# Lab Assignment III: FM simulation (13 Apr 2015)

```Apr 13th, 2015
IZMIR UNIVERSITY OF ECONOMICS
EEE 302 LABORATORY ASSIGNMENT III
In this assignment, you can use the provided Matlab file, FM_simulation.m, to simulate
narrowband and wideband Frequency Modulated (FM) waves and analyze their frequency
spectrum.
(1) Develop a Matlab code to simulate the modulation of a single-tone FM wave with 100 kHz
carrier (of unit amplitude) and a modulating wave
m(t )  sin( 2 1000t )
Plot the time-domain FM signals for modulation indices {0.1, 0.5, 1, 5, 10}.
(2) Write a Matlab code to compute and plot the magnitude and phase of the spectrum (using fft()
function) of the corresponding FM signals generated in part (1).
(3) For a single-tone FM signal, the spectral lines are located at the frequencies,
f c  k1 f m1 , k1  0,1,2,...
The power in the spectral line at fc+k1 fm1 is given by
Pk1 , k 2  J k1 (  ) P
2
where P is the total power in the modulated carrier (at fc, corresponding to k1=0), and Jk(.) is a
Bessel function of the first kind of order k.
J k (  ) can be computed in Matlab as
&gt;&gt; besselj(k,beta)
The power in a specific harmonic relative to the power in the carrier can be computed as
Pk1
P0
Compute
P1 / P0
as a function of
 20 log[
.
J k1 (  )
J 0 ( )
]
(dBc )
(4) For each  value, determine the power in the harmonics of the modulating frequency
{fm1=1000 Hz) about the carrier {fc+k1 fm1 }. Compute how many side frequencies are required for
90% of the total power in each case?
```