1. Pulse Code Modulation (PCM)

2. Types of Digital Modulation
Base-Band Digital Modulation
Pulsed Analog Modulation
Pulsed Digital Modulation
Band-Pass Digital Modulation
Binary modulation
M-Array Modulation Techniques

3. PCM(Pulse Code Modulation)
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

4. 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

5. The basic elements of a PCM system

8. Regeneration Along the Transmission Path
The ability to control the effects of distortion and noise produced by transmitting a PCM signal over a channel
Equalizer
Shapes the received pulses so as to compensate for the effects of amplitude and phase distortions produced by the transmission
Timing circuitry
Provides a periodic pulse train, derived from the received pulses
Renewed sampling of the equalized pulses

9. Decision-making device
The sample so extracted is compared o a predetermined threshold
ideally, except for delay, the regenerated signal is exactly the same as the information-bearing signal
The unavoidable presence of channel noise and interference causes the repeater to make wrong decisions occasionally, thereby introducing bit errors into the regenerated signal
If the spacing between received pulses deviates from its assigned value, a jitter is introduced into the regenerated pulse position, thereby causing distortion.

10. Quantization Process
Amplitude quantization
The process of transforming the sample amplitude x(nTs) of a baseband signal x(t) at time t=nTs into a discrete amplitude xq(nTs) taken from a finite set of possible levels.
Representation level (or Reconstruction level)
The amplitudes vk , k=1,2,3,……,L
Quantum (or step-size)
The spacing between two adjacent representation levels

12. Uniform quantizer

13. Waveforms in PCM

14. PCM signal
PCM word

15. Error signals

17. Figure: Two types of quantization: (a) midtread and (b) midrise

18. midtread quantization

19. Mid-raiser quantiser

20. Biased- Quantiser

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

23. SNR Calculation of PCM Quantization Error Step Size with Max=1
PDF of Quantisation
Noise Power = Second Moment
SNR value

24. Pulse-Code Modulation (PCM)
The quantization noise is characterized as a realization of a stationary random process q in which each of the random variables q(n) has uniform pdf.
Where the step size of the quantizer is

25. SNR Calculation of PCM
If :maximum amplitude of signal, and varies to -
The mean square value of the quantization error is :
Measure in dB, The mean square value of the noise is :
The quantization noise decreases by 6 dB/bit.

26. Pulse-Code Modulation (PCM)
Example :
We require an S/N ratio of 60 dB. Then the required word length is ?
60= n
If we sample at 8 KHZ, then PCM require

27. Bit rate and bandwidth requirements of PCM
The bit rate of a PCM signal can be calculated form the number of bits per sample x the sampling rate Bit rate = nb x fs
The bandwidth required to transmit this signal depends on the type of line encoding used.
A digitized signal will always need more bandwidth than the original analog signal.
Price we pay for robustness and other features of digital transmission.

29. 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

30. PCM requires much wider bandwidth
But, Why PCM is so popular ?
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)
The noise performance is superior than that of analog system.
Further enhanced by using appropriate coding techniques

31. 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: Bandwidth B > R/2=n*Fs/2 = 32KHz
If rectangular is used: Bandwidth B = R = n*Fs = 64KHz
SQNR|dB_PK = 46.9 dB (M = 27)
Parity does not affect quantizing noise but decrease errors caused by channels

33. 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

34. Problems
In a PCM system the SNR required is 23dB. Evaluate the number of Quantization levels required.
A Television system having a BW of 5MHz is transmitted with PCM system. Given number of Quantization levels are 512. Determine
1. Code-Length 2. Transmission Bandwidth
3. Bit-Rate 4. SQNR

