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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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Presentation Transcript
slide1

Simulation in

Digital Communication

slide2

chapter # 6

Digital Transmission Through Bandlimited Channels

slide3

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”)

slide4

to determine the spectral characteristics of

the random process V(t), we must evaluate

the power spectrum.

1)mean value

2)autocorrelation function

slide6

The power spectrum of V(t) is the Fourier

transform of the average autocorrelation function.

The power spectrum of amplitude sequence an

slide7

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.

slide10

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.

slide11

SOLUTION

The power spectrum of the PAM signal was given by

from

and using also the data we can replace...

slide14

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

slide15

we can also express it as an

envelope delay (group delay)

:

slide16

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)

slide17

Effect of channel distortion

channel

input

channel

output

equalizer

slide18

Average amplitude and delay characteristics

of a medium-range telephone channel,

slide19

Impulse response of the average channel

with amplitude and delay shown before

slide20

Problem 6.3

Answer

ip_06_03

T.B.D

slide21

Impulse response

Frequency response

of linear phase FIR filter

slide22

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

slide23

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,...)

slide27

Problem 6.5

The impulse response of a two-path(multipath)

radio channel can expressed as:

random processes

the delay between 2 paths

slide28

Answer

ip_06_05

simulate such a channel on the computer

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