** LEARNING SIGNAL AND SYSTEM USING MATLAB (PART _2)**

**Question : 01**

**Give two examples of Odd and Even signals each and plot them in MATLAB.**

**Solution:**

**Example of even signals:**

**1) y=x^2 is a even signal**

Write the following command in the matlab command window.

t=-1:0.01:1;

y_1=(t.^2);

subplot(1,2,1);

plot(t,y);

xlabel('Time axis');

ylabel('Amplitude axis');

title('y=x^2 signal')

As we know if a signal is even the it is symmetric about origion i.e x(t)=x(-t)

y_2=((-t).^2);

subplot(1,2,2)

plot(t,y_2)

xlabel('Time axis');

ylabel('Amplitude axis');

title('y=(-x)^2 signal')

**Out put are shown in figure given below.**

**2) **Next example of even signal is y=(4*t.^4-4*t.^2)

Write the following command in matlab.

>> t=-1:0.01:1;

y_1=(4*t.^4-4*t.^2);

subplot(1,2,1);

plot(t,y_1);

xlabel('Time axis');

ylabel('Amplitude axis');

title('y=4x^4-4x^2 signal')

As function is even so it is symmetric about origion Ii.e x(t)=x(-t)

y_2=(4*(-t).^4-4*(-t).^2);

subplot(1,2,2);

plot(t,y_2);

xlabel('Time axis');

ylabel('Amplitude axis');

title('y=4(-x)^4-4(-x)^2 signal')

**output is shown below:**

**Examples of Odd signals:**

**1)** y=x^3 is a odd signal

t=-1:0.01:1;

y_1=(t.^3);

subplot(1,2,1);

plot(t,y_1);

xlabel('Time axis');

ylabel('Amplitude axis');

title('y=x^3 signal')

Now signal is odd so x(t) is not equal to x(-t).

y_2=((-t).^3);

subplot(1,2,2);

plot(t,y_2);

xlabel('Time axis');

ylabel('Amplitude axis');

title('y=(-x)^3 signal')

** **

**2)** y=tanh(x) is odd signal

>> t=-1:0.01:1;

y_1=tanh(t);

subplot(1,2,1);

plot(t,y_1);

xlabel('Time axis');

ylabel('Amplitude axis');

title('y=tanh(t) signal')

Now signal is odd so x(t) is not equal to x(-t).

y_2=tanh(t);

subplot(1,2,2);

plot(t,y_2);

xlabel('Time axis');

ylabel('Amplitude axis');

title('y=tanh(-t) signal')

**Question # 2 **

** Periodic and Aperiodic Signals **

**Is the given signal periodic or Aperiodic?**

**Plot the signal in MATLAB to verify your answer.**

**Solution: Write the following code in matlab command window.**

t=0:0.01:1;

a=2;

f=3;

y=a*sin(2*pi*f*t);

time=-1:0.01:0;

y_1=a*cos(2*pi*f*t);

plot(t,y,time,y_1)

As we know that signal is periodic if its repeats itself after an appropriate amount of shift.But this signal is not repeating itself after shifing any amount of time.

**Output:**

**Question # 3**

** Classification of Signals**

**Are y(t) and z(t) Energy signals or Power signals? Give reasons for your answer using the results in last question.**

**Solution :**

Y(t) is neither a energy nor a power signal because both are inf.

Z(t) is a power signal because it have finite power i.e 0.5