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Data over voice using time-warping technique
Signal Processing 34 ( 1993 ) 99-108 Elsevier
99
Data over voice using time-warping technique Dov Wulich and Moshe Bukris Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, POB 653, Israel Received 7 November 1991 Revised 13 April 1992 and 5 January 1993
Abstract. Simultaneous transmission of a digitally modulated signal and a voice signal known as data over voice (DOV) is discussed. In particular a minimum shift keying (MSK) modulation format is considered. A new method is used which is based on a time-warping technique, where having the instantaneous phase (frequency) of the MSK signal, the MSK signal is transformed into a harmonic one with known frequency, while the voice signal, which is broadband, is transformed into another broadband signal. Consequently, after performing the time-warping, it is possible to separate the transformed MSK signal and the transformed voice signal by using a fixed coefficient second order constrained notch filter. The instantaneous phase of the MSK signal, needed for time-warping, is synthesized by using the output of the MSK receiver. It is shown that if the peak value of the voice signal is below the amplitude of the MSK signal, then the performance of the MSK receiver is only mildly influenced by the voice signal, and the reconstructed voice signal has high intelligibility. Zusammenfassung. Die gleichzeitige Obertragung eines digital modulierten Signals und eines Sprachsignals, als 'data over voice' (DOV) bekannt, wird diskutiert. Insbesondere wird ein Minimum-Shift-Keying-Format (MSK) betrachtet. Ein neues Verfahren wird verwendet, das auf einer Zeitachsen-Verzerrungstechnikberuht: Bei gegebener Momentanphase (oder Momentanfrequenz ) des MS KSignals wird das MSK-Signal in ein harmonisches Signal bekannter Frequenz transformiert, wiihrend das Sprachsignal mit seiner groBen Bandbreidte in ein anderes Breithandsignal transformiert wird. Folglich ist es nach der Zeitachsenverzerrung mtiglich, das transformierte MSK-Signal and das transformierte Sprachsignal mittels eines zeitinvarianten Kerbfilters mit Zusatzbedingung vom Grade 2 zu trennen. Die for die Zeitachsenverzerrung ben0tigte Momentanphase des MSK-Signals wird mit Hilfe des MSK-Empfiinger-Ausgangs synthetisiert. Es wird gezeigt, dab die Leistungsf'ahigkeit des MSK-Empf'~rigers nut wenig vom Sprachsignal beeinfluBt wird, wenn der Spitzenwert des Sprachsignals unter der MSK-Amplitude bleibt; das rekonstruierte Sprachsignal besitzt eine hohe Verstiindlichkeit. R6sum6. Le probl~me de la transmission simultan6e d'un signal digital modul6 et d'un signal de parole appel6 DOV (en anglais data over voice) est discut6. En particulier, nous consid6rons un format de modulation MS K (minimum shift keying ). Une nouvelle m&hode bas6e sur une technique de distorsion temporelle est utilis6e, o~, 6tant donn6 la phase (fr6quence) du signal MSK, celui-ci est transform6 en un signal harmonique de fr6quence connue; parall~lement, le signal de parole ~ large bande est transform6 en un autre signal ~tlarge bande. Par cons6quent, apr~s cette distorsion temporelle, il est possible de s6parer le signal MSK transform6 ainsi que le signal de parole transform6 en utilisant un filtre coupe-bande 6troit du second ordre h coefficients fixes. La phase instantan6e du signal MSK, n6cessaire pour la distorsion temporelle, est synth6tis6e en utilisant la sortie du r6cepteur MSK. Il est montr6 que si la valeur de pointe du signal de parole est inf6rieure ~tl'amplitude du signal MSK, la performance du r6cepteur MSK n'est alors seulement influenc6e que moyennement par le signal de parole, et le signal de parole reconstruit poss~de un haut degr6 d'intelligibilit6. Keywords. Data over voice; time-warping.
