- Email: [email protected]
Delta Coders with the use of Quantization Steps with Multiplication Factor Equal to Power 2
Copyright @ IFAC Programmable Devices and Systems, Ostrava, Czech Republic, 2000
DELTA CODERS WITH THE USE OF QUANTIZATION STEPS WITH MULTIPLICATION FACTOR EQUAL TO POWER 2
Wlodzimierz Pogribny, Arkadiusz Rajs
Institute of Telecommunications of UTA Ave. Prof. S. Kaliskiego 7. 85-796 Bydgoszcz. POLAND email: [email protected];[email protected]
Abstract: In the papers their have been presented algorithms of small word length coders Adaptive Delta Modulation (ADM) and DPCM using quantization steps with multiplication factor equal to power 2. This steps come down math's operation to simple logical shift, which makes them useful where to speed of performance need to be secured ego neural processors. Such coder it used to process of random signal. The purpose of this work is to design effective algorithms to process random signals especially type of pink noise and voice signal and exam they qualities. Proposal of definitely have been design with computer simulation by the way of minimise approximation errors. The result of simulation show perspective for designer coders. Copyright @20001FAC Keywords: encoders, difference equations, signal processing
I.
modifications whose absolute quantization steps values belong to the set {20 £,2 1£, ...,2c £}, where £minimal value of a non-zero quantization steps, see (Pogribny, 1990; Steeie, 1975; Spilker, 1977). The literature does not present any the methods of optimisation of DM types relating to the selection of parameters and algorithms. The purpose of this paper is to work out effective algorithms of DM with power 2 quantization steeps to process random signals especially type of pink noise and voice signal and exam they qualities. Pink noise represent to a large group of stationary signal come from e.g. detectors in the measuring and communications systems and soon, whereas the voice signal was chose as an example of signal nonstationary process. To the same time security economical codes DM and satisfactory accurate the authors concentrate to 3 bits codes.
INTRODUCTION
Most usually the representation of random signals in a digital form is made in PCM format, which ensures the widest frequency band of the transmitting and processing signals. However, due to the large word length of PCM, the algorithms and devices for transmission and processing of signals not always satisfy the requirement of economy and technological merit. The use of differences for the representation of signals has not these defects. The difference formats include DM too. They allow to represent signals in a digital form with small word length and with an agreed-upon resolution. Some kinds of DM are onebit. This allows to create very efficient communication systems and parallel algorithms and processors, in e.g. the neural structures. DM uses differences quantization between the input signal and approximation signal, which leads to small word length of quantization steps - i.e. output codes. As a result of such coding is the economical of coding compression and resistance to interference. For the transmission itself, and more often for digital signal processing, those DM types whose quantization steps allow to make simple mathematical operations prove most useful. It is well known that when using binary codes which are another power of 2, the multiplication operation is limited to a common code shift. Therefore it is expedient to use such types of DM where quantization steps are subsequent powers of 2. These types include: ADM and DPCM
2. THE CHOICE OF DM CODERS ALGORITHMS
2.1 The choice ofparameters of DM coders. Sampling rate of ADM and the 3-bit DPCM with a maximal quantization steep 4£, we can write on the basis of (Pogribny, and Rajs, 1996; Pogribny, 1998; Pogribny, and Rajs, 1999), in the following way:
105
s~x) ha
(1)
=[2(B;~) $
B;!tJ) -1]- i,
c
.I
B~~ 2 k (5)
k=-q
where
Uk(X)
and in DM-DM format:
the amplitude of the k- sinusoid
-
-----
component of the x(t) signal obtained a·priori. The selection of step sizes is described in (Pogribny. and Rajs. 1996; Pogribny. and Rajs. 1999). To small value of £ is the source of overload error. while a too high value of £ leads to a higher quantization noise. Maximum step size of quantization: £Smax
=
~
4£
S(x) S(h) r
a
= [2(B(x) EE> B(h») -1]· 21,+1" S.r
s.a
(6)
It is visible from here, that the operation of multiplication is transformed into the operation of logic negation of sum on module 2 and a usual left shift of code of number in PCM format or step on DM format on the 1, bits,
ma,x Ix; - x;_11 ;=l,N
2.3 Modification algorithms of ADM and DPCM coders. where: ( X m I-input signal Although non-zero steps of the modernised 3-bit DPCM and I-bit ADM are the same, their algorithms differ. DPCM processes the signal right away, regardless previous quantization steps (codes). ADM processes the signal. i.e. it outputs code combinations depending on previous combinations. Whereas the steps series 1.1,2,4,4.... and -1,-1.-2,-4,-4.... , correspond to the initial series of Is or Os of a I-bit code 11111... and 00000... in classic ADM. the steeps series 1.2,4,4,4,... and -1.2.-4.-4,-4,... correspond to the some initial series of code in modernised ADM. Therefore. the modernised ADM is more accurate for the signals with large steepness, ADM is less accurate than DPCM, however it is more economical. The quantization steps of ADM are belong to set:
Minimum step size of quantization [4]: u(x)
=
l'co
c.> min
l'
C
_<
'W
Ii,
_g_
Il U ~x) - the value of the upper harmonics of the spectra. J1 - the ratio of the DM and PCM sampling where
rate (oversampling).
