ECE 4710: Lecture #9 1 PCM Noise  Decoded PCM signal at Rx output is analog signal corrupted by “noise”  Many sources of noise:  Quantizing noise »Four types: 1)Overload 2) Random 3) Granular 4) Hunting/Idle Channel  Channel noise and/or interference »Thermal noise  Additive White Gaussian Noise (AWGN) »Interference from same-channel users  Improper filtering or channel BW restrictions  ISI and BER

ECE 4710: Lecture #9 2 PCM S/N  Input analog signal must be bandlimited to prevent aliasing  Another possible source of “noise”  distortion  Use low pass anti-aliasing filter prior to PAM generation  What is S/N ratio for PCM??  Assuming only quantizing error for noise source then peak signal power to total average noise power M = # Quantizing Levels P e = Probability of Bit Error

ECE 4710: Lecture #9 3 PCM S/N  Average signal power to average noise power  P e is bit error probability of binary PCM signal at the DAC receiver input, e.g. prior to analog conversion  Value depends on type of communication systems and amount of channel noise  Assuming (best case!) no channel noise and no ISI  P e = 0

ECE 4710: Lecture #9 4 PCM S/N  For P e = 0 then  As M , quantizing step size and roundoff error  so the S / N   Equations are ideal S / N  Peak-to-peak level of input analog signal must be matched to quantizer level from – V to + V volts  Improper matching of signal & quantizer levels leads to additional sources of quantizer noise not considered in developing S / N equations

ECE 4710: Lecture #9 5  Overload Noise  Peak level of analog waveform at input to PCM encoder should not exceed design level of encoder (+ V )  If it does exceed then PCM output will have continuous flat top for time period that the design level is crossed  Significant distortion as error can be much greater than roundoff error and square flat-top produces many high- frequency harmonics Quantizing Noise t +V

ECE 4710: Lecture #9 6  Random Noise  Roundoff error results in random “white” noise if input signal level is properly set  Random noise produces white hissing sound or snowy video image (speckle)  If input signal is not matched to the quantizer and is significantly weaker  random errors are a much larger % of signal power (see next slide) »Ideal S / N equations shown previously are not valid Quantizing Noise

ECE 4710: Lecture #9 7  Granular Noise  Input signal level is much smaller than quantizer design level »Amplitude of human speech is heavily weighted to small values  Roundoff errors are not equally likely (no longer random)  Produces harsh granular sound like rocks poured into barrel  Granular noise can be randomized by assigning more quantization levels to weak signal values »Non-uniform quantization »  -law or A -law quantizers (discussed next) Quantizing Noise

ECE 4710: Lecture #9 8  Hunting or Idle Channel Noise  Occurs when input analog waveform is nearly constant »Including no signal, e.g. zero level like pause in speech  idle channel  Discrete values at quantizer output can oscillate between two adjacent quantization levels »Oscillating signal produces tone at 0.5 f s  Eliminate hunting noise by »Filtering out the tone »Designing quantizer to not have vertical step at constant input value  stair step rather than stair rise  Usually always done for 0 V input Quantizing Noise

ECE 4710: Lecture #9 9 PCM S/N  Since M = 2 n the ideal S/N equation can be written  6-dB rule: Additional 6-dB improvement in S/N for each bit of data added to PCM word  Above equation is valid for many types of input waveforms and quantization characteristics  Value for  will depend on these issues  PCM S/N performance easily tabulated for P e = 0

ECE 4710: Lecture #9 10 PCM S/N 8-bit PCM Encoder is very popular  Landline Telephony

ECE 4710: Lecture #9 11 Example  Digital Compact Disc  16-bit PCM word  Reed-Solomon coding for correcting burst errors due to scratches and fingerprints  f s = 44.1 kHz for each stereo channel  Max BW for FM audio spectrum is ~15 kHz (high-fidelity) »f s  2 B  some oversampling to prevent aliasing  Data rate (w/o coding) = 2 f s 16 = 1.41 Mbps ;  CD storage ~ 640 Mbyte (1 byte = 8 bits)  # minutes = [8 ( )] / [ )] = 60.5 minutes = 15 four minute songs 2 stereo channels

ECE 4710: Lecture #9 12 Non-Uniform Quantizing  Analog voice signals have higher probability of weak amplitudes than peak amplitudes  Non-uniform amplitude distribution  1 V peak signal may have many levels of 0.1 V (20 dB down)  Granular noise is serious problem if step size is not smaller for weak amplitude values  Non-uniform quantizers are required for good PCM digital voice »Variable quantizing step size  nonlinear  Can use non-linear compression amplifier on analog input prior to passing to PCM circuit  Compression amplifier performance can also be approximated using digital circuit

ECE 4710: Lecture #9 13 Non-Uniform Quantizing Note: 4 Levels shown but negative same as positive

ECE 4710: Lecture #9 14 Compression  In U.S. a  -law compression characteristic is used  A  0 corresponds to uniform quantizing  A  255 compression is used by telephone companies in U.S., Japan, and Canada  Another compression ( A -law) is used in Europe (see book for equations)

ECE 4710: Lecture #9 15 Compression

ECE 4710: Lecture #9 16 Compression  For digital circuit implementation the smooth non- linear compression characteristics are approximated using piecewise linear chords  Uniform quantizer with 16 steps used for 8 piecewise linear chords  816 = 128 levels  2 for  V = 256 levels  Step size  is varied for different chords »Smaller  for lower amplitude values »Selected such that full scale value of last chord segment matches peak analog input level  8-chord segmenting technique is used worldwide

ECE 4710: Lecture #9 17 Digital Compression PCM Code Word 1 sign bit + 3 chord bits = 2 3 = 8 chords + 4 step bits = 2 4 = 16 steps / chord + 8 total bits

ECE 4710: Lecture #9 18 Compression  If compression is used in Tx then expansion (decompression) must be used in Rx  Compression/Expander = Compander  What is output S/N for non-uniform quantizers??  6-dB rule still applies but  is different  V is peak design level of quantizer and x RMS is RMS value of analog input signal

ECE 4710: Lecture #9 19 Compression  V / x RMS is called loading factor and is often set to 4 = 12 dB (20 log 4) to prevent overload noise (uniform quantizer only)  This yields  = 4.77 – 12 = -7.3 dB rather than  for average S/N and ideal conditions (Table 3-2, Equation 3-17)  As   then   and consequently starting point for S/N   More compression leads to overall lower starting point for average S/N  Advantage is that S/N performance is much less sensitive to input signal level strength

ECE 4710: Lecture #9 20 Compression S/N