Correspondence to: Dr. Dov Wulich, Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, POB 653, Israel. Tel. +972-57-461537, Fax: +972-57-281340, E-mail: [email protected]
0165-1684/93/$06.00 © 1993 Elsevier Science Publishers B.V. All rights reserved
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D. Wulich, M. Bukris / Data over voice using time-warping
1. I n t r o d u c t i o n
lation format, which belongs to the family of continuous phase frequency shift keying (CPFSK) [3] is considered here. The CPFSK signal has both continuous phase and a constant envelope. Consider the sum x(t)=s(t)+r(t) of a signal r(t) =A cos[ ~ ( t ) + ~b] having constant envelope and continuous phase and any arbitrary signal s(t). As shown in [7] the idea of the separation between r(t) and s (t) is based on a time-warping concept performed by nonuniform sampling of the sum signal x(t). The strategy of nonuniform sampling, the synchronization, is derived from the instantaneous phase of the signal r(t) in such a manner that x(t) is sampled at time instants in which ~ ( t ) increases by equal increments. As a result the nonuniformly sampled signal r(t) becomes a harmonic sequence, while the nonuniformly sampled signal s(t) is, in general, a broadband one. This fact makes it possible to separate between these
The method of transmission of a digitally modulated signal and a voice signal known as data over voice (DOV) is considered. It is assumed that the signals share the same bandwidth and appear simultaneously in time. Therefore, the DOV considered precludes both frequency division multiplexing (FDM) and time division multiplexing (TDM) techniques. In Fig. 1 the typical spectra of the digitally modulated signal (represented here by an MSK) and the voice signal are presented. In this paper a new technique [7] to separate at the receiver end the digitally modulated and the voice signals is used. As shown in [7] one of the signals to be separated must have a constant envelope and continuous phase while the second may have any form. For this reason the minimum shift keying (MSK) modu-
2500 tn
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500 0 0
500
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2588 f
3808
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1000 I 808 I
Peak value = I v
600 400 200 8|
8
500
1880
1588
2088
2588
5888
~>ee
f [Hz]
Fig. 1. Spectrum of the MSK signal and voice signal for ~/= 1. Signal Processing
4808
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D. Wulich, M. Bukris / Data over voice using time-warping
two sequences by using a fixed coefficient second order constrained notch filter (CNF) [7]. In most practical cases, however, the input mixture x(t) is given, and therefore only an estimate of the phase r(t) may be obtained and used for synchronization. The quality of such an estimation depends on additional information available about r(t). In [5] an arbitrary FM (not necessarily CPFSK) signal r(t) is considered, where it is shown that if r(t) is much stronger than the signal s(t), then it is possible to use for synchronization the instantaneous phase of the signal x(t), instead of the phase of r(t). This phase may be obtained by applying x(t) to the FM demodulator followed by an integrator. It is shown in [ 5 ] that only partial separation can be obtained in such a case and further processing is needed where additional information about s(t) is required. In our case, however, the signal r(t) is MSK and therefore its instantaneous phase is piecewise linear with two slopes whose values can be obtained at the output of the MSK demodulator, a hard decision device, which is more 'immune' to the presence o f s ( t ) than the FM demodulator. It will be shown that using the output of the MSK demodulator for creating the synchronization signal gives a much better result than those obtained in [ 5 ]. A coherent demodulator is used. Its synchronization ~ is assumed to be ideal. Such an assumption is not essential at this stage of investigation where the goal is to check the usefulness of time-warping to the DOV system.
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the following equation:
~(t) =2"trk k=0,1,2 .....
(1)
N ' where N is, at this stage, an arbitrary natural number. tk is the solution of (1) for a given k, i.e., qt(t k) =
( 2~r/N)k. As known, the instantaneous frequency of the CPFSK signal is positive and therefore ~ ( t ) is an increasing function (and continuous, of course) and consequently the solutions tk of (1) are unique and tk+l>tk.
Sampling the signal x(t)=r(t)+s(t) at tk yields (s(t) denotes any signal which in a particular case can be a voice signal):
x*(k) -x(tk) = r(tg) + s(tk) = a cos(~k + ~b)+ s* ( k ),
(2)
where the asterisk * denotes the fact that x*(k) represents a nonuniform sampling of x(t). Such a nonuniform sampling is a way to implement the time-warping. Reviewing (2) it can be concluded that x* (k) is composed of the harmonic signal r*(k)=A c o s ( ( 2 ~ / N)k+ qb) with known frequency, and the signal s*(k). Using a fixed parameter second order constrained notch filter (CNF) [2, 7] on x*(k), it is possible to reject r*(k) and to obtain s*(k) at its output. The difference equation of the CNF is given by
y*(k) - 2a cos~s~,y*(k - 1) + a 2 y * ( k - 2) PC
2. Separation between the CPFSK signal and any signal using time-warping. Let r(t) =A cos[ ~ ( t ) + 4'] denote the CPFSK signal. Suppose from the outset that ~ ( t ) is known; A and 4) are unknown. 2 Knowing ~ ( t ) , it is possible to solve 1 It should not be confused with synchronization of nonuniform sampling discussed above. 2 When kV(t) is known, the technique described below can be applied to arbitrary FM signals, not necessarily CPFSK, as shown in [7].
