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COMPANDING



- is 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 receiver).

signals in the

TYPES OF COMPANDING

  

1.

 

2.

Analog Companding a.



- Law b. A - Law

Digital Companding

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PCM SYSTEM WITH ANALOG COMPANDING

µ-LAW COMPANDING

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V out = V max ln(1 + µ{V in ln(1 + µ) /V max })

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

µ-LAW CHARACTERISTIC

A-LAW COMPANDING



In Europe, the ITU-T has established A-law companding to be used to approximate true logarithmic companding V out = V max V out = V max AV in /V max 1 + lnA 1 + ln(AV in /V max ) 1 + lnA 0 ≤ V in V max ≤ 1 A 1 A ≤ V V in max ≤ 1

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DIGITALLY COMPOUNDED PCM SYSTEM

µ-255 COMPRESSION CHARACTERISTIC µ-law companding is a system that divides the analog signal range into fifteen segments encoded into eight-bit digital value.

each eventually

13 SEGMENT SCALE

µ-255 COMPRESSION CHARACTERISTIC

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 compressed code as follows:

    

1.

2.

3.

4.

are encoded into 8-bit Retain the sign bit as the first bit of the 8-bit code.

Count the number of zeros until the occurrence of the first 1 bit.

Subtract the zero count from 7. This is the segment number.

The first occurrence of 1 is assumed during the expanding process, so it is set aside during compression.

Copy the next four bits (ABCD) into the 8-bit compressed code.

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EXAMPLE

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

100001011010 into an 8-bit

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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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WORK Examples



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

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

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WORK



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

     

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

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WORK

    

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

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

PCM problems

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 kilosamples/sec and with a data rate of 64 kbps.

Line Encoding