2,2 The operations on DM steps with multiplication factor equal to power 2. For use in the processing it is expediently to present the non-zero steps of such ADM and DPCM as follows:
{ E· S;X)
= E· sgns;X) i, }.
\if E {O,l,2},
sgns;x) ~ B;~)
\j S ~x) E {-
= sgn ha'
sgnh a
~ B~:>;
1
(2)
I
ha as the binary code
Ih a
1=
i
B~~ 2 k ;
(7)
The word length of ADM is ca=1 bit. The characteristics of the coders of classic and modernised ADM are shown in Fig.l a and I b. The quantization steps of DPCM with word length cd=3 bit belong to set:
and the any number in DPCM format
ha
4,-2,-1,1,2,4}
\i Sd (x)
E {- 4,-2,-1,0,1,2,4}
(8)
The characteristics of the DPCM coder is shown in Fig.l.c, while in Fig.l.d the characteristics of LDM coder is shown. At the computers simulation apart quantization steps from the set (7),(8) was used to it compare also steeps 8£.
VB E {O,l} (3)
k=-q
where c+q+ 1 is the word length for binary representation of the number ha. Let us use the product of signs in kinds of the logic operation over bits of the signs (2). (3)
3. THE SELECTION OF THE OPTIMAL ALGORITHM FOR PROCESSING RANDOM SIGNALS The optimisation of the algorithms is carried out by means of minimising the error of the average quantization in time domain which is described by the following expression:
Then for Vs#> we have a product in mixed DMPCM format:
106
(J
where
{x
x
r } -
maximal sum of product of the same amplitudes of the upper harmonics on the appropriate frequency. Minimal £ step was fixed. In the Table I below some of the studied algorithms for the operation of ADM coders have been shown together with their average quantization errors at the same sampling rate and £ step. ADM quantization steps were taken from the set {-8£, -4£, -2£, -£, 2£, 4£, 8£}, DPCM from the sets {-4£,-2£,1£,0,1£,2£,4£} and {-3£, -2£,1£,0,1£,2£,3£}, and for LDM from the set {-I£, I£}.
=
the samples of the input signal in
multi-bit PCM format,
{x r
}-
the samples of the
approximation signals in ADM, DPCM or LDM formats. This error depends on the choice of sampling rate, E value and the algorithm of a coder's operation which assigns the order of quantization steps at signal increase and decrease.
Table I Accuracy of coder's algorithms for pink noise with f.8-4f, -fD ...£.6=£L=£Q=0.075Ug..
N°
£s 7&
£S
1. 2. 3. 4. 5. 6. 7. 8. 9.
a
10.
11. 12. 13. 14. IS. 16. 17. 18. 19. 20. 21.