2~
=x*(k) - 2 cos-7-,x*(k- 1) + x * ( k - 2 ) . 1v
(3)
As shown in [2, 7] the CNF notches (the right-hand side) the signal r*(k) for any value of a (0~
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D. Wulich, M. Bukris / Data over voice using time-warping
SOLVE
'1
p-
x(t) = r(t) + s(t)
Fig. 2. Separation of CPFSK signal and voice signal.
x(t) = r(t) + s(t)
_1
SYNTHESIS OF ~,'Ct)
cPFsK
v I DEMODULATOR Fig. 3. Synthesis of go(t).
struction of a continuous signal from its nonuniform samples. It will be shown later that with MSK the problem of reconstruction from nonuniformly spaced samples will be reduced to the well solved problem of the reconstruction of a continuous time signal from uniformly spaced samples. Figure 2 shows a block diagram of the scheme based on the concept of separation given above. It should be pointed out again that the separation is possible only because the phase ~ ( t ) is known.
The CPFSK signal r(t) carries digital information represented by a sequence {a.}, i.e. [3], (4)
where d(t) = E . a. p (t - nT), T is the symbol duration andp(t) = 1 for 0 < t < T . It is possible to demodulate the information sequence {a.} by applying x(t) to the CPFSK demodulator. Denote the demodulated sequence (the demodulator SignalProcessing
4. Using the MSK modulation format in the DOV system In the subsequent discussion the MSK modulation format as a special case of CPFSK is considered. In the MSK the phase ~ ( t ) is a piecewise linear function with two slopes which correspond to two different instantaneous frequenciesfn andfL (fL
3. Creating the synchronization signal gt(t)
att(t) = kyf ' d(q-) d~-,
output) by {(ln}. 3 Using (4) and the sequence {ci.} the signal ¢t(t) can be synthesized and taken in (1) for computing the time instants tk, see Fig. 3.
m-1 fL =
Tfb,
m+l , fn = - - ~ f b
(5)
where fb is a bit-rate and m can be any integer. Using this fact the creation of the sequence x* (k) as well as the reconstruction of s(t) from s*(k) will be substantially simplified. 3 Presence of s(t) in x(t) causes errors in demodulation, i.e., ~, =~a, for some n.
D. Wulich, M. Bukris / Data over voice using time-warping
4.1. Nonuniform sampling by decimation Solution of ( 1 ) for ~ ( t ) which represents the MSK signal gives 2.rr
k
fL: q/(t) =2"rrfLt=-~k fH=qt(t)=2~rfnt =
~ k
k
tk-=Nfm=fs--~' ~
tk-~
k
k
fsn"
(6) (7)
From (6) and ( 7 ) two different uniform sampling rates are obtained, namely fs~ = NfL and fs, = Nfn. We can find a sampling frequency S for which: (i) by taking every Hth sample from x(k/fs) when its instantaneous frequency isfn, samples o f x ( t ) atfs,, i.e., x(k/fs,) are obtained, and (ii) by taking every Lth sample from x(k/fs) when its instantaneous frequency isfL, samples o f x ( t ) at f sL, i.e., x( k /f s~) are obtained. From the above it follows that
fs=Hfs,,
fs=LfsL,
(8)
where H and L are natural numbers. Furthermore from (5) and (8),
H(m+ 1) = L ( m - 1).
(9)
To find the frequencyfs it is needed: (i) for given m to determine pairs (H, L) which satisfy (9); (ii) to choose such H (L) for which, for given fb and N, a suitable (in most cases the lowest possible) frequency fs is determined from (8).
4.2. Reconstruction of s(t) from s*(k) by additional decimation By taking every Lth sample from s*(k) when the instantaneous frequency of r(t) is fH and by taking every Hth sample when the instantaneous frequency is fL a sequence s**(p) is created, s**(p) represents a uniformly sampled, at a rate fs/ (HL), signal s(t). If additionally by appropriate choice of N, fs/(HL) is above the Nyquist frequency of the signal s(t), then s(t) can be easily reconstructed from s** (p).
