ANALOGUE AND DIGITAL COMMUNICATION

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1 ANALOGUE AND DIGITAL COMMUNICATION Syed M. Zafi S. Shah Umair M. Qureshi Lecture xxx: Analogue to Digital Conversion

2 Topics Pulse Modulation Systems Advantages & Disadvantages Pulse Code Modulation Pulse Amplitude Modulation/Sampling Quantization Encoding Delta Modulation Pulse Width Modulation Pulse Position Modulation

3 In today s class ANALOG TO DIGITAL CONVERSION SAMPLING SAMPLING THEOREM, ALIASING QUANTIZATION QUANTIZATION NOISE

4 Pulse Modulation Systems Systems in which a series of recurring pulses are made to vary in amplitude, duration, shape & time, as a function of modulating signal There are various Pulse Modulation schemes Pulse Amplitude Modulation Pulse Code Modulation Delta Modulation Pulse Width Modulation Pulse Position Modulation

5 Advantages? Noise immunity Inexpensive digital circuitry Can be time division multiplexed with other pulse modulated signal Transmission distance is increased through the use of regenerative repeaters Digital pulse streams can be stored Error detection and correction is easily implemented

6 Disadvantages Require greater BW to transmit and receive as compare to its analog counterpart For high transmission rates, time need specialized encoding techniques Pulse coded stream is difficult to recover For information recovery, it need synchronization between transmitter & receiver

7 Pulse code modulation (PCM) Developed in 1937 at the Paris Laboratories of AT&T Alex H. Reeves is credited for its invention and also of PAM, PWM & PPM Most widely used scheme in today s telecommunication industry such as PSTNs

8 Pulse Code Modulation Pulse Code Modulation is a process through which an analogue signal can be represented (approximated) by a digital signal PCM is a three step process which includes Sampling/Pulse amplitude modulation Quantization Coding

9 Need for A/D conversion We know by now the benefits of digital signals and systems But most signals of practical interest are still analog Voice, Video RADAR signals Biological signals etc So in order to utilize those benefits, we need to convert our analog signals into digital This process is called A/D conversion

10 Three step process Analog to Digital conversion is really a three step process involving Sampling Conversion from continuous-time, continuous valued signal to discrete-time, continuous-valued signal Quantization Conversion from discrete-time, continuous valued signal to discrete-time, discrete-valued signal Coding Conversion from a discrete-time, discrete-valued signal to an efficient digital data format Represent as bit?

11 Analog signal Binary bits SAMPLING QUANTIZATION CODING CT-CV DT-CV DT-DV DT-DV Arbitrarily, I ve chosen Differential PCM. Can you re-create these graphs?

12 Sampling A continuous-time signal has some value defined at every time instant So it has infinite number of sample points sample every 1 sec sample every 0.1 sec sample every 1 μsec

13 It is impossible to digitize an infinite number of points because infinite points would require infinite amount of memory and infinite amount of processing power So we have to take some finite number of points Sampling can solve such a problem by taking samples at the fixed time interval Sampling is the process of determining the instantaneous voltage at these given intervals of time A technique called pulse amplitude modulation is used to produce a pulse when signal is sampled If an analog signal is not appropriately sampled, aliasing will occur, where a discrete-time signal may be a representation (alias) of multiple continuous-time signals

14 Shannon-Nyquist Sampling theorem The sampling theorem guarantees that an analogue signal can be in theory perfectly recovered as long as the sampling rate is at least twice as large as the highest-frequency component of the analogue signal to be sampled F s 2F max A signal with no frequency component above a certain maximum frequency is known as a band-limited signal (in our case we want to have a signal band-limited to ½ Fs) Some times higher frequency components are added to the analog signal (practical signals are not band-limited) In order to keep analog signal band-limited, we need a filter, usually a low pass that stops all frequencies above ½ Fs. This is called an Anti-Aliasing filter

15 In order to sample a voice signal containing frequencies up to 4 KHz, we need a sampling rate of 2*4000 = 8000 samples/second Similarly for sampling of sound with frequencies up to 20 KHz, we need a sampling frequency of 2*20000 = samples/second What is the sampling rate for CDs? Isn t it more than the one we just calculated?

