This creates a sequence- 1 0 0 0 0 0 0 0

Applying stem function-

>> stem(Imp)

gives the following graph-

Unit Impluse Sequence

To create shifted unit impulse we can use the following matlab statement-

>> Imp_shift= [zeros(1,k-1) 1 zeros(1,N-k)]

If N=8 and k=2,

>> Imp_shift[zeros(1,1) 1 zeros(1,6)]

gives the sequence- 0 1 0 0 0 0 0 0

and,
>> stem(Imp_shift)

gives the following graph-

Shifted Unit Impulse

2. Unit Step Function

The unit step function is defined as-
 \[u(t)=\begin{cases}1 & t \geq 0\\0 & t < 0\end{cases}\]
or,
\[u(n)=\begin{cases}1 & n \geq 0\\0 & n < 0\end{cases}\]

To generate unit step sequence of length N the following matlab statement can be used-

u_step=[ones(1,N)]

let N=8, then we have

>> u_step=[ones(1,8)]

gives the sequence- 1 1 1 1 1 1 1 1

>> stem(u_step)

gives the following graph-

unit step sequence

Similarly, to generate a shifted unit step sequence u(n-k)we can use the following matlab statement-

u_step_shift=[zeros(1,k) ones(1,N)]

let N=8, k=3 then,

>> u_step_shift=[zeros(1,3) ones(1,8)]

gives the sequence-  0 0 0 1 1 1 1 1 1 1 1 (that is, three Zeros followed by eight Ones)

>> stem(u_step_shift)

gives the following graph-

shifted unit step sequence

Another method to generate unit step function is to use the heaviside(x) matlab function. The following command and graph illustrates generation of unit step function using this heaviside(x) command.

>> n = -5:0.01:5;
>> u_step = heaviside(n);
>> plot(n,u_step)

This gives the following graph-

unit step function using heaviside function

It's also easier to use heaviside function to generate a shifted unit step u(t-to) (or u(n-k)) as illustrated below-

>> n = -5:0.01:5;
>> u_step_shift = heaviside(n-2);
>> plot(n,u_step_shift)

shifted unit step function using heaviside function

3. Signum Function

The Signum function is defined as-

\[sign(t)=\begin{cases}1 & t< 0\\0 & t=0\\-1 & t>0\end{cases}\]
or,
\[sign(n)=\begin{cases}1 & n< 0\\0 & n=0\\-1 & n>0\end{cases}\]

To generate the sign(n) function the matlab code is-

>> n=-5:0.01:5;
>> y=sign(n);
>> plot(n,y)

The graph is shown below-

Signum function

4. Square wave signal

Square signals can be generated using the square(t,duty) function. This function generates a periodic square wave with period T=2*pi with +ve and -ve unity peak value over the range defined by parameter t. The parameter duty defines percentage of period T over which the square wave remains positive.

Example: To generate a square wave over two period 2T=4*pi and amplitude of 2

>> t=0:0.001*pi:4*pi;
>> y=2*square(t);
>> plot(t,y)

The plot is shown below-

Square wave signal

5. Rectangular wave signal

To generate rectangular signal in matlab we can use rectpuls(t) or rectpuls(t,w). rectpuls(t) function generates a continuous, aperiodic and unity height rectangular pulses. rectpuls(t,w) is same as rectpuls(t) with additional parameter w which allows to define width of the pulse.

Example:
To generate a rectangular pulse of amplitude 2, pulse width 3 we use the following commands-

>> t=-5:0.01:5;
>> y=2*rectpuls(t,3);
>> plot(t,y)
>> axis([-6 6 -0.5 3]);

The graph generated is shown below-

rectangular pulse