EXAMPLE. The signal s(t) is limited to 3.4 kHz,
103
fb = 1000 bits/sec (Hz), m--=3, N = 20. For such data f c = 5 0 0 HZ, fH = 1000 Hz, fsL = 10 kHz andfs,,=20 kHz. H = 1, L = 2, therefore fs =fs,, = 20 kHz and fs/ (HL) = 10 kHz is above the Nyquist frequency of s ( t ). Figure 4 shows the signals r(t), s(t), sequences r*(k), s*(k) and s**(p). It should be stated here that in order to implement time-warping in general, as follows from ( 1 ), there is no need to know ~b, the initial phase of the MSK signal. However, for performing time-warping by decimation, as presented above, the value of ~bmust be known, i.e., the system must be coherent.
4.3. Performance of the MSK demodulator with the presence of a voice signal s(t) and a background noise n(t) Consider a case where s(t) = v ( t ) + n(t); v(t) represents a voice signal while n(t) is a background (white) noise. The signal s(t) appears at the MSK demodulator together with the signal r(t) and therefore influences the probability of bit error P~. As is known, the voice signal v(t) is a nonstationary process and therefore it is impossible to use the analytic expression for calculation of Pe obtained for white (stationary) noise. For the purpose of this work the influence of the signal s(t) o n Pe has been checked experimentally on a DEC station 5000/200. For this purpose 12.5 sec of male spoken English text sampled atfs =fs, = 20 kHz by a 12-bit A / D converter was stored in the computer. An MSK signal as well as the background noise was synthesized in the computer and together with the real voice signal it was fed through a 5 kHz low pass filter ( - 2 0 dB/sec) into the MSK demodulator, both software implemented. The long term probability density function of used voice signal fits very well the model given by the/'function [ I ]. The estimate of Pe has been found by the MonteCarlo method by counting the number of errors over 12500 bits, Pe mainly depends on two ratios: that of the energy of the MSK signal to the power density of the background noise - Eb/~ (as commonly used), and the ratio y between the peak value of the voice signal and the amplitude of the MSK signal. Obtained values Vol. 34. No. 1, October 1993
104
D. Wulich, M. Bukris / Data over voice using time-warping
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Fig. 4. The signals r(t), s(t), r*(k), s*(k) and s**(p).
Signal Processing
tra~sformed time
* reai~ime
D. Wulich, M. Bukris / Data over voice using time-warping
of ee a s a function of Eb/"0 for T and different pairs (m, fb) as parameters are presented in Fig. 5. There are three types of lines in this figure: dotted, broken and solid. The dotted line represents the performance of the MSK demodulator in the background noise only (without the voice signal) as obtained from analytical considerations [3, 4]. The broken and solid lines represent the performance of the MSK demodulator when both the background noise and the voice signal act at the input of the MSK demodulator. Two different configurations of the MSK signal are considered (m = 6,fb = 600 bits/sec) represented by the broken line and (m = 3,fb = 1000 bits/sec) represented by the solid line. Three curves of each type for T = 0, 0.5 and 1.5 are presented in this figure. For T = 0 and for any of two considered pairs (m, fb) the obtained value of Pe is very close to the analytical results obtained in the presence of white noise only (dotted line). When T increases Pe alSO increases as
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expected. The influence of the voice signal on Pe is not the same for the cases considered. From Fig. 5 it is clearly seen that for ( m = 3, fb = 1000 bits/sec) the presence of the voice signal increases Pe more than for (m = 6,fb = 600 bits/sec). The reason for such behaviour lies in the fact that the voice signal, during a short observation interval ( Tb = 1/fb), can be considered as a stationary process [ 1, 3], and therefore for lowerfb the energy of a bit is higher and consequently the ratio of the MSK signal to the voice signal increases. It is clearly seen that for T = 0.5 and T = 0 the Pe curves are very close. The difference in Eb/rl is only fractions of a dB. This result means that it is possible to transmit a voice signal with peak value slightly lower than the amplitude of the MSK signal ( ,/= 0.5) without significant degradation of the performance of the MSK demodulator. Because of that it is possible to take advantage of the output of the MSK demodulator to reconstruct the instantaneous phase of the MSK.
10 e
peak value of the voice signal ¥= ..... MSK signal amplitude , lO .4
10 "~
Pe le -)
10 -4
l e "~ -2
\ \÷=o.s f •
i 2
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Fig. 5. Pe as a function o f Eb/71 with y a n d (m, fb) as parameters; dotted line: c o m p u t e d f r o m the analytic f o r m u l a ( w i t h o u t the voice signal) ; broken line: simulation forfb = 6 0 0 b i t s / s e c and m = 6; solid line: simulation f o r f b = lO00 b i t s / s e c a n d m = 3. Vol. 34, No. I, October 1993
106
D. Wulich, M. Bukris / Data over voice using time-warping data out
MSK DEMODULATOR
DECISION SYSTEM
i
x(t) -- r(t) + s(t) "~,--
fs
I I ,1_I ,,oiout DELAY
Tb i
SAMPLES [X*(k) =r*(k) + $*(k).._lCONSTRAINEDNoTCH "- I FILTER
,REMOVING
Fig. 6. Block diagram of the entire system.