37. Mapping of Multiple Users to T1 Channels

39. T1 Frame Structure

40. E1 Frame and Multi-Frame Structure

42. E1 Frame and Multi-Frame Structure

44. DESIGN OF A PCM SIGNAL FOR TELEPHONE SYSTEMS
Assume that an analog audio voice-frequency(VF) telephone signal occupies a band from 300 to 3,400Hz. The signal is to be converted to a PCM signal for transmission over a digital telephone system. The minimum sampling frequency is 2x3.4 = 6.8 ksample/sec.
To be able to use of a low-cost low-pass antialiasing filter, the VF signal is oversampled with a sampling frequency of 8ksamples/sec.
This is the standard adopted by the Unites States telephone industry.
Assume that each sample values is represented by 8 bits; then the bit rate of the binary PCM signal is 8
This 64-kbit/s signal is called a DS-0 signal (digital signal, type zero).
The minimum absolute bandwidth of the binary PCM signal is
This B is for a sinx/x type pulse sampling

45. DESIGN OF A PCM SIGNAL FOR TELEPHONE SYSTEMS
If we use a rectangular pulse for sampling the first null bandwidth is given by
We require a bandwidth of 64kHz to transmit this digital voice PCM signal, whereas the bandwidth of the original analog voice signal was, at most, 4kHz.
We observe that the peak signal-to-quantizing noise power ratio is:
Note:
Coding with parity bits does NOT affect the quantizing noise,
However coding with parity bits will improve errors caused by channel or ISI, which will be included in Pe ( assumed to be 0).

46. Effects of Quantizing Noise
If Pe is negligible, there are no bit errors resulting from channel noise and no ISI, the Peak SNR resulting from only quantizing error is:
The Average SNR due to quantizing errors is:
Above equations can be expresses in decibels as,
Where, M = 2n
α = 4.77 for peak SNR
α = 0 for average SNR

48. Example
A sinusoidal Signal of amplitude Am uses all Representation levels provided for Quantization in the case of full load condition. Calculate Signal to Noise ratio in db assuming the number of quantization levels to be 512.
ANS: 55.8 db.

49. Example
SNR for varying number of representation levels for sinusoidal modulation X dB
Number of representation level L
Number of Bits per Sample, R
SNR (dB) 32 5
31.8 64 6
37.8
128 7
43.8
256 8
49.8 49

51. Non Uniform quantizing
Many signals such as speech have a nonuniform distribution.
The amplitude is more likely to be close to zero than to be at higher levels.
For such signals with non-uniform amplitude distribution quantizing noise will be higher for amplitude values near zero.
Nonuniform quantizers have unequally spaced levels
The spacing can be chosen to optimize the SNR for a particular type of signal.

52. Nonuniform Quantization
Output sample
XQ (t) 6 4 2
Example: Nonuniform 3 bit quantizer -8 -6 -4 -2 2 4 6 8
Input sample
X(t) -2 -4 -6

54. Uniform and Nonuniform Quantization

55. Companding Nonuniform quantizers are difficult to make and expensive.
An alternative is to first pass the speech signal through a nonlinearity before quantizing with a uniform quantizer.
The nonlinearity causes the signal amplitude to be Compressed.
The input to the quantizer will have a more uniform distribution.

56. The process of compressing and expanding is called Companding.
Effect of non linear quantizing can be obtained by first passing the analog signal through a compressor and then through a uniform quantizer.
At the receiver, the signal is Expanded by an inverse to the nonlinearity.
The process of compressing and expanding is called Companding. x’
Q(.) y
Uniform Quantizer
C(.) x
Compressor

57. Companding

59. Companding y ^ y ^ y ^ y ^ y ^ y ^ y x ^ X X X X F Q Q F-1 Example
F: y=log(x) F-1: x=exp(y)
F: nonlinear compressing function
F-1: nonlinear expanding function
F and F-1: nonlinear compander 59

60. Input-Output characteristic of Compressor

61. A-law and m-law Companding
These two are standard companding methods.
u-Law is used in North America and Japan
A-Law is used elsewhere to compress digital telephone signals
By convention, A-law is used for an international connection if at least one country uses it.

