Digital Communications

Digital Communications

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Objectives On completing this chapter, you should be able to: 

Compare analog and digital communication techniques and discuss the appropriate use of each,






























Describe pulse code modulation and calculate the number of quantizing levels, the bit rate, and the dynamic range for PCM systems,






























Describe and compare the line codes in terms of frequency components and clock-information content,





























Digital Communications The process of transmitting digital pulses directly (wired (wired system), system), or digitally modulated analog carrier (wireless (wireless system), system), from one point to another.





























Analog & Digital Digital Systems Analog signal with baseband transmission Analog Source

Baseband Channel

Analog Destination

Analog transmission with modulation and demodulation Analog Source

Modulator (Tx)

Channel

Demod. (Rx)

Analog Destination































Analog & Digital Digital Systems Digital signal transmitted by modem Analog Digital Modem Source Channel

Modem

Digital Destination





























Why Digital Communications? Communications?

More noise resistant

Wide BW requirement





























The scientific study of the efficient use of .





























Information Measure 





























Average Information (Entropy) 































Relative Entropy































Redundancy































Example































Example































Information Capacity



















































































































































































































































































































































































































Simplified BD of a Single-Channel Simplex PCM System PCM Transmitter PAM

Parallel Data

BPF

Sample & Hold

ADC

P-S

Sample pulse

Conversion clock

Line speed clock

Input

Serial PCM Code

PCM Receiver

Regenerative Repeater

Serial PCM Code





























PCM Sampling Process of periodically sampling a continually varying analog input signal, then converting these samples to a multi-level PAM signal.

Sampling Techniques





























The incoming analog signal is lowpass filtered and then multiplied by pulse train. It is when tops of the sample pulses retain their natural





























A sample-and-hold circuit is used to keep the amplitude of the sample constant for the duration of the pulse. Aperture Error  an

error

introduced





























Natural v.s. Flat-top Sampling Natural

Flat-topped

Analog Signal

Analog Signal

Sampling Pulse

Sampling Pulse































Sample and Hold Circuit Sampling pulse

+ Analog input

Z1

Q1

+

Z2

PAM out





























Input and Output Waveform Input waveform





























Sample Problem 1.

For the sample-hold-circuit, determine the largest value of capacitor that can be used. Use an output impedance for Z1 of 10 Ω, an on





























Nyquist (1928) (1928) Sampling Sampling Theorem The minimum sampling rate (f s ) for a given PCM system must be twice the highest frequency of the analog input. i nput.





























Aliasing/Fold-Over Aliasing/Fold-Ov er Distortion Occurs when the sampling rate is less than the Nyquist minimum sampling rate.































Alias Frequency































Solution to Aliasing:































Effects of Aliasing































Effects of Aliasing































Sample Problems



















































































































































































































































































































































































































Folded Binary Code Sign

Magnitude

Decimal Value

Quantization Range

1

11

+3

+ 2.5 V to + 3.5 V

1

10

+2

+ 1.5 V to + 2.5 V

1

01

+1

+ 0.5 V to + 1.5 V

1

00

+0

+ 0 V to + 0.5 V

0

00

- 0

+ 0 V to - 0.5 V





























Quantization Error (Qe) A.k.a Quantization Noise (Qn) Results when a given PAM is quantized. (magnitude is rounded off to the nearest available level).





























Illustration of Qe 111

+3V

110

+2V

101

+1V

100

+0V

000

-0V

001

-1V

010

-2V

011

-3V

111

+3V

110

+2V

101

+1V

2.6 V 2V

Analog input

- 1 V

Sample pulse t1

t2

t3





























Reduced Qe Analog input

Sample pulse t1

t2

t3

tN





























Linear Input v.s. Output Transfer Curve Vout

Vout Analog signal quantization quantizatio n error

Vin

Vin

Maximum negative quantizing error

Maximum positive quantizing error































Sample Problems 1.

