PULSE CODE MODULATION (PCM) 1. 1. PCM quan antization Techniq - - PowerPoint PPT Presentation

PULSE CODE MODULATION (PCM)

1.

• 1. PCM quan

antization Techniq iques 2.

• 2. PCM Tran

ansmis ission Ban andwid idth 3.

• 3. PCM Cod
• ding Techniq

iques 4.

• 4. PCM In

Integrated Cir ircu cuits 5.

• 5. Advantages of
• f PCM

6.

• 6. De

Delt lta Mod

• dula

lation 7.

• 7. Adaptive De

Delt lta Mod

• dulation

8.

• 8. Di

Differentia ial l PCM ECE 416 – DIGITAL COMMUNICATION Friday, 09 March 2018

SYLLABUS

KEY POINTS ABOUT PCM

• 1. While PCM is a pulse modulation technique much like PWM, PAM
• r PPM.
• 2. PCM is digital while the others are either analogue in time or

amplitude, i.e PCM pulses are discrete in time and amplitude unlike PAM, PWM or PPM.

• 3. Essential aspects of a PCM transmitter are sampling, quantizing and

encoding.

• 4. PCM is not a modulation in the conventional sense because it does

not rely on varying a characteristic of a carrier (amplitude, frequency or phase).

PCM TRANSMITTER

Low-pass Filter Sample and Hold q-level quantizer Binary encoder Parallel to serial converter Timer Analogue signal x(t) PAM Signal X(nTs) Quantized PAM Xq(nTs) Sampling clock signal 𝒈𝒕 ≥ 𝟑𝒈𝒏 PCM out r = ufs Analogue to Digital Converter ADC

BINARY EQUIVALENTS AND PULSE CODE WAVEFORMS

PCM TRANSMISSION PATH

• PCM transmission path refers to the path the the signal travels

between the transmitter and the receiver.

Regenerative Repeater Regenerative Repeater From Transmitter Distorted PCM Signal Clean PCM Pulse Distorted PCM Signal Clean PCM Pulse To Receiver

PCM REPEATER

Amplitude and Phase Equalizer Decision Making Circuit Timing Circuit Distorted PCM Signal Clean PCM Pulse Compensates for the effects of amplitude and phase distortions Makes a decision on whether the equalized PCM wave is a zero or one The timing clock is extracted from the PCM pulse- stream

PCM RECEIVER

Regenerative Repeater Serial to Parallel converter Digital to Analogue Converter Sample and Hold circuit Low pass filter, fm Timer Clean PCM Pulse train Distorted PCM Pulse Trainl Analogue Signal x(t)

TYPES OF QUANTIZERS

Quantization Uniform Quantization Non-Uniform Quantization Midtread Quantization Midrise Quantization Step size is the same throughout the input signal range Step size varies according the input signal values

MIDTREAD QUANTIZER

• 1. A midtread quantizer assumes values of

the form ∆Hi ⋅where ∆ is the step size and Hi = 0, ±1, ±2, ±3, ...

• 2. It is called mid-tread because the origin

lies in the middle of a tread of a staircase- like graph.

• 1. A mid-riser quantizer has output levels are

given by

∆ 2Hi, where ∆ is the step size and Hi

= ±1, ±2, ±3, ....

• 2. The origin lies in the middle of the rising

part of the staircase-like characteristic graph.

MIDRISER QUANTIZER

PCM TRANSMISSION BANDWIDTH

• 1. Assume the a PCM encoder has q levels which are encoded to 𝜑

bits.

• 2. We can infer

𝑟 = 2𝜑

• 3. The number of bits per second can be expressed as:

𝑔

𝑞𝑑𝑛 = 𝜑𝑔 𝑡

where 𝑔

𝑡 ≥ 2𝑔 𝑛 (Nyquist criterion)

• 4. It therefore follows that the bandwidth, BW of a PCM channel is

bounded by: 𝐶𝑋

𝑞𝑑𝑛 ≥ 2𝜑𝑔 𝑛

EXAMPLE 1

• 1. A TV signal with a bandwidth of 4.2 MHz is transmitted using binary

PCM system using 512 quantization levels. Determine (a) Code word-length (b) The PCM bandwidth/bit rate SOLUTION (a) 𝑔

𝑛 = 4.2 𝑁𝐼𝑨

𝑟 = 2𝜑 = 512 𝜑 = 𝑚𝑝𝑕2512 = 9 bits (b) Bandwidth, BW = 2𝜑𝑔

𝑛 = 2 x9 × 4.2 = 75.6 Mb/s

WHY IT IS NECESSARY TO HAVE NON-UNIFORM QUANTIZATION?