-7&
a)
b)
£s
ADM (l bit) Algorytm £,2£,4£,-£, -2£,-4£ £,£,2£,2£,4£,-£,-£,-2£,-2£,-4£ £,2£,4£,-2£,-£,-2£,-4£ £,2£,4£,-2£,-4£ £,£,4£,4£, -£,-£,4£ £,£,2£,4£,-£,-£,-2£,-4£ £,£,2£,4£, -2£,-£, -£, -2£,-4£ £,£,2£,2£,4£,4£,-2£, -2£, -4£ £,4£,4£,-2£, -4£,2£, -£,£,4£ £,4£,-£,-4£ £,£,2£,4£,-2£,-4£ £,£,2£,2£,4£,4£,8£,-4£,-4£,-8£ £,£,4£,-2£,-4£,2£,-£,£,4£ £,2£,4£,8£,-£,-2£,-4£,-8£ £,£,2£,2£,4£,4£,8£,-£,-£,-2£ £,£,2£,4£,8£, -£,-£,-2£, -4£, -8£ £,2£,4£,8£,-4£,-2£,-£,£,2£,4£,8£ £,£,2£,4£,8£,-4£,-8£,4£,8£ £,2£,4£,8£,-4£,-8£ £,£,2£,4£,8£,-4£,-2£,-£ £,£,2£,4£,£,2£,4£,-2£,-4£
(JA
0.126 0.129 0.129 0.140 0.140 0.143 0.144 0.145 0.153 0.156 0.161 0.164 0.164 0.169 0.169 0.175 0.179 0.195 0.198 0.202 0.286
LDM (1 bit) Algorytm* {I£, -It}
(JL
0.661
DPCM (3 bits) Algorytm {0,1£,2£,3£} 10,1 £,2£,4£} c)
(JD
0.104 0.034
DPCM (4 bitv)
d)
Algorytm {O, 1£,2£,3£,4£,...7£} {O, 1£,2£,4£,... ,64£)
Fig. I. The characteristics of the codes for typical ADM (a), modernised ADM (b), DPCM (c), LDM (d).
(JD
0.014 for £=0.048 0.025 for £-0.017
3.1 Optimal algorithm for processing the pink noise.
3.2 Optimal algorithm for processing the voice signal.
The selection of the optimal algorithm was carried out by means of the simulation of the coder's operation while processing the pink noise. Sampling rate was calculated on the basis of (I) for the
The exploration were conducted for voice signal which is a man voice on the sampling rate 441 OOHz. The example of results for a word "dom" (polish language) contains
107
Table 2 Accuracy of coder's algorithms for voice signal
obtain to use DPCM coders (3 and 4 bits) on modification algorithm
Ne
ADM (1 bit) Algorithm crA 3.26 I ~.2£.4£.-E.-2£.-4£ 2.90 2.F.£.2£.2£.4£. -E. -E. - 2£. -2£. -4£ 3.23 3 F.2£.4£.-2£.-£.-2£.-4E 3.28 4 ~.2£.4£.-2E.-4£ 3.07 5 ¥.£,4£.4£. -E. -£.4£ 2.80 6¥:.£.2£.4£. -E. -E.-2£. -4£ 2.77 7 ~.£.2E.4£. -2E, -E. -£, -2£. -4£ 2.83 8. ,E,2£.2£.4£.4£.-2£.-2E.-4£ 4.31 9 .4E.4£.-2£.-4£.2£. -£.£.4£ 4.39 0 .4£.-£.-4E 2.77 I..£.2£.4£.-2£.-4£ 2 .£,2£.2£.4£.4£,8£,-4£,-4£,-8£ 2.64 3.04 3 F,£.4£.-2£.-4£.2£,-£.£.4£ 2.93 4 F.2E.4£.8E.-£.-2£.-4E.-8£ 2.80 5.t;.£.2£,2£.4£.4£. 8£.-E. -E. - 2£ 2.72 6. .£.2£.4£,8£. -E. -E. - 2£. -4£. -8£ 7.F.2£.4£.8£,-4£.-2£.-£.£.2£.4£,8£ 2.71 2.51 8 £,£.2£.4£,8£,-4£.-8£.4£.8£ 2.81 9. ,2£.4£.8E.-4£,-8£ 2.66 0"',£.2£.4£.8£.-4£.-2£.-£ 2.86 1 ~.E.2£.4£,£,2£.4£.-2£,-4£ LDM (l bit) Algorithm £ crL 4.69 4.8 {lE. -le} 5 PCM (3 bits) crD 23.15 DPCM (3 bits) Algorithm £ crD 4.5 1.55 {0.1£.2£.3£} 0 1.26 3.7 {O.I E.2£.4£} 0 DPCM (4 bits) Algorithm £ crD 0.84 2.5 {O, I£.2£.3£....7£} 0 0.55 1.0 {O, 1£.2£.4£....,64£} 0
increase
£ SNR [dB] 2.17 17.35 2.86 18.36 2.57 17.42 2.80 17.30 2.85 17.87 2.94 18.66 2.95 18.78 2.95 18.57 14.93 1.64 14.77 1.53 2.95 18.78 2.58 19.20 2.70 17.97 1.65 18.27 2.80 18.66 2.26 18.93 1.50 18.96 1.41 19.63 1.56 18.63 2.36 19.11 2.94 18.48
......... 2s ~&
compare
to
xCA ) (t)
-.