16 Types of Sampling Critical Sampling When the sampling frequency is chosen to be equal to twice the max. frequency component F s 2F max Ideally, we should be able to recover the Analog signal from Digital samples Under Sampling When the sampling frequency is chosen to be less than twice the max. frequency component F s 2F max We would not be able to recover the analog signal from Digital samples

17 Over Sampling When the sampling frequency is chosen to be greater than twice the max. frequency component We would be able to recover the Analog signal from Digital samples F s 2F max It would also help to control the effect of Aliasing To understand this, we must look into time & frequency domain view of sampled signal Require more memory!

18 Relationship between Analog & Digital Frequencies Consider a continuous-time signal, y(t) Acos(2 Ft) y(t) Acos( t) which is sampled at instant T, the discrete-time signal can be represented as, y[nt] Acos(2 FnT ) y[nt] Acos( nt) The sampling instant T is the reciprocal of the sampling frequency Fs, i.e. T 1 F s

19 So the discrete-time signal becomes F Acos 2 Fs n y[nt] y[nt] AcosnT y[nt] Acos2fn y[nt] Acosn Comparing these equation with their analog counterparts, we find f F F s T

20 As Therefore F F F F F f s F F F T s f

21 Example 1: For the following analog signal, find the Nyquist sampling rate, also determine the digital signal frequency and the digital signal x( t) 3cos(70 )t The maximum frequency component is x(t) is 70 Fmax 35 2 Hz Therefore according to Nyquist, we need a sampling rate of F s 2F max 70 Hz The digital signal would have a frequency 35 w 2 70 The digital signal can be represented as x[ n] 3cos( n)

22 Example 2: Consider two analog signals cos2 (10 t y ( t) cos2 (50) t x ( t) ) sampled at 40 Hz, determine the digital signal x[ n] cos 2 n y[ n] cos 2 n x[ n] cos n 2 y[ n] 5 cos n 2 cos 2n n 2 cos n 2 Both signals are represented by the same discrete-time signal ALIAS, as a general rule of thumb, an alias will be present every Fs F k F 0 kf s

23 Anti-aliasing filters Anti-aliasing filters are analog filters as they process the signal before it is sampled. In most cases, they are also low-pass filters unless band-pass sampling techniques are used The ideal filter has a flat pass-band and the cut-off is very sharp, since the cut-off frequency of this filter is half of that of the sampling frequency, the resulting replicated spectrum of the sampled signal do not overlap each other. Thus no aliasing occurs

24 Practical low-pass filters cannot achieve the ideal characteristics. What can be the implications? Firstly, this would mean that we have to sample the filtered signal at a rate that is higher than the Nyquist rate to compensate for the transition band of the filter That s why the sampling rate of a CD is 44.1 KHz, much higher than the 40 KHz we calculated Go through the assignment it has some reading task along with some problems

25 Example 3: Find the Nyquist s rate for the following signal x( t) 3cos(50 )t 10sin(300 )t -cos(100 )t This composite signal comprises three frequencies f 1 = 25 Hz, f 2 = 150 Hz, f 3 = 50 Hz So, we need to sample at or greater than 300 Hz However, for the sine term, the sampled signal has values sin(πn), meaning the samples are taken at the zero crossings, so the sine term is not counted in the process Therefore, a solution is to sample at higher than twice the max. freq component

26 Quantization Now that we have converted the continuous-time, continuous-valued signal into a discrete-time, continuous-valued signal, we STILL need to make it discrete valued This is where Quantization comes into picture The process of converting analog voltage with infinite precision to finite precision For e.g. if a digital processor has a 4-bit word, the amplitudes of the signal can be segmented into 16 levels

Quantization 4-bit ADC 2 4 =16 levels 1111 1110 1101 1100

27 Quantization 4-bit ADC 2 4 =16 levels

28 If the discrete-time signal x[n] falls between two quantization levels, it will either be rounded up or truncated Rounding replaces x[n] by the value of the nearest quantization level Truncation replaces x[n] by the value of the level below it

29 General rules for Quantization Important properties of the quantizer include Number of quantizer levels Quantization resolution Note the minimum & maximum amplitude of the input signal Ymax = 1 Ymin & Ymax Ymin =

30 Note the word-length of DSP m-bits Number of levels of quantizer is equal to L = 2 m The resolution of the quantizer is given as ( ymax ymin ) L 1 volts Resolution of a quantizer is the distance between two successive quantization levels More quantization levels, better resolution! Whats the downside of more quantization levels?

