Chapter #5 Pulse Modulation

Chapter #5Pulse Modulation1st semester 1434-1435

King Saud University College of Applied studies and Community Service1301CTBy: Nour Alhariqi

OutlineSamplingDigital communication systemAnalog pulse modulationDigital pulse modulationSampling ProcessThe sampling process is a basic operation in the digital communication.In this process, the continuous-time analog signal signal is sampled by measuring its amplitude at a discrete instants.So, the continuous-time analog signal is converted into a corresponding sequence of samples that are usually spaced uniformly in time.It is necessary to choose the sampling rate properly, so the sequence of samples uniquely defines the original analog signal.

The Sampling TheoremThe sampling theorem shows that a continuous-time signal which is a band-limited to fm Hz can be represented perfectly by a series of samples spaced Ts ( 1/2 fm) seconds apart. Ts called sampling periodThe band-limited signal is a signal which its Fourier transform is nonzero for -2 fm < < 2 fm.When m(t) is sampled uniformly at intervals ofTsseconds, the resultant sequence is denoted bym(nTs), for all integer values ofn.

S(t) is band- limited signalTssampling period

The Sampling TheoremLets define a sampling rate fs = 1 / Ts which is the number of samples per second.Thus, the sampling theorem states that a band-limited signal can be recovered completely from a set of samples taken at the rate of fs ( 2 fm) samples per second. The preceding sampling theorem is often called the uniform sampling theorem for baseband or low-pass signal.The minimum sampling rate, 2fm samples per second, called the Nyquist rate; its reciprocal 1/2fm is called Nyquist interval

Sampling ProcessSampling g(t) at a rate of fs Hz (fs samples per second) can be accomplished by multiplying g(t) by an impulse train Ts(t), consisting of unit impulses repeating periodically every Ts seconds, where Ts = 1 / fs

Let g(t) be a signal whose spectrum is band-limited to fm Hz

Sampling ProcessThis results sampled signal (t) consists of impulses spaced every Ts seconds.The nth impulse, located at t=n Ts has a strength g(nTs), the value of g(t) at t = n Ts

Sampling Process

Sampling Process

Sampling Process

Sampling Process

2 fm1/2fmAliasingWhat happens if we sample the signal at a frequency that is lower that the Nyquist rate?If the Nyquist criterion is not satisfied, the adjacent copies of g(t) spectrum will overlap, this phenomenon calledaliasing

AliasingWith aliasing :- Some of the frequencies in the original signal will be lost in the reconstructed signal- unwanted components will be presence in the reconstructed signal. these components were not present when the original signal was sampled. In addition,. Aliasing occurs because signal frequencies will overlap if the sampling frequency is too low. ExampleWhat Nyquist rate is needed for a signal with a bandwidth 10,000Hz ( 1000 to 11,000 Hz)?

The Nyquist rate is equal to twice the highest frequency in the signal Nyquist rate = 2 * 11,000 = 22,000 samples/secAnalog 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 signalDelta ModulationIntroductionPCM is a very complex technique. Other techniques have been developed to reduce the complexity of PCM. The simplest is delta modulation. PCM finds the value of the signal amplitude for each sample; DM finds the change from the previous sample.Delta ModulationIn Delta Modulation, only one bit is transmitted per sample That bit is a one if the current sample is more positive than the previous sample, and a zero if it is more negativeSince so little information is transmitted, delta modulation requires higher sampling rates than PCM for equal quality of reproduction

Delta Modulation1- A staircase approximation of the message signal is derived The analog signal is approximated with a series of segments ( staircase approximation signal)Each segment of the approximated signal is compared to the message signal:If the approximation fall below the signal at any sampling epoch the segment is increased by .If the approximation lies above the signal at any sampling epoch the segment is diminished by .So, the time and amplitude axes are quantized.

Delta Modulation2- encodingThis scheme sends only one bit each segment. if the segment at time tn+1 is higher in amplitude value than the segment at time tn, then a bit 1 is used to indicate the positive value.If the segment is lower in value resulting in a negative value, a 0 is used.

This scheme works well for small changes in signal values between samples.If changes in amplitude are large, this will result in large errors.

Merits of Digital Communication SystemsMerits of Digital Communication1- Digital signals are very easy to receive. The receiver has to just detect whether the pulse is low or high ( one or zero).2- AM & FM signals become corrupted over much short distances as compared to digital signals.3 - In digital signals, the original signal can be reproduced accurately.

Merits of Digital Communication4- as known, the signals lose power as they travel, which is called attenuation. When AM and FM signals are amplified, the noise also get amplified. But the digital signals can be cleaned up to restore the quality and amplified by the regenerators.5- The noise may change the shape of the pulses but not the pattern of the pulses.

Merits of Digital Communication 6 - AM and FM signals can be received by any one by suitable receiver. But digital signals can be coded so that only the person, who is intended for, can receive them.7- The digital signals can be stored.