MODULE 15

COMPANDING

Prepared by: Engr. Jo-Ann C. Viñas

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OBJECTIVES

1. Advantages and Disadvantages of Digital Communications

2. Review of Pulse Code Modulation (PCM)3. Introduce the concept of companding2. State the importance of companding3. Discuss the two types of companding4. Solve problems involving companding

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PCM APPLICATIONS

PCM is the most commonly used technique in digital communications

1. Telephone System2. Digital Audio Recording3. CD Laser disks4. Voice mail5. Digital Video

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ANALOG

“ANALOG means ‘similar’ or a ‘copy’.”

“An Analog audio signal is an electronic copy of an original audio signal as sound in nature, with a continually

varying signal.”

“Analog copies of any original sound suffers some degree of signal degradation, called generational loss, and signal strength lessens and noise increases for each successive

copy.”

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DIGITAL

“A digital recording is no more than a series of numbers, and hence can be copied through an indefinite number of

generations without degradation. This implies that the life of a digital recording can be truly indefinite, because even if the medium (CD, DAT, etc) begins to decay physically,

the sample values can be copied to a new medium with no loss of information.”

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The established sampling rates for digital audio are:

1. 32 kHz for broadcast digital audio2. 44.1 kHz for CDs3. 48 kHz for digital audiotape (DAT) and digital videotape

( mini-DV and DV)4. 96 kHz or 192. 4 kHz for DVD-audio and BD-ROM (Blu

ray disc) audio

5. 2.8224 MHz for SACD (Super Audio CD) & DSD (Direct Stream Digital)

NOTE:

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ADVANTAGES OF DIGITAL COMMUNICATIONS

1. Digital communication is more rugged than analog communication

2. The viability of regenerative repeaters3. Digital hardware implementation is flexible4. Digital signals can be coded5. It is easier and more efficient to multiplex several

digital signals

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REMOVAL OF NOISE AND DISTORTION FROM DIGITAL SIGNAL

TYPICAL FOUR-LEVEL SIGNAL USING 1, 2, 3, & 4V

BINARY SIGNAL

REGENERATION OF DIGITAL SIGNAL OPERATING WITH 1- AND 5V LEVELS

ANALOG SIGNAL AMPLIFIER STAGES ADD NOISE AT EACH POINT WHILE INCREASING SIGNAL AMPLITUDE, THUS REDUCING SNR

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HARDWARE IMPLEMENTATION IS FLEXIBLE

0 TO +1V ANALOG SIGNAL

2 BITS RESOLUTION

3 BITS RESOLUTION

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DISADVANTAGE OF DIGITAL COMMUNICATIONS

1. Increased bandwidth of transmission

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ADVANTAGES OF DIGITAL COMMUNICATIONS

Audio compression is typically used for 3 reasons:

1. To reduce the file size so that more audio may be stored on a given media format (digital audio players, DVD-video disc, Minidisc. Etc)2. To reduce the file size so that files will download from a Web site faster.3. To reduce the data rate so that files will stream (broadcast) over a network such as the Internet.

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CRITERIA FOR SIGNAL ENCODING

What determines how successful a receiver will be in interpreting an incoming signal?

1. Signal-to-Noise Ratio2. Data Rate3. Bandwidth

An increase in data rate increases bit error rate

An increase in SNR decreases bit error rateAn increase in bandwidth allows an increase in data rate

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PULSE CODE MODULATION

- is a method of modulating in which a continuous analog wave is transmitted in an equivalent digital mode.

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NOTE:

“If a band-limited signal is sampled at regular intervals of time and a a rate equal to or higher than twice the highest significant signal frequency, then the sample contains all the information of the original signal. The original signal may then be reconstructed by use of a low-pass filter.”

PCM TRANSMIT BLOCKS

SAMPLINGSAMPLING QUANTIZINGQUANTIZING ENCODINGENCODING

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QUANTIZATION

Changing from CONTINUOUS IN VALUE to DISCRETE IN VALUE.

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SAMPLING

Changing from CONTINUOUS IN TIME to DISCRETE IN TIME.

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CODING

Code value of sample into 1s and 0s.

