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 signals in the receiver).

TYPES OF COMPANDING 1. Analog Companding a.  - Law b. A - Law 2. Digital Companding

PCM SYSTEM WITH ANALOG COMPANDING

Vmax ln(1 + µ{Vin /Vmax}) µ-LAW COMPANDING Vmax ln(1 + µ{Vin /Vmax}) Vout = 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

A-LAW COMPANDING In Europe, the ITU-T has established A-law companding to be used to approximate true logarithmic companding AVin /Vmax Vin 1 Vout = 0 ≤ ≤ Vmax Vmax A 1 + lnA 1 + ln(AVin /Vmax) 1 Vin Vout = ≤ ≤ 1 Vmax A Vmax 1 + lnA

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

8-BIT COMPRESSED CODE FORMAT

µ-255 ENCODING TABLE

µ-255 DECODING TABLE

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.

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

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.

WORK Examples For the following 12-bit linear PCM codes, determine the eight-bit compressed code to which they would be converted: a. 100011110010 b. 000001000000 c. 000111111000 d. 111111110010 e. 000000100000

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

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 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