2.
-&
~I£
y
y
y
..
&
-E
&
.
E
-E
E
~~
E
-&
l;,r
;,.
-E
E
-&
-&
&
-E
~
-&
&
-&
t; . •
-&
'"
7~.
"'~
stability
~Ii ....
•••
..
y
decrease
Fig. 2. Algorithm of ADM coder # I
increase ~
~
...
~
~
;s.~,~,:,~
+
r-----++-1-,--++------"'-+,:--='........... ".::<-..<-----~. ~,~~,
......
,--_ _-+-+-f-+-+----'4:>+--='-2",-O,--"----"'--<'-'-_-~. ~~·120,2£,2£ ,. ~~'~
,------1-+-+--1I---+--------'---+-...,:-'"---'·'---+'"---''---+c~ .• ~,p.~
stability
SNR [dB] 14.20
.....£
-2c -c
-£
-(
-la -41 -e. -c
-I:
'--------=!-.+-_.=!----o!--.::L--o~ .•
-k -k -2& -2& -2&
SNR [dB] 3.67
-"
(_le
-I'
fi ...
-1£ -le -8£ -&I: -8£ 'f
SNR [dB) 23.83
'f
'f
'f
'f
decrease
Fig. 3. Algorithm of ADM coder # 18 25.58
r
SNR [dB] 29.11 32.75
The exploration shown us. that the best results give us use ADM coder with algorithm £,£,2£.4£,8£,-4E. -8£.4£,8£ (Fig 2). Insignificantly worse is well known algorithm £,£.2£.4£,-£,-£,-2£.-4£. Worse or definitely worse works coders which use the algorithms with fast change quantization steeps. In Fig. 4 and Fig. 5 time graphs have been presented which illustrate the operation of the three selected coders. These graphs show fragment of coding CP ) random signal with use of 3 bits PCM modernising ADM
4. : 2&
and DPCM
Fig. 4. Fragment of coding of random signal with use of 3 bits PCM CP ) the least accuracy
x
(t) -
approximation, and modernising ADM CAl more precisely approximation.
x (t) -
x (t ). xCD ) (t)
compare to input signal x(t)
input signal x(t). The best results is
108
th
Proceed of the 6 Intern. Con! MIXDES'99 (Andrzej Napieralski. (Ed)), pp. 399-404. Tech. Univ. of Lodz, Lodz, Poland. Spilker, J.J. (1977) Digital Communications by Satellite, Prentice - Hall, Inc., Englewood Cliffs, New Jersey. Steele, R. (1975) Delta Modulation Systems, Pentech Press, London.
r
• ,'M)l6 • •
•-1 Ml).Ol ._:
Fig. 5. Fragment of coding of random signal with use of 3 bits PCM X(P)
(t) - the
approximation, and DPCM
least accuracy
X(D)
(t) - more
precisely approximation, compare to input signal x(t)
4. CONCLUSIONS
The optimisation of the operation of the coders of the Adaptive Delta Modulation (ADM) and DPCM with quantization steps which are the multiplication of the powers of 2 allow to increase the accuracy of the signal response. The methods offered in this paper also permit to determine the parameters of DM on the basis of the a'priori information about a signal's spectrum. Such algorithms are useful in the communication and in multi-processor systems, such as neural systems that works in real time. The exploration shown us , that recommendation optimal algorithm work of ADM coders separate to signal pink noise type and to voice signal are different to each other. That's why should to select coder's algorithm to application on code particular type of signal.
REFERENCES: Pogribny, W. (1990). Delta - Modulation in Digital Signal Processing, Radio i Sviaz', Moscow (in Russian). Pogribny, W. and A. Rajs (1996). Metodyka wykorzystania adaptacyjnej modulacji delta do filtracji cyfrowej. In. Krajowe Sympozjum Telekomunikacji '96, pp. 88-94. IT PW, Warszawa, Poland (in Polish). Pogribny, W. (1998). Filtering algorithms with delta modulation oriented on the homogeneous th computing environments. In. Proceed of the 5 Intern. Con! MIXDES'98 (Andrzej Napieralski. (Ed)), pp. 299-302. Tech Univ. of Lodz, Lodz, Poland. Pogribny, W. and A. Rajs (1999). Optimization of DM coders algorithms with the use of steps with multiplication factor equal to power 2. In.
