digital communication principles-1

ETI 2413Digital Communication PrinciplesBy

Isaac Warutumo

ETI 2413 Digital Communication Principles

2 Isaac Warutumo September 22, 2014

PrerequisitesETI2404 Signals and Communications IPurposeThe aim of this course is to enable the student to;1. Understand the operation of A/D converters2. Appreciate the importance of wave shaping in digital communications3. Know the characteristics of various digital modulations schemes4. Understand the effects of noise in digital communicationsLearning OutcomesAt the end of this course, the student should be able to;



1. Describe the operation of A/D converters2. Calculate bandwidth requirements in digital communications3. Compute data transmission rates in the presence of noiseCourse Description Principles of analogue-to-digital and digital-to-analogue converters Digital signals: quantization, digitization, transmission and recognitiontechniques.

Detection techniques of digital signals from noise: Baseband analysis,filtering and pulse-shaping.

Effects of inter-symbol interference.

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Performance of various modulation schemes: M-array, amplitude shift,frequency shift, continuous Binary Phase Shift Keying (BPSK), QuaternaryPhase Shift Keying (QPSK), Gaussian Minimum Shift Keying (GMSK),differential phase shift keying (DPSK) with noise and ideal filters.

Circuit realization for binary, quaternary, differential continuous phaseshift keying and differential phase shift keying modems.

Errors in digital communication systems: types, sources andmeasurements.

Digital spread-spectrum system: Direct Sequence Code DivisionMultiplexing Access (DS-CDMA), Frequency Hoping Spread Spectrum(FHSS).

Advanced modulation techniques: Orthogonal Frequency DivisionMultiplexing (OFDM), Ultra Wideband (UWB)

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Application to communication systems. Digital receivers



Digital transmission of Analogue Data

A digital signal is superior to an analog signal because it is more robust tonoise and can easily be recovered, corrected and amplified. For thisreason, the tendency today is to change an analog signal to digital data

Figure 1: General communication scenario



PCM consists of three steps to digitize an analog signal: Sampling Quantization Binary encoding

Before we sample, we have to filter the signal to limit the maximumfrequency of the signal as it affects the sampling rate.

Filtering should ensure that we do not distort the signal, i.e. remove highfrequency components that affect the signal shape.



Figure 2: Digitization Process An analogue to Digital Converter (ADC) converts a continuous (analogue)signal to binary digital data.

Analog signals are continuous, with infinite values in a given range.



Digital signals have discrete values such as on/off or 0/1. Limitations of analog signals

o Analog signals pick up noise as they are being amplified.o Analog signals are difficult to store.o Analog systems are more expensive in relation to digital systems.

Advantages of digital systems (signals)o Noise can be reduced by converting analog signals in 0s and 1s.o Binary signals of 0s/1s can be easily stored in memory.o Technology for fabricating digital systems has become so advancedthat they can be produced at low cost.

The major limitation of a digital system is how accurately it representsthe analog signals after conversion.

A typical system that converts signals from analog to digital and back toanalog includes:



o A transducer that converts non-electrical signals into electrical signalso An A/D converter that converts analog signals into digital signalso A digital processor that processes digital data (signals)o A D/A converter that converts digital signals into equivalent analogsignals

o A transducer that converts electrical signals into real life non-electrical signals (sound, pressure, and video)



Figure 3: system that converts signals from analog to digital andback to analog



A/D Converter In order to change an analog signal to digital, the input analog signal issampled at a high rate of speed.

The amplitude at each of those sampled moments is converted into anumber equivalent this is called quantization.

These numbers are simply the combinations of the 0s and 1s used incomputer language this called encoding.



Figure 4: A typical A/D converter









Sampler Sampling is the first stage of the ADC process Analog signal is sampled every TS seconds. Ts is referred to as the sampling interval. fs = 1/Ts is called the sampling rate or sampling frequency. There are 3 sampling methods:

o Ideal - an impulse at each sampling instanto Natural - a pulse of short width with varying amplitudeo Flattop - sample and hold, like natural but with single amplitude value

The process is referred to as pulse amplitude modulation (PAM) and theoutcome is a signal with analog (non integer) values



Figure 5: Different sampling Methods



The analogue signal is sampled at regular intervals. To ensure regularsampling, an accurate clock is needed. The sampling rate is determinedaccording of the sampling theorem which states that: -an analogue signal that has no frequency components higher than fm Hz can be

uniquely represented by a sampled signal if the samples are made at a rate of f0samples per second where 0 2 mf f

The original signal can be recovered from the sampled signal by passing itthrough a low pass filter (LPF), whose bandwidth fB is given 02M B ff f Hz

The frequency 0 2 mf f is called. The Nyquist frequency or Nyquist rate The output of the sampler are sampled values at the sampling instants,hence discrete



Quantizer This device maps the sampled analog signal to discrete values which areincremented stepwise

For an analog signal which has a maximum value of l volts and a minimumof a Volts, the analog signal is mapped in Q stepped discrete values

For such a signal, the step sizel a

Q

(1)

In digital communications, the number of quantization steps is chosen suchthat

2qQ (2)



Where q is an integer which represents the number of binary digits used toencode a single sample

Figure 6 shows a typical signal at the output of the quantizer

Figure 6: Quantized signal



As can be seen in figure 6, the quantized value is held constant over thesampling period T.

