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Simulation in Digital Communication. chapter # 6 Digital Transmission Through Bandlimited Channels. 6.2 - The power Spectrum of a Digital PAM Signal. A digtal PAM signal at the input to a communication channl. reciprocal of the symbol rate. pulse waveform.

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Simulation in Digital Communication

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Simulation in digital communication

Simulation in

Digital Communication


Simulation in digital communication

chapter # 6

Digital Transmission Through Bandlimited Channels


Simulation in digital communication

6.2 - The power Spectrum of a Digital PAM Signal

A digtal PAM signal at the input to a communication channl

reciprocal of the symbol rate

pulse waveform

scale factor (where 2d is the “Euclidean distance”)


Simulation in digital communication

to determine the spectral characteristics of

the random process V(t), we must evaluate

the power spectrum.

1)mean value

2)autocorrelation function


Simulation in digital communication

3)average autocorrelation function


Simulation in digital communication

The power spectrum of V(t) is the Fourier

transform of the average autocorrelation function.

The power spectrum of amplitude sequence an


Simulation in digital communication

Problem 6.1

Answer

ip_06_01

Determine the power spectrum of V(t) when {an}

is an uncorrelated sequence and g(t) is the following

rectangular pulse.


Simulation in digital communication

The Fourier trasform of g(t) is

and


Simulation in digital communication

This power spectrum is illustrated in the following

Figure:


Simulation in digital communication

Problem 6.2

Answer

ip_06_02

Suppose the autocorrelation function of the sequence

{an} is

and g(t) is the rectangular pulse.shown at the previous

problem. Evaluate Sv(f) in this case.


Simulation in digital communication

SOLUTION

The power spectrum of the PAM signal was given by

from

and using also the data we can replace...


Simulation in digital communication

Consequently,


Simulation in digital communication

This power spectrum is illustrated in the following

Figure:


Simulation in digital communication

6.3 - Characterization of bandlimited channels and channels distortion

We can characterize many communication

channels as bandlimited linear filters, described

by their frequency response

phase response

Amplitude response


Simulation in digital communication

we can also express it as an

envelope delay (group delay)

:


Simulation in digital communication

nondistorting (ideal) channel

Amplitude response -constant

phase response - linear function of frequncy

(envelope delay -constant)

distorting channel

Amplitude distortion -

Amplitude response isn’tconstant

delaydistortion-

envelope delayisn’tconstant)


Simulation in digital communication

Effect of channel distortion

channel

input

channel

output

equalizer


Simulation in digital communication

Average amplitude and delay characteristics

of a medium-range telephone channel,


Simulation in digital communication

Impulse response of the average channel

with amplitude and delay shown before


Simulation in digital communication

Problem 6.3

Answer

ip_06_03

T.B.D


Simulation in digital communication

Impulse response

Frequency response

of linear phase FIR filter


Simulation in digital communication

Problem 6.4

Window method

if the desired channel response

is C(f) for |f|<W and C(f)=0 for

|f|>W then

Impulse response

for example: if channel is ideal, then C(f)=1, |f|<W

and hence


Simulation in digital communication

Answer

ip_06_04

Let us design an FIR filter with:

W=2000 Hz and Fs =1/Ts=10KHZ.

(this digital filter may be implemented

by sampling h(t) at t=nTs, where Ts

is the sampling interval and n = 0,+/-1,+/-2,...)


Simulation in digital communication

Samples of h(n)


Simulation in digital communication

Frequency response (rectangular window)


Simulation in digital communication

Frequency response (Hanning window)


Simulation in digital communication

Problem 6.5

The impulse response of a two-path(multipath)

radio channel can expressed as:

random processes

the delay between 2 paths


Simulation in digital communication

Answer

ip_06_05

simulate such a channel on the computer


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