1. Analog-to-Digital Conversion
PAM(Pulse Amplitude Modulation)
PCM(Pulse Code Modulation)

2. PAM(Pulse Amplitude Modulation)
Conversion of analog signal to a pulse type signal where the amplitude of signal denotes the analog information
Two class of PAM signals
Natural sampling (gating)
Easier to generate
Instantaneous sampling
Flat-top pulse
More useful to conversion to PCM

3. PAM with natural sampling
W(t) t
Ws(t) t
S(t) t Ts 
Duty Cycle D=/Ts=1/3
W(t)
S(t)
Ws(t)
=W(t)S(t)
Analog bilateral switch

4. Spectrum of PAM with natural sampling
|W(f)|
-B B f 1
Spectrum of input analog signal
Spectrum of PAM
D=1/3, fs=4B
BT= 3fs = 12B
|Ws(f)|
-3fs fs fs B B fs fs fs
D=1/3

5. PAM with flat-top sampling
W(t) t
Ws(t) t Ts 
S(t) t
Sample and Hold

6. Spectrum of PAM with flat-top sampling
|W(f)|
-B B f 1
Spectrum of Input
Spectrum of PAM
/Ts=1/3, fs=4B
BT= 3fs = 12B
|Ws(f)|
-3fs fs fs B B fs fs fs
D=1/3

7. Summary of PAM Require very wide bandwidth Bad noise performance
Not good for long distance transmission
Provide means for converting a analog signal to PCM signal
Provide means for TDM(Time Division Multiplexing)
Information from different source can be interleaved to transmit all of the information over a single channel

8. PCM(Pulse Code Modulation)
Definition
PCM is essentially analog to digital conversion of a signal type where the information contained in the instantaneous samples of an analog signal is represented by digital words in a serial bit stream
Analog signal is first sampled at a rate higher than Nyquist rate, and then samples are quantized
Uniform PCM : Equal quantization interval
Nonuniform PCM : Unequal quantization interval

9. Why PCM is so popular ? PCM requires much wider bandwidth But,
Inexpensive digital circuitry
PCM signal from analog sources(audio, video, etc.) may be merged with data signals(from digital computer) and transmitted over a common high-speed digital communication system (This is TDM)
Regeneration of clean PCM waveform using repeater.
But, noise at the input may cause bit errors in regenerated PCM output signal
The noise performance is superior than that of analog system.
Further enhanced by using appropriate coding techniques

10. PCM transmitter/receiver
LPF
BW=B
Sampler
& Hold
Quantizer
No. of levels=M
Encoder
Analog
signal
Bandlimited
Analog signal
Flat-top
PAM signal
Quantized
PCM
Channel, Telephone lines with regenerative repeater
Decoder
Reconstruction
Signal
output

11. Waveforms in PCM Uniform quantizer Error signals Waveform of signals
PCM signal
PCM word

12. Encoder Usually Gray code is used
Only one bit change for each step change in quantized level
Single errors in received PCM code word will cause minimum error if sign bit is not changed
In text, NBC(Natural Binary Coding) is used
Multilevel signal can be used
Much smaller bandwidth than binary signals
Requires multilevel circuits

13. Uniform PCM Let M=2n is large enough Uniform distribution =2Xmax/M x
Distortion x
-/ /2

14. SQNR of PCM
Distortion
SQNR
Let normalized input :

15. Bandwidth of PCM Hard to analyze because PCM is nonlinear
If sinc function is used to generate PCM
, where R is bit rate
If rectangular pulse is used
, first null bandwidth
If fs=2B (Nyquist sampling rate)
Lower bound of BW:
In practice, is closer to reality

16. Performance of PCM Quantizer Level, M 2 4 8 16 32 64 128 256 512 1024
2048
4096
8192
16384
32768
65536
n bits
M=2n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Bandwidth
>nB 2B 4B 6B 8B
10B
12B
14B
16B
18B
20B
22B
24B
26B
28B
30B
32B
SQNR|dB_PK
4.8+6n
10.8
16.8
22.8
28.9
34.9
40.9
46.9
52.9
59.0
65.0
71.0
77.0
83.0
89.1
95.1
101.1

17. PCM examples Telephone communication Voice frequency : 300 ~ 3400Hz
Minimum sampling frequency = 2 x 3.4KHz = 6.8KHz
In US, fs = 8KHz is standard
Encoding with 7 information bits + 1 parity bit
Bit rate of PCM : R = fs x n = 8K x 8 = 64 Kbits/s
Buad rate = 64Ksymbols/s = 64Kbps
Required Bandwidth of PCM
If sinc function is used: B > R/2 = 32KHz
If rectangular is used: B = R = 64KHz
SQNR|dB_PK = 46.9 dB (M = 27)
Parity does not affect quantizing noise but decrease errors caused by channels

18. PCM examples CD (Compact Disk) For each stereo channel
16 bit PCM word
Sampling rate of 44.1KHz
Reed-Solomon coding with interleaving to correct burst errors caused by scratches and fingerprints on CD
High quality than telephone communication

19. Homework
Illustrative Problems
4.9, 4.10, 4.11, 4.12
Problems
4.14

20. Nonuniform quantization
Example: Voice analog signal
Peak value(1V) is less appears while weak value(0.1V, 20dB down) around 0 is more appears (nonuniform amplitude distribution)
Thus nonuniform quantization is used
Implementation of nonuniform quantization
Compression
(Nonlinear)
filter
PCM with
Uniform
Quantization
Analog
Input
PCM
output

21. Nonuniform Quantization
Two types according to compression filter
-law : used in US
See Figure 4.9, Page 155
A-law : used in Europe

22. Nonuniform Quantization
Compandor = Compressor + Expandor
Compressor: Compression filter in transmitter
Expander: Inverse Compression filter in receiver
-law :
SQNR
Uniform quantizing:
-law:
A-law:

23. Homework
Illustrative Problems
4.13, 4.14
Problems
4.17