1. Using linear quantization, the quantization error is given by: 𝜗 =

∆ 2

2. If q quantization levels of a bipolar signal are used, we can write: ∆ = 2𝑦𝑛𝑏𝑦 𝑟 3. Consider a PCM system with 𝜑 = 4 bits and 𝑦𝑛𝑏𝑦 = 16 Volt, then: 𝑟 = 24 = 16 ∆ =

2 𝑟 = 2 16 = 1 8

The maximum quantization error is therefore 𝜁𝑛𝑏𝑦 = ∆ 2 = 1 16 4. At maximum, the relative error is 1 volt out of 16 volts or 6.25% 5. At lower levels, e.g. 2 volts, the relative error is 1 volt out of 2 volts

• r 50%.

6. To reduce this high relative error at low levels, PCM systems use non- uniform quantization .

COMPANDING

1. With uniform sampling, the quantization step is fixed thus resulting in uniform quantization noise power. 2. However signal power is not constant, it is proportional to the square of the signal

• amplitude. This means Quantization Noise is very significant at low amplitudes.

3. To reduce quantization noise at lower amplitudes, we use commanding: Companding = Compressing + Expanding

Compressor Uniform Quantizer Expander Input Output

Provides High Gain to Weak Signals and Low Gain to strong Signals Provides Low Gain to Weak Signals and High Gain to strong Signals

COMPRESSING WITH MIDRIZER QUANTIZER

COMPANDING IN COMMUNICATION SYSTEMS

• 1. The loudest sound that can be tolerated (120 dB SPL)

is about one-million times the amplitude of the weakest sound that can be detected (0 dB SPL).

• 2. If the quantization levels are equally spaced (uniform

quantization), 12 bits must be used to obtain telephone quality speech.

• 3. However, only 8 bits are required if the quantization

levels are made unequal (companding) to match the characteristics of human hearing.

THREE METHODS OF REALIZING COMPANDING IN COMMUNICATION SYSTEMS

1. Run the analog signal through a nonlinear circuit before reaching a linear 8 bit ADC, 2. Use an 8 bit ADC that internally has unequally spaced steps, or 3. Use a linear 12 bit ADC followed by a digital look- up table (12 bits in, 8 bits out).

• Each of these three options requires the same

nonlinearity, just in a different place: at analog circuit, at the ADC, or a digital circuit after the ADC.

19

COMPANDING STANDARDS

(1) μ255 law used in North America (2) "A" law, used in Europe.

20

"A" LAW COMPANDING

Where A is the compression parameter

21

µ-LAW COMPANDING

where µ is 255 for 8 bits.

BINARY ENCODING

• 1. Encoding converts the

quantized samples into a form that is more convenient for the purpose of transmission.

• 2. It is a one-to-one mapping of

the quantized samples by using code elements or symbols of the required length per sample.

FOLDED BINARY CODE

• The folded binary code

(also called the sign- magnitude representation) assigns the first (left most) digit to the sign and the remaining digits are used to code the magnitude.

• This code is superior to the

natural code in masking transmission errors when encoding speech.

INVERTED FOLDED BINARY CODE

• 1. If only the amplitude digits of a

folded binary code are complemented (1's changed to 0's and 0's to 1's), an inverted folded binary code results. 2. This code has the advantage of higher density of 1's for small amplitude signals, which are most probable for voice messages.

• 3. The higher density of 1's relieves

some system timing errors.

GRAY CODE

• 1. With natural binary encoding, a

number of codeword digits can change even when a change of

• nly one quantization level occurs.