109
DELTA CODERS WITH THE USE OF QUANTIZATION STEPS WITH MULTIPLICATION FACTOR EQUAL TO POWER 2
Wlodzimierz Pogribny, Arkadiusz Rajs
Institute of Telecommunications of UTA Ave. Prof. S. Kaliskiego 7. 85-796 Bydgoszcz. POLAND email: [email protected];[email protected]
Abstract: In the papers their have been presented algorithms of small word length coders Adaptive Delta Modulation (ADM) and DPCM using quantization steps with multiplication factor equal to power 2. This steps come down math's operation to simple logical shift, which makes them useful where to speed of performance need to be secured ego neural processors. Such coder it used to process of random signal. The purpose of this work is to design effective algorithms to process random signals especially type of pink noise and voice signal and exam they qualities. Proposal of definitely have been design with computer simulation by the way of minimise approximation errors. The result of simulation show perspective for designer coders. Copyright @20001FAC Keywords: encoders, difference equations, signal processing
I.
modifications whose absolute quantization steps values belong to the set {20 £,2 1£, ...,2c £}, where £minimal value of a non-zero quantization steps, see (Pogribny, 1990; Steeie, 1975; Spilker, 1977). The literature does not present any the methods of optimisation of DM types relating to the selection of parameters and algorithms. The purpose of this paper is to work out effective algorithms of DM with power 2 quantization steeps to process random signals especially type of pink noise and voice signal and exam they qualities. Pink noise represent to a large group of stationary signal come from e.g. detectors in the measuring and communications systems and soon, whereas the voice signal was chose as an example of signal nonstationary process. To the same time security economical codes DM and satisfactory accurate the authors concentrate to 3 bits codes.
INTRODUCTION
Most usually the representation of random signals in a digital form is made in PCM format, which ensures the widest frequency band of the transmitting and processing signals. However, due to the large word length of PCM, the algorithms and devices for transmission and processing of signals not always satisfy the requirement of economy and technological merit. The use of differences for the representation of signals has not these defects. The difference formats include DM too. They allow to represent signals in a digital form with small word length and with an agreed-upon resolution. Some kinds of DM are onebit. This allows to create very efficient communication systems and parallel algorithms and processors, in e.g. the neural structures. DM uses differences quantization between the input signal and approximation signal, which leads to small word length of quantization steps - i.e. output codes. As a result of such coding is the economical of coding compression and resistance to interference. For the transmission itself, and more often for digital signal processing, those DM types whose quantization steps allow to make simple mathematical operations prove most useful. It is well known that when using binary codes which are another power of 2, the multiplication operation is limited to a common code shift. Therefore it is expedient to use such types of DM where quantization steps are subsequent powers of 2. These types include: ADM and DPCM
2. THE CHOICE OF DM CODERS ALGORITHMS
2.1 The choice ofparameters of DM coders. Sampling rate of ADM and the 3-bit DPCM with a maximal quantization steep 4£, we can write on the basis of (Pogribny, and Rajs, 1996; Pogribny, 1998; Pogribny, and Rajs, 1999), in the following way:
105
s~x) ha
(1)
=[2(B;~) $
B;!tJ) -1]- i,
c
.I
B~~ 2 k (5)
k=-q
where
Uk(X)
and in DM-DM format:
the amplitude of the k- sinusoid
-
-----
component of the x(t) signal obtained a·priori. The selection of step sizes is described in (Pogribny. and Rajs. 1996; Pogribny. and Rajs. 1999). To small value of £ is the source of overload error. while a too high value of £ leads to a higher quantization noise. Maximum step size of quantization: £Smax
=
~
4£
S(x) S(h) r
a
= [2(B(x) EE> B(h») -1]· 21,+1" S.r
s.a
(6)
It is visible from here, that the operation of multiplication is transformed into the operation of logic negation of sum on module 2 and a usual left shift of code of number in PCM format or step on DM format on the 1, bits,
ma,x Ix; - x;_11 ;=l,N
2.3 Modification algorithms of ADM and DPCM coders. where: ( X m I-input signal Although non-zero steps of the modernised 3-bit DPCM and I-bit ADM are the same, their algorithms differ. DPCM processes the signal right away, regardless previous quantization steps (codes). ADM processes the signal. i.e. it outputs code combinations depending on previous combinations. Whereas the steps series 1.1,2,4,4.... and -1,-1.-2,-4,-4.... , correspond to the initial series of Is or Os of a I-bit code 11111... and 00000... in classic ADM. the steeps series 1.2,4,4,4,... and -1.2.-4.-4,-4,... correspond to the some initial series of code in modernised ADM. Therefore. the modernised ADM is more accurate for the signals with large steepness, ADM is less accurate than DPCM, however it is more economical. The quantization steps of ADM are belong to set:
Minimum step size of quantization [4]: u(x)
=
l'co
c.> min
l'
C
_<
'W
Ii,
_g_
Il U ~x) - the value of the upper harmonics of the spectra. J1 - the ratio of the DM and PCM sampling where
rate (oversampling).