Determine the quantized level, quantization error and PCM code using Three-bit sign-magnitude (resolution of 1 V) PCM code for the analog





























No. of PCM bits per Sample 

Max. allowable input amplitude



Resolution





























Mathematically: DR

V max 

V min

DR



2

n



1





























Coding Efficiency A numerical indication indicati on efficiently a PCM code is utilized.

Mathematically:

of

how





























Sample Problems 1.

For a PCM system with following parameters, determine: (a) minimum sample rate, (b) minimum number of bits used in the PCM code,































Signal-to-Quantization Noise Ratio































Mathematically:































Sample Problems































Assignment































Linear v.s. Non-Linear PCM Codes



















































































































































































































































































































































































































Sample Problems 1.

For a compressor with A = 5, determine a. the voltage gain for the following relative values of Vin: Vmax, 0.75 Vmax, 0.5 Vmax and 0.25 Vmax. b. The compressed output voltage for a maximum input voltage of 4 V. c. Input and Output Dynamic ranges and





























Digital Compandin Companding g Involves compression in the transmitter after the input has been converted to a linear PCM code and then expansion in the receiver prior to PCM decoding.





























PCM System w/ Digital Companding PCM Transmitter

PAM Parallel Data

BPF

Sample and Hold Ckt.

Compressed PCM Digital Compressor

ADC

P-S

Input Sample pulse Serial PCM Code

PCM Receiver

Conversion clock Line speed clock

Regenerative Repeater PAM

Serial PCM Code





























12-bit-to-8-bit Digital Companding





























Digital Compression Error A numerical indication indicati on efficiently a PCM code is utilized.

Mathematically:

of

how































Sample Problems 1.

Determine the 12-bit linear code, the quantization error, the 8-bit compressed code, the decoded 12-bit code, analog





























Two Main Main Categories of Data Data Compression Compression 1.

Lossless Compression 

Involves transmitting all the data in the original signal





























Lossless Compression 

Look for redundancies in the data which is a technique called





























Lossy Compression 

Can involve reducing the number of bits per sample or reducing the sampling rate





























Vocoder (voice coder) 

is a special voice encoder/decoder used for digitizing speech signals



Is designed to reproduce only the short-term































Encoding Techniques































Encoding Techniques































Encoding Techniques































Encoding Techniques































Encoding Techniques



















































































































































































































































































































































































































Pulse Transmission 

Approximately 90% of the signal contained within the first spectral null.

power

is





























Intersymbol Interference (ISI) 

Happens when the ringing tails of several pulses overlapped, thus interfering the with the major pulse lobe. Energy in the form of spurious responses from the third and fourth impulses from one pulse appears during the sampling instant (T = 0) of another pulse.



Rectangular pulses will not remain rectangular in less than an infinite bandwidth. The narrower the bandwidth, the more rounded the pulses.



It causes crosstalk between channels

that occupy






























Four Primary Causes

1.

Timing Inaccuracies Causes if the rate of transmission does not conform to the ringing frequency designed into the channel 

2.

Insufficient Bandwidth






























Four Primary Causes of ISI

3.

Amplitude Distortion Pulse Distortion  results when the frequency characteristics of a communications channel depart from the normal or expected values. It occurs when the peaks are reduced, causing improper ringing frequencies in the time t ime domain. Amplitude Equalization  compensation for pulse distortion

4.

Phase Distortion





























Eye Pattern or Eye Diagram 

is a convenient technique for determining the effects of the degradations introduced into the pulses as they travel to the regenerator



All waveforms are superimposed over adjacent signaling intervals































Sample Eye Diagram 

Vertical Hairs  represent decision time Horizontal

Hairs































ISI Degradation

Where:

H = ideal vertical opening (cm)





























Signal Power in Binary Digital Signals Binary Digital Signals a.

when τ/T < 0.5

b.

When τ/T = 0.5

Digital Communications

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