DSP Lab Experiments - Digital Signal Processing: An Introduction with MATLAB and Applications - page 324

Task 5

In the above code, use the other two approximations for the delta function and
repeat the procedure in Task 4. Plot the three MSE curves on one figure and
compare your results. Decide which approximation is better for practical
implementation of the delta function. Take Ts = 0.005 , repeat the same steps,
and see whether the MSE is reduced.

Experiment # 2: Generation and Demodulation of AM Signals

Introduction

Information-bearing signals are normally of low-frequency nature. For example,
the frequency content of the human speech signal ranges from 200 to 4 kHz, while
audio signals (in general) can reach up to 20 kHz. For long-range transmission of
signals, we should convert them to radio waves and transmit them through
antennas. The antenna dimensions [length or diameter (for dish antenna)] should be
proportional to k/4 or k/2, k being the wavelength, where c = kf = 3 9 10 8 m/s.
Hence, for baseband radio transmission of a speech signal through, we need an
antenna of length c =ð 4 4000 Þ 18 : 7km : Therefore, we should increase the
frequency of the signal (without changing the information) before radio
transmission. This is called modulation. In fact, high frequency is also more
resistive to noise in space. Mobile phones operate near 900 MHz, UHF TV operates
in the range 300-800 MHz, and satellite links operate in the frequency range from
few hundred MHz to 40 GHz or more.
Amplitude modulation (AM) is widely used in communication systems. The
standard AM modulator multiplies the message m(t) by a scaling factor b (called
the modulation index) and a high-frequency sinusoid called the carrier,
c ð t Þ¼ A c cos ð x c t Þ , and then add the result to the carrier (for synchronization
purposes) to get the standard AM signal

x ð t Þ¼ A c ½ 1 þ bm ð t Þ cos ð x c t Þ ð 1 Þ

The magnitude spectrum of this signal is given by:

" (

d ð f f c Þþ d ð f þ f c Þ ) þ b
2

(

M ð f f c Þþ M ð f þ f c Þ )

#

1
2

X ð f Þ¼ A c ð 2 Þ

For demodulation of the AM signal at the receiver, an envelope detector is
usually used. However, if the AM signal is weak and the modulation index is
small, it is better to use a square-law device followed by a low-pass filter as shown
in Fig. D.3 below, where r(t) is the received AM signal and s(t) is the demodulated
signal.