2,2 The operations on DM steps with multiplication factor equal to power 2. For use in the processing it is expediently to present the non-zero steps of such ADM and DPCM as follows:
{ E· S;X)
= E· sgns;X) i, }.
\if E {O,l,2},
sgns;x) ~ B;~)
\j S ~x) E {-
= sgn ha'
sgnh a
~ B~:>;
1
(2)
I
ha as the binary code
Ih a
1=
i
B~~ 2 k ;
(7)
The word length of ADM is ca=1 bit. The characteristics of the coders of classic and modernised ADM are shown in Fig.l a and I b. The quantization steps of DPCM with word length cd=3 bit belong to set:
and the any number in DPCM format
ha
4,-2,-1,1,2,4}
\i Sd (x)
E {- 4,-2,-1,0,1,2,4}
(8)
The characteristics of the DPCM coder is shown in Fig.l.c, while in Fig.l.d the characteristics of LDM coder is shown. At the computers simulation apart quantization steps from the set (7),(8) was used to it compare also steeps 8£.
VB E {O,l} (3)
k=-q
where c+q+ 1 is the word length for binary representation of the number ha. Let us use the product of signs in kinds of the logic operation over bits of the signs (2). (3)
3. THE SELECTION OF THE OPTIMAL ALGORITHM FOR PROCESSING RANDOM SIGNALS The optimisation of the algorithms is carried out by means of minimising the error of the average quantization in time domain which is described by the following expression:
Then for Vs#> we have a product in mixed DMPCM format:
106
(J
where
{x
x
r } -
maximal sum of product of the same amplitudes of the upper harmonics on the appropriate frequency. Minimal £ step was fixed. In the Table I below some of the studied algorithms for the operation of ADM coders have been shown together with their average quantization errors at the same sampling rate and £ step. ADM quantization steps were taken from the set {-8£, -4£, -2£, -£, 2£, 4£, 8£}, DPCM from the sets {-4£,-2£,1£,0,1£,2£,4£} and {-3£, -2£,1£,0,1£,2£,3£}, and for LDM from the set {-I£, I£}.
=
the samples of the input signal in
multi-bit PCM format,
{x r
}-
the samples of the
approximation signals in ADM, DPCM or LDM formats. This error depends on the choice of sampling rate, E value and the algorithm of a coder's operation which assigns the order of quantization steps at signal increase and decrease.
Table I Accuracy of coder's algorithms for pink noise with f.8-4f, -fD ...£.6=£L=£Q=0.075Ug..
N°
£s 7&
£S
1. 2. 3. 4. 5. 6. 7. 8. 9.
a
10.
11. 12. 13. 14. IS. 16. 17. 18. 19. 20. 21.