For example, a change from level 7 to 8 entails every bit changing in the 4-bit code illustrated. 2. In some applications, this behavior is undesirable and a code is desired for which only one digit changes when any transition

• ccurs between adjacent levels.
• 3. The Gray Code has this property

4-BIT PCM TRANSMITTER - CIRCUIT SCHEMATIC

PCM FOR BI-POLAR SIGNALS

PCM INTEGRATED CIRCUITS - MC14LC5480

• 1. The MC14LC5480 is a general purpose per

channel PCM Codec–Filter with pin selectable µ–Law or A–Law companding, and is offered in 20–pin DIP, SOG, and SSOP packages.

• 2. MC14LC5480 performs voice digitization and

reconstruction as well as the band limiting and smoothing required for PCM systems.

• 3. MC14LC5480 designed to operate in both

synchronous and asynchronous applications and contains an on–chip precision reference voltage.

MC14LC5480 - BLOCK DIAGRAM

μ/A Law Select (Pin 16) This pin controls the compression for the encoder and the expansion for the decoder. Mu–Law companding is selected when this pin is connected to VDD A–Law companding is selected when this pin is connected to VSS.

MC14LC5480 - TYPICAL CONNECTION

MC14LC5480 - COST

KSH 700/=

ADVANTAGES OF PCM

• 1. PCM provides high noise immunity
• 2. Allows regeneration of clean signal

by using repeaters placed between the transmitter and the receiver.

• 3. PCM signals can be stored for later

use or retransmission with high fidelity

• 4. PCM signals can be encrypted

more easily and to very high standards.

DISADVANTAGES OF PCM

• 1. PCM requires complex circuitry to

sample, quantize, code and decode.

• 2. PCM requires large bandwidth

compared with that of the original analog signal.

DELTA MODULATION

ECE 416 Thursday, 08 March 2018

DELTA MODULATION

• 1. Delta modulation seeks to overcome

the problem of high bandwidth requirement in conventional PCM.

• 2. Instead of generating and transmitting

many bits per sample, only one bit is transmitted.

• 3. During coding, the present sample is

compared with the previous and a 0 or 1 transmitted depending on whether the sample is higher or lower than the previous.

PCM code for each sample

SIGNALS IN A DELTA MODULATION SYSTEM

Output from the receiver (decoder) Output from Encoder Original Analog Signal Amplitude Time

DELTA MODULATION TRANSMITTER

One-bit Quantizer Delay 𝑈

𝑡

+

• +

+ 𝑦(𝑜𝑈

𝑡)

error 𝑓(𝑜𝑈

𝑡)

Output Accumulator 𝑦′(𝑜𝑈

𝑡)

𝑐(𝑜𝑈

𝑡)

𝑣(𝑜𝑈

𝑡)

DELTA MODULATION RECEIVER

Delay 𝑈

𝑡

Low-pass filter + + Accumulator Demodulated Signal

ADVANTAGES OF DELTA MODULATION

Delta Modulation:

• 1. Requires very small bandwidth since it

transmits only one bit per sample

• 2. Has very simple transmitter and receiver

circuitry .

Delta modulation has: a) Slope and overload distortion b) Granular and Idle noise

DISADVANTAGES OF DELTA MODULATION

SLOPE OVERLOAD

• Slope-overload occurs when the

step size is too small to follow a steep segment of the input waveform x(t ).

GRANULARITY

• Granularity refers to a situation where the staircase function x(t)

hunts around a relatively flat segment of the input function, with a step size that is too large relative to the local slope characteristic of the input.

ADAPTIVE DELTA MODULATION

ECE 416 – Digital Communication Thursday, 08 March 2018

THE PRINCIPLE OF ADAPATIVE DELTA MODULATION

• Adaptive Delta

Modulation seeks to

• vercome quantization

errors arising from slope

• verload and granular

noise by varying the step size in accordance to the signal amplitude.