4.4. The entire system The entire system is presented in Fig. 6. The output of the MSK demodulator d, is used to determine which one of the two frequencies fn or fL is currently at the input to the system. According to that, the samples at the appropriate time instants are removed as it was explained in Subsections 4.1 and 4.2. Thus r*(k) is obtained as a harmonic sequence and can be rejected by the CNF leaving s*(k) as its output. Removing appropriate samples from s*(k) yields s**(p) which represents uniformly sampled voice signal (with a background noise) which can be reconstructed by using a D / A converter and a low-pass filter.
(MOS). A score of 5.0 implies perfect quality, while a score of 4.5 is regarded as a necessary condition for tool quality, the quality of commercial telephony [ 1]. The parameters of the MSK signal are m = 3 , f b = 1 0 0 0 bits/sec, fs=fsn=20 kHz, fsL=10 kHz. The speech signal is fed into the computer through 12bit A/D.
EXPERIMENT NO. 1. The mixture of the voice signal with the MSK signal, 7 = 1, no background noise, is presented to the listeners (the MSK signal is not rejected here by the CNF). The intelligibility in this case is very poor and the quality is practically 0.
EXPERIMENT NO. 2. Only the voice signal, sampled 5. Experimental results The aim of the experiment is to check the quality and intelligibility of the voice at the output of the system when there are errors at the MSK demodulator. For this we assume that there is no noise, i.e. Eb/~ = ~, and that the errors are caused by the high level of the voice signal ( T > 1). The quality and intelligibility is determined by subjecting 12.5 sec of the reconstructed voice signal g(t) to the judgement of 11 independent listeners. The quality of the reconstructed voice signal is measured by formal subjective testing based on mean opinion score SignalProcessing
atfs = 20 kHz and reconstructed by a D / A converter plus low-pass filter is presented to the listeners. The intelligibility is practically equal to that of the original, while the MOS quality is 4.67 with a standard deviation of 0.39.
EXPERIMENTNO. 3. No noise (Eb/r/= oo). The value of bit error rate (BER) is set to be 0/12500, 20/12500, 60/12500 = 0 and 100/12500. The value of the CNF parameter a is set to be 0.95, 0.999, 0.9999. For all cases of BER and a the intelligibility is practically equal to that of the original. The quality however is affected by the value of BER and the value of a. The results are presented in Table 1, where for each value
D. Wulich, M. Bukris / Data over voice using time-warping Table I Quality of reconstructed voice,
Eb/"r I =
~, male speaker
BER
0/12500
20/12500
60/12500
100/12500
y VSR [dB]
1.65 - 12.94
3 -7.78
3.85 -5.66
4.6 -4.16
3.06
2.45
2.37
2.55
0.74
0.63
0.51
0.43
4.38
3.81
3.23
3.16
0.62
0.84
0.74
0.60
4.40
3.99
3.35
3.30
0.52
0.57
0.69
0.64
ot = 0.95 Mean Standard deviation a = 0.999 Mean Standard deviation ot = 0.9999 Mean Standard deviation
of BER the value of Y (which ensures such a BER), the voice to MSK signal ratio: V S R = 10 log P i P , (Ps, P, are average powers of the voice signal and MSK signal, respectively), mean and standard deviation of quality are shown. Analyzing the results obtained it is possible to reach two conclusions: (a) When a increases the quality increases too, as expected. It is observed however that the quality remains almost the same for a = 0 . 9 9 9 and ce = 0.9999. This observation helps us to choose an optimal value of a. (b) When BER increases the quality decreases. The influence of BER on the quality however is not significant. For example for a = 0.999 the quality degrades from 4.38 (for zero errors) to 3.16 (at Pe = 10-2!), a value which is quite acceptable in medium-complexity coders at 16 kbits/sec. On the other hand for the case of zero errors the tool quality, i.e., ~ 4.5, is obtained [ 1 ].
