Chapter 10 Applications in Communications · © School of IS&E, SDU. Copyright Reserved 2/ 47...

© School of IS&E, SDU. Copyright Reserved1/ 47

Chapter 10Applications in Communications

School of Information Science and Engineering, SDU.


Introduction

Some methods for digitizing analog waveforms:

Pulse-code modulation (PCM)Differential PCM (DPCM) Adaptive differential PCM (ADPCM)Delta modulation (DM)Adaptive delta modulation (ADM)Linear predictive coding (LDC)


Pulse-Code Modulation (PCM)

PCM is used for quantizing an analog signal to transmit storing the signal in digital formSpeech transmission Telemetry systems


μ- law compressor

A logarithmic compressor employed in U.S. and Canadian telecommunications systems

s : the mormalized input;y : the normalized output;

sgn(·) : the sign funciton;μ : a parameter that is selected to give

the desired compression characteristic.

( )( ) ( )

ln 1 sy sgn s ; s 1, y 1

ln 1+µ

= ≤ ≤+µ


A – law compressor

The logarithmic compressor standard used in European telecommunication systems:

where A is chosen as 87.56.

( ) ( )

( )

1 ln A s 1sgn s , s 11 ln A AyA s 1sgn s , 0 s

1 ln A A

⎧ +≤ ≤⎪⎪ += ⎨

⎪ ≤ ≤⎪⎩ +


Figure 10.1 Comparison of μ-law and A-law nonlinearities


Project 10.1: PCM

Purpose of this project:To gain an understanding of PCM comprssion (linear-to-logarithmic) PCM expansion (logaithmic-to-linear).


Three Matlab functions are needed:

A μ-law compressor functionA quantizer function

A μ-law expander funciton


Figure 10.2 PCM project


The signal-to-quantization noise ratio (SQNR) in dB is:

( )

( ) ( )( )

N2

n 110 N 2

qn 1

s nSQNR 10log

s n s n

=

=

⎛ ⎞⎜ ⎟⎜ ⎟=⎜ ⎟−⎜ ⎟⎝ ⎠

∑

∑


Differential PCM (DPCM)

s(n): the current sample of speech: the predicted value of s(n)

a(i): the predictor coefficients

( ) ( ) ( )p

i 1s n a i s n i

=

= −∑

( )s n


The error function is the sum of squared errors, so we select the a(i) to minimize:

where rss(m) is the autocorrlation function of s(n)

( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( ) ( )

2pN N2

pn 1 n 1 n 1

p p p

ss ss ssn 1 i 1 j 1

e n s n a i s n i

r 0 2 a i r i a i a j r i j

= = =

= = =

⎡ ⎤ε = = − −⎢ ⎥

⎣ ⎦

= − + −

∑ ∑ ∑

∑ ∑∑

( ) ( ) ( )N

ssi 1

r m s i s i m=

= +∑


Figure 10.3 Block diagram of a DPCM transcoder


The output of the predictor is

The difference

is the input to the quantizer.

( ) ( )p

i 1s a i s n i

=

= −∑

( ) ( ) ( )e n s n s n= −


The estimate value of s(n) is obtained by taking a linear combination of past values , k=1,2,…,p.The estimate of s(n) is

( )s n

( )s n k−

( ) ( ) ( ) ( ) ( )p p

i 1 i 1

s n a i s n i b i e n i= =

= − + −∑ ∑


Project 10.2: DPCM

Generate correlated random sequences using a pole-zero signal model of the form:

where x(n) is a zero-mean unit variance Gaussian sequence.

( ) ( ) ( ) ( ) ( )0 1s n a 1 s n 1 b x n b x n 1= − + + −

filter function


Some modules for this project:A model predictor functionA DPCM encoder function A DPCM decoder function


Figure 10.4 DPCM modified by the linearly filtered error sequence


Adaptive PCM (ADPCM) and DPCM

Adaptive quantizer:feedforward adaptive quantizer

Adjust its step size for each signal sample

feedback adaptive quantizerEmploy the output of the quantizer in the adjustment of the step size.


