Module 15 Comp An Ding Wit

MODULE 15

COMPANDING

Prepared by: Engr. Jo-Ann C. Viñas

OBJECTIVES

1. Advantages and Disadvantages of Digital Communications 2. Review of Pulse Code Modulation (PCM) 3. Introduce the concept of companding 2. State the importance of companding 3. Discuss the two types of companding 4. Solve problems involving companding

PCM APPLICATIONS

PCM is the most commonly used technique in digital communications 1. 2. 3. 4. 5.

Telephone System Digital Audio Recording CD Laser disks Voice mail Digital Video

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.”

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.”

NOTE:

The established sampling rates for digital audio are: 1. 2. 3. 4. 5.

32 kHz for broadcast digital audio 44.1 kHz for CDs 48 kHz for digital audiotape (DAT) and digital videotape ( mini-DV and DV) 96 kHz or 192. 4 kHz for DVD-audio and BD-ROM (Blu ray disc) audio 2.8224 MHz for SACD (Super Audio CD) & DSD (Direct Stream Digital)

ADVANTAGES OF DIGITAL COMMUNICATIONS

1. Digital communication is more rugged than analog communication 2. The viability of regenerative repeaters 3. Digital hardware implementation is flexible 4. Digital signals can be coded 5. It is easier and more efficient to multiplex several digital signals

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

HARDWARE IMPLEMENTATION IS FLEXIBLE

0 TO +1V ANALOG SIGNAL

2 BITS RESOLUTION

3 BITS RESOLUTION

DISADVANTAGE OF DIGITAL COMMUNICATIONS

1.

Increased bandwidth of transmission

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, DVDvideo 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.

CRITERIA FOR SIGNAL ENCODING

What determines how successful a receiver will be in interpreting an incoming signal? 1. 2. 3.

Signal-to-Noise Ratio Data Rate Bandwidth An increase in data rate increases bit error rate An increase in SNR decreases bit error rate An increase in bandwidth allows an increase in data rate

PULSE CODE MODULATION

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

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

SAMPLING SAMPLING

QUANTIZING QUANTIZING

ENCODING ENCODING

QUANTIZATION

Changing from CONTINUOUS IN VALUE to DISCRETE IN VALUE.

SAMPLING

Changing from CONTINUOUS IN TIME to DISCRETE IN TIME.

CODING

Code value of sample into 1s and 0s.

PCM PARAMETERS

1. 2. 3. 4. 5. 6. 7.

Number of Levels or Codewords (M) Bandwidth (Data Rate) (BW) Dynamic Range (DR) Resolution (Res) Coding Efficiency (η ) Quantization Error (Qe) Signal-to-Quantization Noise Ratio (SQR)

PCM PARAMETERS

1.

Number of Levels or Codewords (M)

M = 2n

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

PCM PARAMETERS

2.

Bandwidth (Data Rate)

BW = nfs = fb

where: fs = sampling rate in Hz fb = bit rate in bps

PCM PARAMETERS

3.

Dynamic Range

DR = 2n - 1

where: Vmax = maximum input voltage Vmin = minimum input voltage

Vmax DR = Vmin

DYNAMIC RANGE OF ANALOG SIGNAL

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)

PCM PARAMETERS

4.

Resolution

Resolution = VLSB

where: VLSB = voltage of the least significant bit

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)

PCM PARAMETERS

5.

Coding Efficiency (η )

β η = β

min max

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

X 100

PCM PARAMETERS

6.

Quantization Error

Qe =

VMIN 2

Resolution Qe = 2

PCM PARAMETERS

7.

Signal-to-Quantization Noise Ratio

V SQR = 10.79 dB + 20 logS q

PCM PARAMETERS

A.

Ideal Signal-to-Quantization Noise Ratio

a. In unitless

S = 3M2 N

S 3 2n = (2 ) N 2

b. In dB

S N

dB

= 6.02n + 1.76

MOST USED...

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.

CODING

-Practical PCM systems use 7- and 8-level binary code, 27 = 128 quantum steps 28 = 256 quantum steps

or

LINEAR QUANTIZATION - SIGNAL AMPLITUDE VERSUS QUANTIZATION VALUE

NOTE:

-Two methods are used to reduce the quantum steps to 128 or 256 without sacrificing fidelity. 1. Use nonuniform quantizing performed in the process. 2. Use companding prior to quantizing

coding

LINEAR VERSUS NON LINEAR PCM CODES

NON-LINEAR STEP QUANTIZING

COMPANDING

-

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

BASIC COMPANDING PROCESS

2 TYPES OF COMPANDING

1. Analog Companding a. µ - Law b. A - Law 2.

Digital Companding

PCM SYSTEM WITH ANALOG COMPANDING

2 TYPES OF COMPANDING

A - Law

µ - Law

iginally defined by the Comite -European defined by the T1 Standards Committee e Postes et Telecommunicationsthe (CEPT) USA

are recognized by the telephony section of the International Telecommu (ITU-T), the supreme international standards organization for telephony

- is probably the most wide spread - is dominant in the world’s largest syste internationally in North America

acteristics allow small signals to be processed as accurately as large si produce much improved signal to noise ratio SNR.”

A-law produces slightly better SNR - while for the µ-law has less noise on an id small signals channel

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

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:

EXAMPLE

b)

c)

The compressed output voltage for a maximum input voltage of 4V. Input and output dynamic ranges and compression in dB.

µ-LAW CHARACTERISTIC

Where: V = Output Voltage Vr = Reference Voltage c = Chord Number s = Step Number

A-LAW COMPANDING

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

Vout = Vmax Vout = Vmax

AVin /Vmax 1 + lnA 1 + ln(AVin /Vmax ) 1 + lnA

0≤

Vin Vmax

≤

1 A

Vin 1 ≤ ≤ 1 Vmax A

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

8-BIT COMPRESSED CODE FORMAT

µ-255 ENCODING TABLE

µ-255 DECODING TABLE

PROCESS OF DIGITAL COMPRESSION

Digitally, the 12-bit values compressed code as follows:

are

encoded

into

8-bit

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.

EXAMPLE

Code the 12-bit code compressed µ-law code.

100001011010

into

an

8-bit

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

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.

QUANTIZATION ERROR

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

COMPRESSION ERROR

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

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)

12-bit encoded voltage - 12-bit decoded voltage

% error =

X 100

12-bit decoded voltage

CODEC

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

EXAMPLE

Expand the compressed code of the above example.

SEATWORK

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

SEATWORK

For the following 12-bit linear PCM codes, determine the eight-bit compressed code to which they would be converted: a. b. c. d. e.

100011110010 000001000000 000111111000 111111110010 000000100000

SEATWORK

For the following 8-bit compressed codes,determine the expanded 12-bit code. a. b. c. d. e. f.

11001010 00010010 10101010 01010101 11110000 11011011

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