6. Conclusion and discussion A new method of data over voice is considered where
107
the digitally modulated signal belongs to the CPFSK family. In particular the MSK modulation format is used, which significantly simplifies the time-warping procedure as well as the reconstruction of the voice signal. The most important question which should be asked in the DOV system is: What is the influence of the voice on data signals and vice versa? In our case it was found that if the peak value of voice signal is below the amplitude of the MSK signal, then the influence of the voice signal on the performance of the MSK demodulator is negligible. On the other hand, the ability of the CNF to reject the MSK signal depends on the error rate at the MSK receiver. Occurrence of error(s) causes a loss of 'nonuniform sampling' synchronization, and consequently the CNF, during the time interval of a bit, is unable to reject the MSK signal. As a result one or more spikes, with time duration equal to the time of one bit, will appear together with the reconstructed voice signal. As follows from Table 1, the quality however is very weakly influenced by that: the appearance of 100 errors in 12.5 sec degrades the quality from 4.38 to only 3.16 for c~= 0.999. In the presented analysis of the DOV system, it was assumed that the channel is noisy but with a flat and unlimited transfer function. As is well-known, real systems are always bandlimited. If the bandwidth is comparable with that of the MSK signal, the MSK signal will be distorted and as a consequence its envelope will vary. In such a situation, even if there are no decision errors, the MSK signal will not be rejected in full by the CNF and some part of it will appear at the voice output as a residual MSK signal. At the present stage of investigation the problem of residual MSK seems to be a serious one and its solution will be presented in future publications.
References [ 1 ] N.S. Jayant and P. Noll, Digital Coding of Waveforms, Prentice Hall, Englewood Cliffs, NJ, 1984. [2] A. Nehorai, " A m i n i m u m parameter adaptive notch filter with constrained poles and zeroes", IEEE Trans. Acoust. Speech Signal Process., Vol. ASSP-33, 1985, pp. 983-996. Vol. 34, No. I, October 1993
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[3] J.G. Proakis, Digital Communications, McGraw-Hill, New York, 1989. [ 4] H. Taub and D.L. Schilling, Principles of Communication Systems, McGraw-Hill, New York, 1986. [5] D. Wulich, E.L Plotkin, M.N.S. Swamy and Wen Tong, "PLL based discrete time varying filter for estimation of parameters of a sine signal corrupted by a closely spaced FM interference", 1990 IEEE lnternat. Symposium on Circuits and Systems, New Orleans, LA, 1-3 May 1990.
SignalProcessing
[6] D. Wulich, E.I. Plotkin and M.N.S. Swamy, "Synthesis of discrete time-varying null filters for frequency-varying signals using the time-warping technique", IEEE Trans. Circuits and Systems, Vol. 37, 1990, pp. 977-990. [ 7 ] D. Wulich, E.I. Plotkin and M.N.S. Swamy, "Constrained notch filtering of nonuniformly spaced samples for enhancement of an arbitrary signal corrupted by a strong FM interference", IEEE Trans. Signal Process., Vol. 39, 1991, pp. 2359-2363.
99
Data over voice using time-warping technique Dov Wulich and Moshe Bukris Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, POB 653, Israel Received 7 November 1991 Revised 13 April 1992 and 5 January 1993
Abstract. Simultaneous transmission of a digitally modulated signal and a voice signal known as data over voice (DOV) is discussed. In particular a minimum shift keying (MSK) modulation format is considered. A new method is used which is based on a time-warping technique, where having the instantaneous phase (frequency) of the MSK signal, the MSK signal is transformed into a harmonic one with known frequency, while the voice signal, which is broadband, is transformed into another broadband signal. Consequently, after performing the time-warping, it is possible to separate the transformed MSK signal and the transformed voice signal by using a fixed coefficient second order constrained notch filter. The instantaneous phase of the MSK signal, needed for time-warping, is synthesized by using the output of the MSK receiver. It is shown that if the peak value of the voice signal is below the amplitude of the MSK signal, then the performance of the MSK receiver is only mildly influenced by the voice signal, and the reconstructed voice signal has high intelligibility. Zusammenfassung. Die gleichzeitige Obertragung eines digital modulierten Signals und eines Sprachsignals, als 'data over voice' (DOV) bekannt, wird diskutiert. Insbesondere wird ein Minimum-Shift-Keying-Format (MSK) betrachtet. Ein neues Verfahren wird verwendet, das auf einer Zeitachsen-Verzerrungstechnikberuht: Bei gegebener Momentanphase (oder Momentanfrequenz ) des MS KSignals wird das MSK-Signal in ein harmonisches Signal bekannter Frequenz transformiert, wiihrend das Sprachsignal mit seiner groBen Bandbreidte in ein anderes Breithandsignal transformiert wird. Folglich ist es nach der Zeitachsenverzerrung mtiglich, das transformierte MSK-Signal and das transformierte Sprachsignal mittels eines zeitinvarianten Kerbfilters mit Zusatzbedingung vom Grade 2 zu trennen. Die for die Zeitachsenverzerrung ben0tigte Momentanphase des MSK-Signals wird mit Hilfe des MSK-Empfiinger-Ausgangs synthetisiert. Es wird gezeigt, dab die Leistungsf'ahigkeit des MSK-Empf'~rigers nut