ECE 4710: Lecture #9 1 PCM Noise Decoded PCM signal at Rx output is analog signal corrupted by...

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


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

eoutpk PMM

NS

)1(413

2

2

M = # Quantizing Levels

Pe = Probability of Bit Error


PCM S/N

Average signal power to average noise power

Pe 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

Pe = 0

ePMM

NS

)1(41 2

2

out


PCM S/N

For Pe = 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

and 3 2

out

2

outpk

MNS

MNS


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


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


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


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 fs

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


PCM S/N

Since M = 2n 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 Pe = 0

n

NS

dB

02.6S/N

S/N

peak for 77.4

averagefor 0


PCM S/N

8-bit PCM Encoder is

very popular

Landline Telephony


Example

Digital Compact Disc 16-bit PCM word Reed-Solomon coding for correcting burst errors due to scratches and

fingerprints

fs = 44.1 kHz for each stereo channel

Max BW for FM audio spectrum is ~15 kHz (high-fidelity)

» fs 2 B some oversampling to prevent aliasing

Data rate (w/o coding) = 2 fs 16 = 1.41 Mbps ;

CD storage ~ 640 Mbyte (1 byte = 8 bits) # minutes = [8 • (640•106)] / [60 • 1.41•106)] = 60.5 minutes = 15 four

minute songs

2 stereo channels


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


Non-Uniform Quantizing

Note: 4 Levels shown but

negative same as positive


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)

0 and 1|)(| where)1ln(

|))(|1(ln|)(|

twtw

tw inin

out


Compression


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 8•16 = 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


Digital Compression

PCM Code Word

1 sign bit +

3 chord bits = 23 = 8 chords +

4 step bits = 24 = 16 steps / chord +

8 total bits


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 xRMS is RMS value of analog input signal

n

NS

dB

02.6 companding lawln1log2077.4

companding law)1ln(log2077.4

quantizing uniform)/log(2077.4

AA

xV RMS


Compression

V / xRMS 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

n

NS

dB

02.6


Compression S/N

ECE 4710: Lecture #9 1 PCM Noise Decoded PCM signal at Rx output is analog signal corrupted by...

Documents

Transcript of ECE 4710: Lecture #9 1 PCM Noise Decoded PCM signal at Rx output is analog signal corrupted by...