∆𝒐+𝟐≠ ∆𝒐 ∆𝑜 Amplitude Time 1 1 1 1 1 1 1

ADAPTIVE DELTA MODULATION TRANSMITTER

One-bit Quantizer Logic for step control Delay 𝑈

𝑡

+

• +

+ 𝑦(𝑜𝑈

𝑡)

error 𝑓(𝑜𝑈

𝑡)

Output Accumulator 𝑦′(𝑜𝑈

𝑡)

ADAPTIVE DELTA MODULATION RECEIVER

Logic for step-size control Delay 𝑈

𝑡

Low-pass filter + + + + Accumulator Receiver Output Receiver Input

DIF IFFERENTIAL PULSE CODE MODULATION (D (DPCM)

ECE 416 – Digital Communication Thursday, 08 March 2018

DIFFERENTIAL PULSE CODE MODULATION

• 1. Some signals such as speech have high correlation between

adjacent samples.

• 2. When such highly correlated samples are encoded using basic

PCM, the resulting code contains a lot of redundant information.

• 3. In such cases, basic PCM scheme is not the preferred coding

method.

• 4. By removing this redundancy before encoding an efficient

coded signal can be obtained.

• 5. One method of removing redundancy is by using the

Differential PCM (DPCM) method.

• 6. DPCM is based on the principle that by knowing the past

behaviour of a signal up to a certain point in time, it is possible to predict future values.

DPCM TRANSMITTER

𝑦′(𝑜𝑈

𝑡)

𝑓 𝑜𝑈

𝑡 = 𝑦 𝑜𝑈 𝑡 − 𝑦′(𝑜𝑈 𝑡)

𝑦(𝑜𝑈

𝑡)

𝐵𝑜𝑏𝑚𝑝𝑕𝑣𝑓 𝑇𝑗𝑕𝑜𝑏𝑚 X(t) 𝑦′(𝑜𝑈

𝑡)

𝑐 𝑜𝑈

𝑡 = 𝑑𝑝𝑒𝑓𝑒 𝑔𝑝𝑠𝑛 𝑝𝑔

𝑦 𝑜𝑈

𝑡 − 𝑦′ 𝑜𝑈 𝑡

𝑅𝑣𝑏𝑜𝑢𝑗𝑨𝑓𝑒 𝑤𝑏𝑚𝑣𝑓 𝑝𝑔 𝑓 𝑜𝑈

𝑡 = 𝑦 𝑜𝑈 𝑡 − 𝑦′(𝑜𝑈 𝑡)

𝑣 𝑜𝑈

𝑡 = 𝑦^(𝑜𝑈 𝑡)

Predictor uses 𝑦^(𝑜𝑈

𝑡) and previous

values to predict 𝑦′(𝑜𝑈

𝑡)

DPCM RECEIVER

𝑓 𝑜𝑈

𝑡 = 𝑦 𝑜𝑈 𝑡 − 𝑦′(𝑜𝑈 𝑡)

𝑦′(𝑜𝑈

𝑡)

Predictor uses 𝑦^(𝑜𝑈

𝑡) and previous

values to predict 𝑦′(𝑜𝑈

𝑡)

𝑐 𝑜𝑈

𝑡 = 𝑑𝑝𝑒𝑓𝑒 𝑔𝑝𝑠𝑛 𝑝𝑔

𝑓 𝑜𝑈

𝑡

𝑧 𝑜𝑈

𝑡 = 𝑦(𝑜𝑈 𝑡)

COMPARISON OF PCM, DELTA MODULATION AND ADAPTIVE PULSE CODE MODULATION

N0 PARAMETER PULSE CODE MODULATION (PCM) DELTA MODULATION ADAPTIVE DELTA MODULATION 1 Levels and Step Size Number of levels depend

• n number of bits

Level size is fixed Step size is fixed Step size varies according to the rate at which the signal is varying 2 Number of Bits Can take 4, 8 or 16 bits per sample One bit per sample One bit per sample 3 Quantization errors and distortion Quantization noise is present Has lope overload and granular noise Quantization noise is present 4 Bandwidth Highest bandwidth Low bandwidth required Least bandwidth required 5 Feedback in transmitter or receiver No feedback Feedback in transmitter Feedback in transmitter 6 Complexity in implementation High Simple Simple