EXPERIMENT 3: AM MATLAB & Actual Experimentation
I. OBJECTIVES
The main objectives of this experiment are:
1. To gain a clearer understanding about double-sideband suppressed carrier (DSB-SC) and
amplitude modulation (AM).
2. To learn how to simulate modulation/demodulation system for DSB-SC and AM using
MATLAB for synthetic and real signals (such as speech).
II. PRE-LAB WORK
1. Read the relevant material in your textbook (Chapter 4)
2. Using MATLAB, perform the following:
a. X = [ 0 1 2 3 4 5]
b. Y= [ 1 2 3 4 5 6]
Now multiply x by y using two ways. The first one is the usual MATLAB multiplication
(star(x*y)) and the other one is what we called point-wise array multiplication (a dot
followed by a star (x.*y.). What is the difference between the two?
3. Using MATLAB generate a vector t= [ 0: 0.001: 1]. Then generate m=cos(2*pi*t). Plot m,
v, and the product x = mv. Are you going to use multiplication between matrices or
vectors that are representing a function?
III. INTRODUCTION
Amplitude modulation (AM) is the family of modulation schemes in which the amplitude
of a sinusoidal carrier is changed as a function of the modulating message signal. This type
of modulation schemes includes many variants, such as double- sideband suppressed carrier
(DSB-SC), single sideband (SSB) conventional AM, and vestigial- sideband (VSB). Refer to
your textbooks for ample details on amplitude modulation techniques. In this lab, we focus
in particular on DSB-SC and conventional AM.
DSB-SC AM:
In DSB-SC AM, the amplitude of the modulated signal is proportional to the message signal.
The time-domain representation of this scheme is given by:
() = ()( )
Where ( ) is the carrier signal frequency and () is the message signal. The transmission
bandwidth is twice the bandwidth of the message signal.
Conventional AM:
AM is similar to DSB-SC, but it also includes a pure carrier (non-modulated) component in the
Transmitted signal. The message signal () is replaced by [ + ()], () is the normalized
message signal and Is the modulation index. Therefore, the AM signal will be:
() [ + ()]( )
The existence of the sinusoidal component makes the AM scheme less economical in terms of
power utilization as compared to DSB-SC scheme. However, the demodulation of AM signals is much
cheaper than the demodulation process of DSB-SC signals. The conventional AM demodulation process
is simply done by employing envelope detectors.
For the bandwidth, the AM signal has the same transmission bandwidth as the DSB-DC transmission
bandwidth.
IV. LAB WORK
1. Use MATLAB to simulate the following block diagram
Assume = and let () = (). Use a carrier frequency of = .
Plot x(t), y(t), w(t),and v(t), and their magnitude spectrums each in a two-panel figure.
Define the time vector t as [: ] where ts is the step size given by =
At the receiver end, you need to design a Low Pass Filter (LPF). In MATLAB, you can use a type of filters
known as Butterworth filters. For example, you can design a given filter with some order n and cut off
frequency w, which is typically normalized in MATLAB and given by 2fcts (where ts is the sampling step
size). To obtain the filter coefficients, the statement will be [numden]=buttef(n, 2fcts), where num and
den are the numerator and denominator coefficients of the rational representing the analog filter. You
can use n = 5 for example. Once you obtain these coefficients, you can use the MATLAB function filter to
filter the signal w(t) using the designed LPF. That is, v=filter(num,den,w).
Refer to the additional notes below for the further discussion on how to use filters in MATLAB.
Using MATLAB Functions: cos, fftshift(fft( )), butter, filter, abs, plot, subplot, figure, xlabel, ylabel, title.
2. Repeat Part 1 with 2 different values for the receiver phase offset: = & . What do
you notice at the receiver end? Is there any difference between the recovered signal
here and the one obtained in Part 1? Why is that? And what is the solution to this
problem?
Repeat Part 1 by making () = ( + ())( ) where is the
modulation index of the AM wave, is the carrier amplitude (set it equal to 4), and
() is the normalized version of x(t). Set it to be 0.5 (50% modulation).
3. At the demodulator, you can implement the functionality of the simple envelope
detector that you studied in class (built with a diode, a capacitor and resistor) by using
simple MATLAB code to produce full-wave rectification (absolute value function),
followed by low-pass filtering. This is illustrated in the following block diagram. You
need to think about setting the appropriate cutoff frequency for the LPF. In addition,
you can also add a mechanism to remove the DC component from the signal
4. Repeat Part 3 by letting the modulation index equal to 1.2. What will happen to the r
received signal? Explain.
5. Load the file called Exp3Part5.mat. This data file contains:
a. A vector called ms, which is speech signal sampled with = /
b. A vector called t that represents time.
With a carrier of 24kHz, transmit and receive ms using the AM system in part 3 with =
. & . . For both cases show the following:
a. In one figure with two panels, the time and frequency domain representations of
the modulated waves.
b. Listen to ms by typing (sound(ms,96E3), pause, then press Enter to continue). Also
listen to the received signal v by typing soung(v,96E3).
Comment on the differences between the two signals.
Note: In order to be able to see the spectrum of the signal ms, after plotting the magnitude spectrum of
ms, (denoted by Ms) vs. f, type:
axis((-4E3, 4E3, 0, max(|Ms|)])
Useful MATLAB Functions: load, sound, pause, axis.
V. Additional Notes (Filters in MATLAB):
To further understand how to use filters in MATLAB, recall from EE207 that the rational
transfer function of a filter can be expressed in terms of the Laplace variable s by:
+ + + +
() =
+ + + +
Where the as and bs define the transfer function coefficients. These coefficients
completely characterize the filter response. MATLAB returns these two vectors as a
result of designing a filter with a certain type (e.g., Butterworth, etc) and cutoff
frequency. For example, with num=[ , 1 , , 0 ] and den[ , 1 , , 0 ] the
filter design is done by: [num,den]=butter(n,2*fcts).
Notice also that the filter order n is important to specify. For example, t is shown that
for these Butterworth type filters, as the filter order increase the filter response will
approach that of an deal brick-wall response.