wenig vom Sprachsignal beeinfluBt wird, wenn der Spitzenwert des Sprachsignals unter der MSK-Amplitude bleibt; das rekonstruierte Sprachsignal besitzt eine hohe Verstiindlichkeit. R6sum6. Le probl~me de la transmission simultan6e d'un signal digital modul6 et d'un signal de parole appel6 DOV (en anglais data over voice) est discut6. En particulier, nous consid6rons un format de modulation MS K (minimum shift keying ). Une nouvelle m&hode bas6e sur une technique de distorsion temporelle est utilis6e, o~, 6tant donn6 la phase (fr6quence) du signal MSK, celui-ci est transform6 en un signal harmonique de fr6quence connue; parall~lement, le signal de parole ~ large bande est transform6 en un autre signal ~tlarge bande. Par cons6quent, apr~s cette distorsion temporelle, il est possible de s6parer le signal MSK transform6 ainsi que le signal de parole transform6 en utilisant un filtre coupe-bande 6troit du second ordre h coefficients fixes. La phase instantan6e du signal MSK, n6cessaire pour la distorsion temporelle, est synth6tis6e en utilisant la sortie du r6cepteur MSK. Il est montr6 que si la valeur de pointe du signal de parole est inf6rieure ~tl'amplitude du signal MSK, la performance du r6cepteur MSK n'est alors seulement influenc6e que moyennement par le signal de parole, et le signal de parole reconstruit poss~de un haut degr6 d'intelligibilit6. Keywords. Data over voice; time-warping.
Correspondence to: Dr. Dov Wulich, Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, POB 653, Israel. Tel. +972-57-461537, Fax: +972-57-281340, E-mail: [email protected]
0165-1684/93/$06.00 © 1993 Elsevier Science Publishers B.V. All rights reserved
100
D. Wulich, M. Bukris / Data over voice using time-warping
1. I n t r o d u c t i o n
lation format, which belongs to the family of continuous phase frequency shift keying (CPFSK) [3] is considered here. The CPFSK signal has both continuous phase and a constant envelope. Consider the sum x(t)=s(t)+r(t) of a signal r(t) =A cos[ ~ ( t ) + ~b] having constant envelope and continuous phase and any arbitrary signal s(t). As shown in [7] the idea of the separation between r(t) and s (t) is based on a time-warping concept performed by nonuniform sampling of the sum signal x(t). The strategy of nonuniform sampling, the synchronization, is derived from the instantaneous phase of the signal r(t) in such a manner that x(t) is sampled at time instants in which ~ ( t ) increases by equal increments. As a result the nonuniformly sampled signal r(t) becomes a harmonic sequence, while the nonuniformly sampled signal s(t) is, in general, a broadband one. This fact makes it possible to separate between these
The method of transmission of a digitally modulated signal and a voice signal known as data over voice (DOV) is considered. It is assumed that the signals share the same bandwidth and appear simultaneously in time. Therefore, the DOV considered precludes both frequency division multiplexing (FDM) and time division multiplexing (TDM) techniques. In Fig. 1 the typical spectra of the digitally modulated signal (represented here by an MSK) and the voice signal are presented. In this paper a new technique [7] to separate at the receiver end the digitally modulated and the voice signals is used. As shown in [7] one of the signals to be separated must have a constant envelope and continuous phase while the second may have any form. For this reason the minimum shift keying (MSK) modu-
2500 tn
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500 0 0
500
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2588 f
3808
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¥FT - UOICE S i ? n a l
1000 I 808 I
Peak value = I v
600 400 200 8|
8
500
1880
1588
2088
2588
5888
~>ee
f [Hz]
Fig. 1. Spectrum of the MSK signal and voice signal for ~/= 1. Signal Processing
4808
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D. Wulich, M. Bukris / Data over voice using time-warping
two sequences by using a fixed coefficient second order constrained notch filter (CNF) [7]. In most practical cases, however, the input mixture x(t) is given, and therefore only an estimate of the phase r(t) may be obtained and used for synchronization. The quality of such an estimation depends on additional information available about r(t). In [5] an arbitrary FM (not necessarily CPFSK) signal r(t) is considered, where it is shown that if r(t) is much stronger than the signal s(t), then it is possible to use for synchronization the instantaneous phase of the signal x(t), instead of the phase of r(t). This phase may be obtained by applying x(t) to the FM demodulator followed by an integrator. It is shown in [ 5 ] that only partial separation can be obtained in such a case and further processing is needed where additional information about s(t) is required. In our case, however, the signal r(t) is MSK and therefore its instantaneous phase is piecewise linear with two slopes whose values can be obtained at the output of the MSK demodulator, a hard decision device, which is more 'immune' to the presence o f s ( t ) than the FM demodulator. It will be shown that using the output of the MSK demodulator for creating the synchronization signal gives a much better result than those obtained in [ 5 ]. A coherent demodulator is used. Its synchronization ~ is assumed to be ideal. Such an assumption is not essential at this stage of investigation where the goal is to check the usefulness of time-warping to the DOV system.
