EE511 Day 2 Class Notes
Laurence Hassebrook
Updated 8-29-03
Friday 8-29-03
GENERIC COMMUNICATIONS SYSTEM
A generic communication system is a mechanism for moving information from point A to point B
over time.
Generic Communications System
8-26-03
LGH
A/D
Computer
Encoder
Modulator
Transmitter
Transducer
Medium
Sensor
Demodulator
Receiver
Decoder
Computer
D/A
TRADITIONAL “NARROW” BAND MODULATION
Traditional “narrow” band modulation consists of a carrier sinusoidal waveform modulated by an
information signal. There are two basic forms of modulation, (1) amplitude modulation and (2)
frequency modulation. Amplitude modulation modulates the amplitude of the carrier waveform and
frequency modulation amplifies the frequency, or phase of the carrier waveform. We refer to this
approach as narrow band because the frequency bandwidth of the information signal (i.e.,
“baseband”) is assumed to be much less than the carrier frequency. Multiple narrow band
“channels” are combined by separating them in frequency by having sufficiently different carrier
frequencies. A generic narrow band equation is
st   at cos2 f c t t   t 
where a(t) is the “amplitude” modulation, fc(t) is the carrier frequency and “frequency” modulation
is accomplished by varying either fc(t) or (t).
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CONTEMPORARY “WIDE” BAND MODULATION
A problem with narrow band modulation is that the frequency spectrum is used us by multiple
channels and the antenna/transducer technology needed to transmit and receive the information
becomes more complicated and expensive. A solution is to modulate information so that it spans the
same frequency range and different channels can be summed together, transmitted and received
across the medium, then separated into the original channels of information. Thus the channels
share the same spectrum and a single simpler antenna/transducer may be used to interface to the
medium. The modulation technique for this is sometimes called spread spectrum. The most well
known approach is to define symbols as finite length random signals. So if two random signals are
chosen to represent two symbols, then a binary communication channel can be implemented. The
random signals are chose to contain the same amount of energy yet when multiplied and integrated
together, the result is 0. In other words the symbols are chosen to be orthogonal and not share any
redundant information.
EXAMPLE OF WIDE BAND MODULATION
The most basic form of wide band is spread spectrum such that each symbol is represented by a
random function, T seconds long. The functions are designed to have an energy E and are
orthogonal to each other.
INTEGRATION
The Fourier Transform (FT) as well as many other methods for signal analysis are based on
integration. Integration yields characteristics about an individual signal as well as a comparison
between signals.
TIME AVERAGE

T / 2 a
  1 T / 2a dt  1  rect  t  a dt
T
T 
 T 
RECTANGLE FUNCTION
 t  1
rect    
 T  0
t T /2
else
MOVING AVERAGE
Moving Average is same as time average except “a” is a variable that is scanned as part of the
output such that

1 T / 2 a
1
t a

f a,   
dt   rect 
dt

T
/
2

a
T
T 
 T 
PROJECTION INTEGRAL
2
y ab 
t2
1
at bt dt

t 2  t1 t1
ENERGY
y aa   a t a t dt  E
t2
t1
AVERAGE POWER
t2
1
y aa 
at at dt  Pave
t 2  t1 t1
ORTHOGONALITY
t2
1
y ab 
at bt dt  0

t 2  t1 t1
Example: a(t)=cos(2fct), b(t)=sin(2fct)
Show example for yab, yaa and ybb. Use trig identities for cos2, sin2 and sinAcosA.
NORMALIZED PROJECTION
Normalized projection is used to define a variation range of yab such that
at bt 
y ab 
a 2 t  b 2 t 
where
0  y ab  1
which is convenient measure for automatic signal detection.
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