How to plot Message Signal using MATLAB ?? (Quick Question Need Help)

Hi,

I have an output for a FM transmitter in the form:

y(t) = cos ( 2*pi*t + 2*pi (integral from 0,t of m(tau) dtau ) )

I need to create a message signal of the following:

m_1(t) =

{

   1  when cos(t) >= 0

   -1  when cos(t) <  0

}

I need to create the message signal above in MATLAB and then find the corresponding FM signal.

However, I am unclear on how to graph the message signal.. Can you please show me how?

Thank you.

Answer 1

[Richard Brown]

First, note that the integral of the message will be zero up to any multiple of 2*pi. The integral will then be a piecewise linear function that only requires evaluating on [0,2*pi). It's straightforward to do this by hand

pp = interp1([0, pi/2, 3*pi/2, 2*pi], [0, pi/2, -pi/2, 0], 'linear', 'pp');
int_m = @(t) ppval(pp, mod(t, 2*pi));

Then a plot of your FM signal will be

fplot(@(t) cos(2*pi*t) + 2*pi*(int_m(t)), [0 20])

[PG]

Thanks a lot!

Answer 2

[Richard Brown]

m_1 = @(t) 2*(cos(t) >= 0) - 1

t = linspace(0, 100);
stairs(t, m_1(t))

[PG]

Thanks!

So if i want to find the corresponding FM signal

would this be the correct code:

fplot(@(t) cos((2*pi*t) + 2*pi*(quad(m_1,0,t)))

??

Thanks!

[Richard Brown]

No, don't do that, it will be horrible!! (not wrong, just horrible)

See new answer below

[PG]

Well the question asks to find the corresponding FM signal for frequency = 1 in the equation

FM transmitter:

y(t) = cos(2pi*t + 2pi(frequency) * integral (0 to t) of m(tau) dtau

so how would i do that?

Answer 3

[Walter Roberson]

Try a stair plot.

[PG]

but m_1(t) changes value all the time, so its not constant..

it's basically a bunch of unit step functions added together but i don't know how to code that ..