PCM PARAMETERS

1. Number of Levels or Codewords (M)2. Bandwidth (Data Rate) (BW)3. Dynamic Range (DR)4. Resolution (Res)5. Coding Efficiency ()6. Quantization Error (Qe)7. Signal-to-Quantization Noise Ratio (SQR)

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1. Number of Levels or Codewords (M)

PCM PARAMETERS

M = 2n

where:M = # of levels, symbols or codewordsn = # of PCM bits used (sign bit excluded) = # of bits per sample

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2. Bandwidth (Data Rate)

PCM PARAMETERS

BW = nfs = fb

where:fs = sampling rate in Hzfb = bit rate in bps

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3. Dynamic Range

PCM PARAMETERS

DR = 2n - 1 DR = Vmax

Vmin

where:Vmax = maximum input voltageVmin = minimum input voltage

DYNAMIC RANGE OF ANALOG SIGNAL

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EXAMPLE

What is the dynamic range of an 8-bit linear sign magnitude PCM spectrum whose maximum decode voltage at the receiver is 1.27 Vp? (ECE BOARD EXAM NOV 2002)

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4. Resolution

PCM PARAMETERS

Resolution = VLSB

where:VLSB = voltage of the least significant bit

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EXAMPLE

Determine the resolution for an 8-bit linear sign-magnitude PCM for a maximum decode voltage of 2.55Vp. (ECE BOARD EXAM NOV 2002)

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5. Coding Efficiency ()

PCM PARAMETERS

=min

max

X 100

where:min = Min # of bits (including the sign bit)max= Actual # of bits (including the sign bit)

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6. Quantization Error

PCM PARAMETERS

Qe =VMIN

2 Qe =

Resolution

2

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7. Signal-to-Quantization Noise Ratio

PCM PARAMETERS

SQR = 10.79 dB + 20 log VS

q

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A. Ideal Signal-to-Quantization Noise Ratio

PCM PARAMETERS

= 3M2SN

SN

32= (22n)

a. In unitless

b. In dB

= 6.02n + 1.76SN dB

MOSTUSED...

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EXAMPLE

Determine the signal-to-quantization noise ratio in dB, if an audio signal with a bandwidth of 3.2 kHz is converted to PCM signal by sampling at 8 kilo samples/sec and with a data rate of 64 kbps.

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CODING

- Practical PCM systems use 7- and 8-level binary code, or

27 = 128 quantum steps28 = 256 quantum steps

LINEAR QUANTIZATION - SIGNAL AMPLITUDE VERSUS QUANTIZATION VALUE

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NOTE:

- Two methods are used to reduce the quantum steps to 128 or 256 without sacrificing fidelity.

1. Use nonuniform quantizing performed in the coding process.

2. Use companding prior to quantizing

LINEAR VERSUS NON LINEAR PCM CODES

NON-LINEAR STEP QUANTIZING

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COMPANDING

- the process of compressing and then expanding

- with companded system, the higher amplitude analog signals are compressed (amplified less than the lower- amplitude signals) prior to transmission and then expanded) amplified more than the lower amplitude signals in the receiver).

BASIC COMPANDING PROCESS

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2 TYPES OF COMPANDING

1. Analog Compandinga. - Lawb. A - Law

2. Digital Companding

PCM SYSTEM WITH ANALOG COMPANDING

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2 TYPES OF COMPANDING

A - Law - Law

- originally defined by the Comite European de Postes et Telecommunications (CEPT)

- defined by the T1 Standards Committee in the USA

- is probably the most wide spread internationally

- is dominant in the world’s largest system in North America

“Both are recognized by the telephony section of the International Telecommunication Union (ITU-T), the supreme international standards organization for telephony.”

- A-law produces slightly better SNR for small signals

- while the µ-law has less noise on an idle channel

“Both characteristics allow small signals to be processed as accurately as large signals, and produce much improved signal to noise ratio SNR.”

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µ-LAW COMPANDING

Vout = Vmax ln(1 + µ{Vin /Vmax})

ln(1 + µ)

Where: Vmax = maximum uncompressed analog input amplitude (volts)Vin = amplitude of the input signal at particular instant of time (volts)µ = parameter used to define the amount of compression(unitless)Vout = compressed output amplitude (volts)

µ-LAW CHARACTERISTIC

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EXAMPLE

For a compressor with a µ = 255, determine:

a) The voltage gain for the following relative values of Vin shown in the table below:

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EXAMPLE

b) The compressed output voltage for a maximum input voltage of 4V.

c) Input and output dynamic ranges and compression in dB.