The quantized value is not always equal to the sampled value and thisabsolute difference is called Quantization error.

The signal power to quantization noise power is given as2 1s Q

N (3)

Where Q= number of quantization steps, When expressed in dB,

2( ) 10log( 1)s dB QN

(4)



Quantization Error When a signal is quantized, we introduce an error - the coded signal is anapproximation of the actual amplitude value.

The difference between actual and coded value (midpoint) is referred to asthe quantization error.

The more zones, the smaller which results in smaller errors. BUT, the more zones the more bits required to encode the samples ->higher bit rateQuantization Error and SNQR

Signals with lower amplitude values will suffer more from quantizationerror as the error range: /2, is fixed for all signal levels.



Non linear quantization is used to alleviate this problem. Goal is to keepSNQR fixed for all sample values.

Two approaches:o The quantization levels follow a logarithmic curve. Smaller s atlower amplitudes and larger s at higher amplitudes.

o Companding: The sample values are compressed at the sender intologarithmic zones, and then expanded at the receiver. The zones arefixed in height.***research more***Bit rate and bandwidth requirements of PCM

The bit rate of a PCM signal can be calculated form the number of bits persample x the sampling rate

b s sBit rate n x f q f



The bandwidth required to transmit this signal depends on the type of lineencoding used (discussed later).

A digitized signal will always need more bandwidth than the originalanalog signal. Price we pay for robustness and other features of digitaltransmission.

Example:We have a low-pass analog signal of 4 kHz. If we send the analogsignal, we need a channel with a minimum bandwidth of 4 kHz. If wedigitize the signal and send 8 bits per sample, we need a channel with aminimum bandwidth of 8 4 kHz = 32 kHz.

PCM Encoder This device converts the step value to a binary number for transmission.



The number of bits to encode the binary number is obtained fromequation (2) above as

2logq Q (5) For example, for a system with Q=8, the binary digits per sample

2log 8 3q The output of the PCM encoder is binary data, which can be stored in acomputer file.

In this way, analog signal data can be handled as any other data stored in acomputer.


24 Isaac Warutumo September 22, 2014Figure 7: different quantization levels



Example Given that an analog signal has a minimum value of 0V, a maximum valueof 4V, and the number of quantization steps is 8, draw a table showing stepnumber, binary PCM codes for the step and the value of voltagerepresented by the PCM code

Step size 4 0 0.58

V

The number of bits per PCM code is 2log 8 3q Stepnumber

0 1 2 3 4 5 6 7

Binary 000 001 010 011 100 101 110 111



CodeVoltage 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Quantization rules(i) Quantization step size

l aQ

(6)

Where l is the highest analog value, a is the minimum analog valueAnd Q is the number of quantization steps

(ii) the quantized value1( ) ( ) ( ) ( )q i i s ix kT m if x t x kT x t (7)



Where im is the quantized ith step value, ( )ix t is the analog scale value,( )ix t a i and ( )sx kT is the analogue sampled scale value

2im a i (8)Or

12

i ix x

im (9)



Figure 8: Analog Signal and its quantized signal



Figure 8 above illustrates an analogue signal ( )x t , the sample values( )sx kT , as well as the quantized values ( )qx kT according to the

quantization rules above. The number of quantization steps Q=8 The quantized values i( ) mqx kT always lie within the analog rangebecause q i Qx m x

The quantization error is given by( ) ( )error s q

error

Q x kT x kand Qwhere step size



At the receiver, the quantized signal can be recovered from the receivedPCM encoded data because the maximum and minimum values b and a areknown.

The original analog signal corrupted by noise can then be recovered bypassing the reconstructed quantized signal through a low pass filter (LPF)as shown in

Figure 9: reconstruction of the analog signal



ExampleThe range of an analog signal is 0-4V. 8 quantization steps are used. Table 1below shows the sampled values at the sampling instants

Table 1: Sampled signalTime (mS) 0 1 2 3 4 5 6 7Sampled value (V) 0.1 1.2 2.1 2.7 3.3 3.8 3.4 2.3

a) Calculate the transmitted PCM code for each sampleb) Sketch on the same scale the quantized signal and the approximated analogsignal Solution



Quantization step size 4 0 0.58

l aQ

Analog scale ix a i wherei is the step number Quantized scale 2im a i The quantized value 1( ) ( ) ( ) ( )q i i s ix kT m if x t x kT x t The quantized step number i and the quantized value ( )qx kT arecalculated for each sample

---to do ---



Time(mS)

0 1 2 3 4 5 6 7

Sampledvalue (V)

0.1 1.2 2.1 2.7 3.3 3.8 3.4 2.3

L 0 2 4 5 6 7 7 4mi 0.25 1.25 2.25 2.75 3.25 3.75 3.75 2.25xq(kT) 0.25 1.25 2.25 2.75 3.25 3.75 3.75 2.25PCM (i) 000 010 100 101 110 111 111 100



--to dodraw the sketch Quiz Explain the seeming backward rotation of the wheels of a forward-movingcar in a movie

A complex low-pass signal has a bandwidth of 200 kHz. What is theminimum sampling rate for this signal?

A complex bandpass signal has a bandwidth of 200 kHz. What is theminimum sampling rate for this signal?



We want to digitize the human voice. What is the bit rate, assuming 8 bitsper sample? ( Make a realistic assumption regarding the highest frequencyof the human voice)

The end

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