-7&
a)
b)
£s
ADM (l bit) Algorytm £,2£,4£,-£, -2£,-4£ £,£,2£,2£,4£,-£,-£,-2£,-2£,-4£ £,2£,4£,-2£,-£,-2£,-4£ £,2£,4£,-2£,-4£ £,£,4£,4£, -£,-£,4£ £,£,2£,4£,-£,-£,-2£,-4£ £,£,2£,4£, -2£,-£, -£, -2£,-4£ £,£,2£,2£,4£,4£,-2£, -2£, -4£ £,4£,4£,-2£, -4£,2£, -£,£,4£ £,4£,-£,-4£ £,£,2£,4£,-2£,-4£ £,£,2£,2£,4£,4£,8£,-4£,-4£,-8£ £,£,4£,-2£,-4£,2£,-£,£,4£ £,2£,4£,8£,-£,-2£,-4£,-8£ £,£,2£,2£,4£,4£,8£,-£,-£,-2£ £,£,2£,4£,8£, -£,-£,-2£, -4£, -8£ £,2£,4£,8£,-4£,-2£,-£,£,2£,4£,8£ £,£,2£,4£,8£,-4£,-8£,4£,8£ £,2£,4£,8£,-4£,-8£ £,£,2£,4£,8£,-4£,-2£,-£ £,£,2£,4£,£,2£,4£,-2£,-4£
(JA
0.126 0.129 0.129 0.140 0.140 0.143 0.144 0.145 0.153 0.156 0.161 0.164 0.164 0.169 0.169 0.175 0.179 0.195 0.198 0.202 0.286
LDM (1 bit) Algorytm* {I£, -It}
(JL
0.661
DPCM (3 bits) Algorytm {0,1£,2£,3£} 10,1 £,2£,4£} c)
(JD
0.104 0.034
DPCM (4 bitv)
d)
Algorytm {O, 1£,2£,3£,4£,...7£} {O, 1£,2£,4£,... ,64£)
Fig. I. The characteristics of the codes for typical ADM (a), modernised ADM (b), DPCM (c), LDM (d).
(JD
0.014 for £=0.048 0.025 for £-0.017
3.1 Optimal algorithm for processing the pink noise.
3.2 Optimal algorithm for processing the voice signal.
The selection of the optimal algorithm was carried out by means of the simulation of the coder's operation while processing the pink noise. Sampling rate was calculated on the basis of (I) for the
The exploration were conducted for voice signal which is a man voice on the sampling rate 441 OOHz. The example of results for a word "dom" (polish language) contains
107
Table 2 Accuracy of coder's algorithms for voice signal
obtain to use DPCM coders (3 and 4 bits) on modification algorithm
Ne
ADM (1 bit) Algorithm crA 3.26 I ~.2£.4£.-E.-2£.-4£ 2.90 2.F.£.2£.2£.4£. -E. -E. - 2£. -2£. -4£ 3.23 3 F.2£.4£.-2£.-£.-2£.-4E 3.28 4 ~.2£.4£.-2E.-4£ 3.07 5 ¥.£,4£.4£. -E. -£.4£ 2.80 6¥:.£.2£.4£. -E. -E.-2£. -4£ 2.77 7 ~.£.2E.4£. -2E, -E. -£, -2£. -4£ 2.83 8. ,E,2£.2£.4£.4£.-2£.-2E.-4£ 4.31 9 .4E.4£.-2£.-4£.2£. -£.£.4£ 4.39 0 .4£.-£.-4E 2.77 I..£.2£.4£.-2£.-4£ 2 .£,2£.2£.4£.4£,8£,-4£,-4£,-8£ 2.64 3.04 3 F,£.4£.-2£.-4£.2£,-£.£.4£ 2.93 4 F.2E.4£.8E.-£.-2£.-4E.-8£ 2.80 5.t;.£.2£,2£.4£.4£. 8£.-E. -E. - 2£ 2.72 6. .£.2£.4£,8£. -E. -E. - 2£. -4£. -8£ 7.F.2£.4£.8£,-4£.-2£.-£.£.2£.4£,8£ 2.71 2.51 8 £,£.2£.4£,8£,-4£.-8£.4£.8£ 2.81 9. ,2£.4£.8E.-4£,-8£ 2.66 0"',£.2£.4£.8£.-4£.-2£.-£ 2.86 1 ~.E.2£.4£,£,2£.4£.-2£,-4£ LDM (l bit) Algorithm £ crL 4.69 4.8 {lE. -le} 5 PCM (3 bits) crD 23.15 DPCM (3 bits) Algorithm £ crD 4.5 1.55 {0.1£.2£.3£} 0 1.26 3.7 {O.I E.2£.4£} 0 DPCM (4 bits) Algorithm £ crD 0.84 2.5 {O, I£.2£.3£....7£} 0 0.55 1.0 {O, 1£.2£.4£....,64£} 0
increase
£ SNR [dB] 2.17 17.35 2.86 18.36 2.57 17.42 2.80 17.30 2.85 17.87 2.94 18.66 2.95 18.78 2.95 18.57 14.93 1.64 14.77 1.53 2.95 18.78 2.58 19.20 2.70 17.97 1.65 18.27 2.80 18.66 2.26 18.93 1.50 18.96 1.41 19.63 1.56 18.63 2.36 19.11 2.94 18.48
......... 2s ~&
compare
to
xCA ) (t)
-.