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µ-LAW CHARACTERISTIC

Where:V = Output VoltageVr = Reference Voltagec = Chord Numbers = Step Number

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A-LAW COMPANDING

In Europe, the ITU-T has established A-law companding to be used to approximate true logarithmic companding

Vout = AVin /Vmax

1 + lnAVmax

1 + ln(AVin /Vmax)

1 + lnAVout =

0 ≤

Vin

Vmax

Vmax

≤

1 A

1 A

≤

Vin

Vmax

≤

1

DIGITALLY COMPOUNDED PCM SYSTEM

µ-255 COMPRESSION CHARACTERISTIC

- µ-law companding is a system that divides the analog signal range into fifteen segments each eventually encoded into eight-bit digital value.

13 SEGMENT SCALE

µ-255 COMPRESSION CHARACTERISTIC

PCM QUANTIZATION LEVELS - CHORDS & STEPS

QUANTIZATION ERROR - RECOVERED STEP LEVELS DO NOT MATCH PAM LEVELS

LINEAR QUANTIZATION - ANOTHER VIEW

LOGARITHMIC QUANTIZATION - ANOTHER VIEW

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8-BIT COMPRESSED CODE FORMAT

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µ-255 ENCODING TABLE

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µ-255 DECODING TABLE

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PROCESS OF DIGITAL COMPRESSION

Digitally, the 12-bit values are encoded into 8-bit compressed code as follows:

1. Retain the sign bit as the first bit of the 8-bit code.

2. Count the number of zeros until the occurrence of the first 1 bit. Subtract the zero count from 7. This is the segment number.

3. The first occurrence of 1 is assumed during the expanding process, so it is set aside during compression.4. Copy the next four bits (ABCD) into the 8-bit compressed code.

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EXAMPLE

Code the 12-bit code 100001011010 into an 8-bit compressed µ-law code.

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EXAMPLE

Determine the 12-bit linear code, the eight-bit compressed code, the decoded 12-bit code, the quantization error, and the compression error for a resolution of 0.01 V and analog sample voltages of

(a) + 0.053 V(b) -0.318 V (c) +10.234 V

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PROCESS OF DIGITAL EXPANSION

Expanding back digitally, reverses the process:

1. Retain the sign bit.2. Take the segment number, subtract from 7 and add

that many 0s.3. Make the next bit a 1.4. The next bits are ABCD values.5. Add a 1 and sufficient 0s to complete the 12-bit value.

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QUANTIZATION ERROR

- error is error due to rounding off the sample voltage in the encoder to the closest PCM.

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COMPRESSION ERROR

- error caused by forcing the truncated bit to a 1 in the receiver.

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DIGITAL COMPRESSION ERROR

The magnitude of the compression error is not the same for all samples. However, the maximum percentage is the same in each segment (other than segments 0 and 1, where there is no compression error)

% error =12-bit encoded voltage - 12-bit decoded voltage

12-bit decoded voltage X 100

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CODEC

A single integrated chip that performs the encoding and decoding process of PCM.

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EXAMPLE

Expand the compressed code of the above example.

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SEATWORK

For the following values of μ, Vmax, and Vin, determine the compressor gain:

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SEATWORK

For the following 12-bit linear PCM codes, determine the eight-bit compressed code to which they would be converted:

a. 100011110010b. 000001000000c. 000111111000d. 111111110010e. 000000100000

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SEATWORK

For the following 8-bit compressed codes,determine the expanded 12-bit code.

a. 11001010b. 00010010c. 10101010d. 01010101e. 11110000f. 11011011

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SEATWORK

A 12-bit linear sign-magnitude PCM code is digitally compressed into 8 bits. For a resolution of 0.016 V, determine the following quantities for the indicated input voltages: a. 12-bit linear PCM code

b. eight-bit compressed code c. decoded 12-bit code

d. decoded voltage

For Vin = -6.592 V, +12.992 V, -3.36 V