ece 4710: lecture #7 1 overview chapter 3: baseband pulse & digital signaling encode analog...

ECE 4710: Lecture #7 1

Overview

Chapter 3: Baseband Pulse & Digital Signaling Encode analog waveforms into baseband digital signals

» Digital signaling is low cost, flexible, and has many other benefits

Compute spectrum for the digital signals» What is the bandwidth required for effective transmission of digital

signal?

Filter baseband signals to minimize bandwidth» Required to ensure efficient utilization of available spectrum

Examine affect of filtering on ability to recover digital information» Filtering can introduce Inter Symbol Interference (ISI) leading to

imperfect recovery of digital data


Pulse Amplitude Modulation

Pulse Amplitude Modulation = PAM Basic method for converting analog signal to a pulse-type

signal where amplitude of pulse represents analog information

First step required for converting an analog waveform to a PCM (digital) signal » PCM = Pulse Code Modulation (studied next)

PAM is used by itself in a few limited applications Two classes of PAM signals:

» Natural sampling or gating easy to generate» Instantaneous “flat-top” sampling PCM conversion


Natural Sampling PAM

Natural Sampling PAM Let w(t) be analog waveform bandlimited to B Hz

fs = 1 / Ts 2 B (Nyquist Sampling)

= duration of sampling pulse < Ts

d = duty cycle = / Ts

» % time the pulse is “on” in a each period

k

s

s

kTtts

tststwtw

)( bygiven waveform

switchingr rectangula a is )( where)()()(


Natural Sampling PAM

w(t) s(t)

ws(t) = w(t) • s(t)


PAM Generation

Generation of natural sampling PAM is easily done with existing CMOS hardware bi-lateral switch + clock


PAM Spectrum

What is frequency spectrum of natural sampling PAM?

Recall impulse sampling results:

Multiplication in time is convolution in frequency:

Spectrum of impulse sampled signal is the spectrum of the unsampled signal that is repeated every fs Hz

n

ssn

ss

ss nffWT

nffT

fWtwfW )(1

)(1

)()]([)(

tTs

f

fs 2fs-fs-2fs 0

. .

.. . .

......s(t) )]([ ts


PAM Spectrum

In the limit as 0 then PAM s(t) impulse sampling Natural sampling PAM is a real-world way of impulse

sampling It should not be surprising that spectrum of the unsampled

signal is repeated every fs Hz in the PAM signal spectrum What is effect of non-ideal ( 0) PAM sampling?

Series of impulse functions whose amplitudes vary as a function of sin x / x

dn

dndcnffctsfS n

nsn

sin where)()]([)(


PAM Spectrum

Ideal Impulse Sampling

Non-ideal natural sampling PAM

tTs

f

fs 2fs-fs-2fs 0

. .

.. . .

......s(t) )]([ ts

ft

Ts

fs 2fs-fs-2fs 0 . .

.. . .

......s(t)

)]([ ts


PAM Spectrum

PAM spectrum is convolution of baseband analog signal spectrum, W(f), with non-ideal PAM sampling function

Assume rectangular baseband spectrum:dn

dndcfnfWcfW

fnffWcfnfcfWfSfWfW

nsn

ns

sn

nn

sns

sin ere wh)()( that so

)()()()()()()(

fs 2fs-fs-2fs 0 . . .

. .

.


Baseband spectrum repeated @ harmonics of sampling frequency

PAM BW is many times larger than original signal BW For d = 1/3 and fs = 4 B the FNBW is 3 fs = 12 B for PAM signal

factor of 12 increase !!

PAM Spectrum


PAM Recovery

Original spectrum can be recovered using LPF on n = 0 harmonic Harmonics have identical replicas of shape (not amplitude) of W(f) assuming

Nyquist sampling fs 2 B (no aliasing or spectral folding)

Why choose fs = 4 B (example) when Nyquist rate is fs = 2 B ?? Oversampling is often done since ideal “brick wall” LPF is not physically

realizable Real LPF filter rolloff can allow signal energy from adjacent spectral copies to

distort baseband signal spectrum

Previous example assumes bandlimited baseband signals Pre-filtering of large bandwidth baseband analog signals is done to limit

bandwidth and eliminate aliasing


Product detection can also be used to recover baseband spectrum from other harmonics, e.g. n = 1, 2, 3, etc. Multiply PAM signal with cos (2 n fs t ) and then LPF

» Shifts frequency band @ n fs back to baseband (f = 0)

Why?» Baseband PAM signal

may be corrupted by low

frequency noise» Higher bands are usually

free of most noise» Use more complicated product

detection to get better signal

PAM Recovery


Flat-Top PAM

Instantaneous sample and hold of analog signal produces “Flat-Top PAM”

Instantaneously sampled w(t) determines amplitude of constant rectangular pulse

Compare to natural sampling PAM

Amplitude variation of w(t) preserved within pulse width

2/||

2/||

,0

,1t h(t) where)()()(

t

tkTthkTwtw

ksss

k

ss

kTttwtw

)()(


Flat-Top PAM

w(t) s(t)

ws(t) = w(t) • s(t)


Flat-Top PAM Spectrum

Spectrum for flat-top PAM is given by

The amplitude of original baseband spectrum W(f) is distorted by H(f) !!

Compare to natural sampling PAM

cn is constant and does not distort spectral shape of W(f)

k

ss

s ff

fHfkfWfHT

fW sin

)( e wher)()(1

)(

dndn

dcfnfWcfW nsn

ns sin

ere wh)()(



Assume bandlimited baseband spectrum for W(f)


Harmonic (n 0) replicas of W(f) significantly distorted by H(f)

Baseband (n = 0) W(f) replica has small distortion at higher frequencies



Flat-Top PAM Recovery

LPF baseband spectrum Can compensate for high-frequency distortion by adding

additional gain to higher frequencies of low pass filter response» Equalization filter with transfer function 1/ H(f)

Product detection can also be used Add pre-filter before product multiplier to make spectrum

flat


PAM Signal Transmission

Large BW of PAM signals is undesirable for wireless and/or long-distance transmission PAM BW is many times larger than original baseband

signal BW Magnitude and phase response of channel will likely

distort PAM signal considerably S/N performance of PAM is worse than straight

transmission of analog signal Primary use of PAM is for conversion to PCM

Digital PCM signal has many performance advantages compared to analog or PAM signal transmission

ece 4710: lecture #7 1 overview chapter 3: baseband pulse & digital signaling encode analog...

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