2.
-&
~I£
y
y
y
..
&
-E
&
.
E
-E
E
~~
E
-&
l;,r
;,.
-E
E
-&
-&
&
-E
~
-&
&
-&
t; . •
-&
'"
7~.
"'~
stability
~Ii ....
•••
..
y
decrease
Fig. 2. Algorithm of ADM coder # I
increase ~
~
...
~
~
;s.~,~,:,~
+
r-----++-1-,--++------"'-+,:--='........... ".::<-..<-----~. ~,~~,
......
,--_ _-+-+-f-+-+----'4:>+--='-2",-O,--"----"'--<'-'-_-~. ~~·120,2£,2£ ,. ~~'~
,------1-+-+--1I---+--------'---+-...,:-'"---'·'---+'"---''---+c~ .• ~,p.~
stability
SNR [dB] 14.20
.....£
-2c -c
-£
-(
-la -41 -e. -c
-I:
'--------=!-.+-_.=!----o!--.::L--o~ .•
-k -k -2& -2& -2&
SNR [dB] 3.67
-"
(_le
-I'
fi ...
-1£ -le -8£ -&I: -8£ 'f
SNR [dB) 23.83
'f
'f
'f
'f
decrease
Fig. 3. Algorithm of ADM coder # 18 25.58
r
SNR [dB] 29.11 32.75
The exploration shown us. that the best results give us use ADM coder with algorithm £,£,2£.4£,8£,-4E. -8£.4£,8£ (Fig 2). Insignificantly worse is well known algorithm £,£.2£.4£,-£,-£,-2£.-4£. Worse or definitely worse works coders which use the algorithms with fast change quantization steeps. In Fig. 4 and Fig. 5 time graphs have been presented which illustrate the operation of the three selected coders. These graphs show fragment of coding CP ) random signal with use of 3 bits PCM modernising ADM
4. : 2&
and DPCM
Fig. 4. Fragment of coding of random signal with use of 3 bits PCM CP ) the least accuracy
x
(t) -
approximation, and modernising ADM CAl more precisely approximation.
x (t) -
x (t ). xCD ) (t)
compare to input signal x(t)
input signal x(t). The best results is
108
th
Proceed of the 6 Intern. Con! MIXDES'99 (Andrzej Napieralski. (Ed)), pp. 399-404. Tech. Univ. of Lodz, Lodz, Poland. Spilker, J.J. (1977) Digital Communications by Satellite, Prentice - Hall, Inc., Englewood Cliffs, New Jersey. Steele, R. (1975) Delta Modulation Systems, Pentech Press, London.
r
• ,'M)l6 • •
•-1 Ml).Ol ._:
Fig. 5. Fragment of coding of random signal with use of 3 bits PCM X(P)
(t) - the
approximation, and DPCM
least accuracy
X(D)
(t) - more
precisely approximation, compare to input signal x(t)
4. CONCLUSIONS
The optimisation of the operation of the coders of the Adaptive Delta Modulation (ADM) and DPCM with quantization steps which are the multiplication of the powers of 2 allow to increase the accuracy of the signal response. The methods offered in this paper also permit to determine the parameters of DM on the basis of the a'priori information about a signal's spectrum. Such algorithms are useful in the communication and in multi-processor systems, such as neural systems that works in real time. The exploration shown us , that recommendation optimal algorithm work of ADM coders separate to signal pink noise type and to voice signal are different to each other. That's why should to select coder's algorithm to application on code particular type of signal.
REFERENCES: Pogribny, W. (1990). Delta - Modulation in Digital Signal Processing, Radio i Sviaz', Moscow (in Russian). Pogribny, W. and A. Rajs (1996). Metodyka wykorzystania adaptacyjnej modulacji delta do filtracji cyfrowej. In. Krajowe Sympozjum Telekomunikacji '96, pp. 88-94. IT PW, Warszawa, Poland (in Polish). Pogribny, W. (1998). Filtering algorithms with delta modulation oriented on the homogeneous th computing environments. In. Proceed of the 5 Intern. Con! MIXDES'98 (Andrzej Napieralski. (Ed)), pp. 299-302. Tech Univ. of Lodz, Lodz, Poland. Pogribny, W. and A. Rajs (1999). Optimization of DM coders algorithms with the use of steps with multiplication factor equal to power 2. In.
109