31 n 0.9 n 0 x[ n] 0 n 0 m = 4, L = 16 Ymin = 0 Ymax = 1 = 1/15 =

32 Quantization error The error caused by representing a continuous-valued signal(infinite set) by a finite set of discrete-valued levels Suppose a quantizer operation given by Q(.) is performed on continuous-valued samples x[n] is given by Q(x[n]), then the quantization error is given by e q [ n] x[ n] x [ n] q

33 Lets consider the signal quantized. x[ n] n n n 0 0, which is to be In the figure (previous slide), we saw that there was a difference between the original signal and the quantized signal. This is the error produced while quantization It can be reduced, however, if the number of quantization levels is increased as illustrated on next slide

34 bit ADC bit ADC x 10-3 Quant. error Quant. error

35 Example 3: The discrete-time signal x[ n] 6.35cos n 10 with resolution =0.1, how many bits are required in the ADC is quantized We will solve this problem using the formula for quantization resolution. Note that the maximum value of x[n] is 6.35 & the minimum value of x[n] 6.35 ( 6.35) 0.1 L L 1 m L m 7 So, a 7-bits ADC would be required 0.1( L 1) 12.7 L 1127 Solve for =0.02

36 Signal-to-Quantization-noise ratio Provides the ratio of the signal power to the quantization noise Mathematically, where Pq N 1 N q n0 N n0 N e n xn x n q P x = Power of the signal x (before quantization) P q = Power of the error signal x q 2

37 Ex 4: An analog signal contains useful frequency upto 100 Hz. What is the Nyquist s rate for this signal? Suppose we sample this signal at 250 samples/sec, what is the highest frequency component that can be represented uniquely at this sampling rate Ex 5: An analog signal is sampled at 600 samples/sec. x( t) sin(480t ) 3sin(720t ) Find (a) Nyquist s rate (b) Folding frequency (c) Frequency of the discrete-time signal

38 Delta Modulation Transmit information only to indicate whether the input analog signal goes up or goes down Present value is greater than or less than the previous value The encoder outputs are highs or lows that instruct whether to go up or down, respectively

39 Delta Modulation-2 After sampling, delta modulation performance 1-bit quantisation on the sampled signal If x(n-1) > x(n) then output bit = 1 If x(n-1) < x(n) then output bit = 0

40 Amplitude (Volts) CT rep DT rep Time (secs)

41 Delta modulation There are two important parameters here, Size of the step assigned to each binary digit (δ) Sampling rate Accuracy is improved by increasing the sampling rate This also increases the data rate as well Advantage of DM over PCM is the simplicity of its implementation

42 Pulse Width Modulation Also known as pulse duration modulation (PDM) A form of modulation in which the width of a pulse carrier is made to vary in accordance with the modulation voltage. The leading edge of the pulse remains fixed, but the occurrence of the trailing edge of the pulse varies Disadvantages? Different pulses of different durations (width) are created Hard to interpret Wider pulses expending more power

43 Pulse Position Modulation It is possible to overcome the flaw of PWM, by preserving only the pulse transitions of the PWM signal This effectively creates Pulse Position Modulation (PPM) PPM differs from PWM in that the position of a pulse is made to vary in accordance of the modulating voltage

44 Pulse modulated schemes

45 Your Assignment CAMPARE/DIFFERENTIATE ALL PULSE MODULATION TECHNIQUES (PCM, DM, PWM & PPM) IN TERMS OF POWER, BANDWIDTH & DESIGN IMPLEMENTATION

Multiplexing Concepts and Introduction to BISDN. Professor Richard Harris

Multiplexing Concepts and Introduction to BISDN Professor Richard Harris Objectives Define what is meant by multiplexing and demultiplexing Identify the main types of multiplexing Space Division Time Division