Figure 10.5 Example of a quantizer with an adaptive step size


Table 10.1 Multiplication factors for adaptive step size adjustment


Figure 10.6 ADPCM block diagram (Encoder part)


Figure 10.6 ADPCM block diagram (Decoder part)


Project 10.3: ADPCM

Figure 10.7 ADPCM interface to PCM system


Delta Modulation (DM)

DM may be viewed as asimplified form of DPCM in which a two-level (1-bit) quantizer is used in conjunction with a fixed first-order predictor.


We note that

Since

It follows that

( ) ( ) ( ) ( )s n s n 1 s n 1 e n 1= − = − + −

( ) ( ) ( ) ( ) ( ) ( )q n e n e n e n s n s n⎡ ⎤= − = − −⎣ ⎦

( ) ( ) ( )s n s n 1 q n 1= − + −


Figure 10.8 Block diagram of a delta modulation system


Figure 10.9 An equivalent realization of a delta modulation system


Adaptive Delta Modulation (ADM)

Figure 10.10 Two types of distortion in the DM encoder


Figure 10.11 An example of a delta modulation system with adaptive step size

Encoder part


Decoder part


Project 10.4: DM and ADM

A Hanning filter that has the impulse response

may be used, where the length N may be selected in the range .

( ) 1 2 nh n 1 cos , 0 n N 12 N 1⎡ π ⎤⎛ ⎞= − ≤ ≤ −⎜ ⎟⎢ ⎥−⎝ ⎠⎣ ⎦

5 N 15≤ ≤


Linear Predictive Coding (LPC) of Speech

The LPC method is based on modeling the vocal tract as a linear all-pole filter.The system function:

p : the number of poles;G : the filter gain;

{ap(k)}: parameters that determine the poles.

( )( )

pk

pk 1

GH z1 a k z−

=

=+∑


Figure 10.12 Block diagram model for the generation of a speech signal


Figure 10.13 Encoder and decoder for LPC


Project 10.5: LPC

The encoder divides speech signals into short-time segments, and process each segment, separately.The decoder that performs the synthesis is an all-pole lattice filter.The output is a synthetic speech signal.


Dual-Tone Multi-frequency (DTMF) Signals

DTMF is the generic name for push-button telephone signaling.DTMF also finds widespread use in electronic mail systems and telephone banking systems.A combination of a high-frequency tone and low-frequency tone represent a specific digit or the characters * and #.


Figure 10.14 DTMF digits


The Goertzel Algorithm

The Goertzel algorithm exploits the periodicity of the phase factors and allows us to express the computation of the DFT as a linear filtering operation.Since , we can multiply the DFT by this factor. Thus

kNW

kNNW 1− =

( ) ( ) ( ) ( )N 1

k N mkNN N

m 0X k W X k x m W

−− −−

=

= = ∑


Figure 10.15 Realization of two-pole resonator for computing the DFT


Project 10.6: DTMF Signaling

Design the following Matlab modules:A tone generation functionA dial-tone generator A decoding funciton


Binary Digital Communications

A binary digital communications system employs two signal waveforms:

s1(t)=s(t)s2(t)=-s(t)

To measure the performance, we normally use the average probability of error, which is often called the bit error rate (BER).


Project 10.7: Binary Data Communications System

Five Matlab functions are required:A binary data generator moduleA modulator module A noise generator A demodulator moduleA detector and error-counting module


Figure 10.16 Model of binary data communications system


Spread-Spectrum Communications

Figure 10.17 Basic spread spectrum digital communications system


Project 10.8: Binary Spread-Spectrum Communications

Figure 10.18 Block diagram of binary PN spread-spectrum system for simulation experiment


That’s all!

Date post:	24-Mar-2020
Category:	Documents
Upload:	others
View:	0 times
Download:	0 times

Chapter 10 Applications in Communications · © School of IS&E, SDU. Copyright Reserved 2/ 47...

Documents