63.  Law/A Law
The -law algorithm (μ-law) purpose is to reduce the dynamic range of an audio signal.
In the analog domain, this can increase the signal to noise ratio achieved during transmission, and in the digital domain, it can reduce the quantization error (hence increasing signal to quantization noise ratio).
A-law algorithm provides a slightly larger dynamic range than the mu- law at the cost of worse proportional distortion for small signals.

64. -Law Companding
Telephones in the U.S., Canada and Japan use -law companding:
Where  = 255 and |x(t)| < 1
Output |x(t)|
Input |x(t)|

66. Example: m-law Companding
x[n]=speech /song/
y[n]=C(x[n])
Companded Signal
Close View of the Signal
Segment of x[n]
Segment of y[n]
Companded Signal

67. A-law and m-law Companding

68. SNR of Compander

69. SNR Performance of Compander
The output SNR is a function of input signal level for uniform quantizing.
But it is relatively insensitive for input level for a compander.
α = Log ( V/xrms) for Uniform Quantizer
V is the peak signal level and xrms is the rms value.
α = log[Ln(1 + μ)] for μ-law companding
α = log[1 + Ln A] for A-law companding

70.  Law 70

71. A Law
EE 541/451 Fall 2006 71

72. The only significant difference is near the origin, shown in (b),
where μ255 law is a smooth curve, and "A" law switches to a straight line.

73. V.90 56-Kbps PCM Computer modem
The V.90 PC Modem transmits data at 56kb/s from a PC via an analog signal on a dial-up telephone line.
A μ law compander is used in quantization with a value for μ of 255.
The modem clock is synchronized to the 8-ksample/ sec clock of the telephone company.
7 bits of the 8 bit PCM are used to get a data rate of 56kb/s

74. Frequencies below 300Hz are omitted to get rid of the power line noise in harmonics of 60Hz).
SNR of the line should be at least 52dB to operate on 56kbps.
If SNR is below 52dB the modem will fallback to lower speeds ( 33.3 kbps, 28.8kbps or 24kbps).

75. If non-uniform quantization is to be implemented using the mu-law with mu = 5 and m_p = 8V. If the input signal to the compander is 2V what will be the output. Figure provided.

77. Implementation of Compander
Diode equation
Piece-wise linear Approach

78. Compressor and expander circuits for compander system

81. Compressor part of a compander uses a differential amplifier to receive voice signals.
Diode attenuator circuits are connected to the differential amplifier output and attenuate the differential amplifier output signals as a function of a rectified signal derived from the compressor output.
Expander part of the compander also uses a differential amplifier to receive voice signals.
The differential amplifier is interconnected by a diode attenuator circuit which varies the gain of the differential amplifier as a function of a rectified signal derived from the expander input.
The compander thus requires no inductors and uses components which are relatively small and compact.

84. DPCM
DM & ADM

85. Differential Pulse Code Modulation (DPCM)
What if we look at sample differences, not the samples themselves?
Δt = xt-xt-1
Differences tend to be smaller

91. Compression using Differential Pulse Code Modulation

95. Prediction
If we know the past behavior of a signal up to a certain point in time, it is possible to make some inference about its future values
Tapped-delay-line filter (discrete-time filter):
A simple and yet effective approach to implement the prediction filter with the basic delay set equal to the sampling period

96. Differential Pulse Code Modulation (DPCM) [3]

97. Differential Pulse Code Modulation (DPCM) [4]
Assume the following predictor
And the difference being
Also assume the quantization scheme to be 
And

98. Differential Pulse Code Modulation (DPCM) [5]
The above table is the result of
Consider the sequence f1…f5=130,150,140,200,230
Initial confiq
Input f2
Input f3
Input f4
Input f3

103. 01/Feb/2007

104. DM & ADM

106. 01/Feb/2007

107. EA C473 -Multimedia Computing
DELTA MODULATION
01/Feb/2007
EA C473 -Multimedia Computing

109. 01/Feb/2007

110. 01/Feb/2007

112. Delta modulation (DM)

113. ADM