Question

I am little confused on this problem..g(t) = 3π sin(8πt + 1.3)cos(4πt − 0.8) e^sin(12πt)

4. For the signal g(x) in problem 1, calculate the energy of the signal in the window te [0.25, 0.75]. Also calculate the power of the signal.

MATHLAB help

Answer 1

The energy in a signal during the time interval [t1 , t2] is given by the following formula

  ${\color{DarkBlue} E=\int_{t_{1}}^{t_{2}}|x(t)|^{2}dt}$

The power of the signal in the time interval [t1,t2] is given by following formula

  
punto crop de

In the question , it is given that  ${\color{DarkGreen} g(t)=3\pi .sin(8\pi t+1.3).cos(4\pi t-0.8)e^{sin(12\pi t))}}$

We are going to find the above integrals using MATLAB . In MATLAB integration is nothing but summation multiplied by step size h. The code is given below followed by output. In the code we defined as array from 0.25 to 0.75 with step size of 0.0001. Then g is calculated at each value of t. Important thing is , In element by element multiplication we should use ' .* ' instead of simple *.

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t = 0.25:0.0001:0.75;

g=3*pi.*sin(8*pi*t+1.3).*cos(4*pi*t-0.8).*exp(sin(12*pi*t));
E=0.0001*sum(abs(g.^2))
P=0.0001*sum(abs(g.^2))/0.5

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The output is  

>> Energy_of_signal

E =

27.3815

P =

54.7630

>>