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Chapter #5 Pulse Modulation

Analog Pulse ModulationIntroduction

Introduction

Introduction

Pulse Amplitude Modulation (PAM)

Pulse Amplitude Modulation (PAM)

Pulse Amplitude Modulation (PAM)

PDM and PPM

Digital Pulse ModulationDigital Pulse ModulationThe digital pulse modulation has two types:Pulse Code Modulation(PCM)Delta Modulation(DM)The process of Sampling which we have already discussed in initial slides is also adopted in digital pulse modulationPulse Code Modulation(PCM)PCM is the most basic form of digital pulse modulation.In PCM, a message signal is represented by a sequence of coded pulses, which is accomplished by representing the signal in discrete form in both time and amplitude.The basic operations performed in the transmitter of a PCM system are sampling, quantizing, and encoding.

The basic elements of a PCM systemBefore we sample, we have to filter the signal to limit the maximum frequency of the signal as it affects the sampling rate.Filtering should ensure that we do not distort the signal, i.e. remove high frequency components that affect the signal shape.

SamplerThe sampler samples the input continuous-time analog signal at a sampling rate fs (= 1/Ts sec).There are 3 sampling methods:Ideal - an impulse at each sampling instantNatural - a pulse of short width with varying amplitudeFlattop - sample and hold, like natural but with single amplitude value

Quantization ProcessThe analog signal has a continuous range of amplitudes and therefore its samples have a continuous amplitude range.In the quantization, the signal with continuous amplitude can be approximated by a signal constructed of discrete amplitudes selected on a minimum error basis from an available set.

QuantizerThe sampling results is a series of pulses of varying amplitude values ranging between two limits: a min and a max.The amplitude values are infinite between the two limits.We need to map the infinite amplitude values onto a finite set of known values.This is achieved by dividing the distance between min and max into L zones, each of height = (max - min)/L

Quantization LevelsThe midpoint of each zone is assigned a value from 0 to L-1 (resulting in L values)Each sample falling in a zone is then approximated to the value of the midpoint.

Quantization ZonesAssume we have a voltage signal with amplitutes Vmin=-20V and Vmax=+20V.We want to use L=8 quantization levels.Zone width = (20 - -20)/8 = 5The 8 zones are: -20 to -15, -15 to -10, -10 to -5, -5 to 0, 0 to +5, +5 to +10, +10 to +15, +15 to +20The midpoints are: -17.5, -12.5, -7.5, -2.5, 2.5, 7.5, 12.5, 17.5

Quantization ErrorWhen a signal is quantized, we introduce an error - the coded signal is an approximation of the actual amplitude value.The difference between actual and midpoint value is referred to as the quantization error.The more zones, the smaller which results in smaller errors.

EncodingIn combining the process of sampling and quantization, the specification of the continuous-time analog signal becomes limited to a discrete set of values.Representing each of this discrete set of values as a code called encoding process.Code consists of a number of code elements called symbols.In binary coding, the symbol take one of two distinct values. in ternary coding the symbol may be one of three distinct values and so on for the other codes.Assigning Codes to ZonesEach zone is assigned a binary code.The binary code consists of bits.The number of bits required to encode the zones, or the number of bits per sample, is obtained as follows: nb = log2 LGiven our example, nb = 3The 8 zone (or level) codes are therefore: 000, 001, 010, 011, 100, 101, 110, and 111Assigning codes to zones:000 will refer to zone -20 to -15001 to zone -15 to -10, etc.

Line CodingAny of several line codes can be used for the electrical representation of a binary data stream.Examples of line coding : RZ, NRZ, and Manchester

210tx(t)Consider the analog Signal x(t).210nX(nTs)The signal is first sampledTs2468n102dividing the range into 4 zonesnassign quantized values of 0 to 3 to the midpoint of each zone.0123

napproximating the value of the sample amplitude to the quantized values.0123nEach zone is assigned a binary code012300011011n01230001101100000101111111The sequence bits if the samples 01111111010000Use one of the line code scheme to get the digital signal