EE471 Digital Communication SystemsLecture 4

Chapter 6: Sampling and pulse modulationAssignment:

HW 2A: 6.2-1, 6.3-1, 6.3-3

6.2: Pulse-amplitude modulation (PAM)

Analog signal and corresponding PAM signal

Flat-top sampling (a) sample & hold circuit (b) waveform

Flat Top Sampled Signalsx p(t )=∑

k

x (k T S ) p(t−k T S )

= p(t)∗∑k

x (k T S)δ (t−k T S )= p (t )∗xδ (t )

where x(k T S )=sampled message, and

p (t−k T S )=pulse that carries the message.

⇒ X p( f )=P ( f )X δ( f )

PAM SignalsWe can ensure that the pulses are unipolar byusing 1+μ x(t )as the input. This is the desiredPAM signal. Reconstruction would requirelowpass filtering, equalization and a DC block.

For adequate pulse resolution, the channel(or transmission) bandwidth must satify

BT≥1

2 τ≫W.

Flat Top Sampled Signal Spectrum

PAM Spectrum

PAM Summary• Rarely used for single channel communication systems,

but used in conjunction with TDM, data telemetry, and

instrumentation systems

• Time-division __________________ (TDM) systems

• Basis for other digital modulation systems

1 of 2

6.3: Pulse time modulation• Pulse ____________________ modulation (PDM).

Also called pulse width modulation (PWM)

• Pulse position modulation (PPM)

• Info in zero crossings ⇒ potential for wideband noise

reduction

Types of pulse-time modulation

Pulse Time Signal Generation

(a) Generation of PDM and PPM signals

(b) waveforms

The previous system produces trailing-edge modulation.

Reversing the sawtooth produces leading-edge modulation,

while a triangular wave would modulate both edges.

The samples are also ________________________ spaced. This

can be corrected by inserting a sample-and-hold circuit.

Pulse duration modulationAssuming uniform sampling, the duration of thek th pulse isk=0[1 x k T S] .The PDM waveform can be expressed asx pt ≈A f S 0[1 xt ]

∑n=1

∞ 2 A n

sin nt cosnS t

wheret = f S 0[1 xt ] .⇒ xt can be recovered by a lowpass filter anda DC block.

Conversion of PDM or PPM into PAM Pulse time modulationTo preserve information content in the demodulation

process, the received signal must have a fast

risetime⇒ tr≪T S.

Since BT≥1

2 tr

⇒ an extremely system.

In-Class Exercises• Problem 6.3-2

2 of 2