101
the following equation:
~(t) =2"trk k=0,1,2 .....
(1)
N ' where N is, at this stage, an arbitrary natural number. tk is the solution of (1) for a given k, i.e., qt(t k) =
( 2~r/N)k. As known, the instantaneous frequency of the CPFSK signal is positive and therefore ~ ( t ) is an increasing function (and continuous, of course) and consequently the solutions tk of (1) are unique and tk+l>tk.
Sampling the signal x(t)=r(t)+s(t) at tk yields (s(t) denotes any signal which in a particular case can be a voice signal):
x*(k) -x(tk) = r(tg) + s(tk) = a cos(~k + ~b)+ s* ( k ),
(2)
where the asterisk * denotes the fact that x*(k) represents a nonuniform sampling of x(t). Such a nonuniform sampling is a way to implement the time-warping. Reviewing (2) it can be concluded that x* (k) is composed of the harmonic signal r*(k)=A c o s ( ( 2 ~ / N)k+ qb) with known frequency, and the signal s*(k). Using a fixed parameter second order constrained notch filter (CNF) [2, 7] on x*(k), it is possible to reject r*(k) and to obtain s*(k) at its output. The difference equation of the CNF is given by
y*(k) - 2a cos~s~,y*(k - 1) + a 2 y * ( k - 2) PC
2. Separation between the CPFSK signal and any signal using time-warping. Let r(t) =A cos[ ~ ( t ) + 4'] denote the CPFSK signal. Suppose from the outset that ~ ( t ) is known; A and 4) are unknown. 2 Knowing ~ ( t ) , it is possible to solve 1 It should not be confused with synchronization of nonuniform sampling discussed above. 2 When kV(t) is known, the technique described below can be applied to arbitrary FM signals, not necessarily CPFSK, as shown in [7].
2~
=x*(k) - 2 cos-7-,x*(k- 1) + x * ( k - 2 ) . 1v
(3)
As shown in [2, 7] the CNF notches (the right-hand side) the signal r*(k) for any value of a (0~
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D. Wulich, M. Bukris / Data over voice using time-warping
SOLVE
'1
p-
x(t) = r(t) + s(t)
Fig. 2. Separation of CPFSK signal and voice signal.
x(t) = r(t) + s(t)
_1
SYNTHESIS OF ~,'Ct)
cPFsK
v I DEMODULATOR Fig. 3. Synthesis of go(t).
struction of a continuous signal from its nonuniform samples. It will be shown later that with MSK the problem of reconstruction from nonuniformly spaced samples will be reduced to the well solved problem of the reconstruction of a continuous time signal from uniformly spaced samples. Figure 2 shows a block diagram of the scheme based on the concept of separation given above. It should be pointed out again that the separation is possible only because the phase ~ ( t ) is known.
The CPFSK signal r(t) carries digital information represented by a sequence {a.}, i.e. [3], (4)
where d(t) = E . a. p (t - nT), T is the symbol duration andp(t) = 1 for 0 < t < T . It is possible to demodulate the information sequence {a.} by applying x(t) to the CPFSK demodulator. Denote the demodulated sequence (the demodulator SignalProcessing
4. Using the MSK modulation format in the DOV system In the subsequent discussion the MSK modulation format as a special case of CPFSK is considered. In the MSK the phase ~ ( t ) is a piecewise linear function with two slopes which correspond to two different instantaneous frequenciesfn andfL (fL
3. Creating the synchronization signal gt(t)
att(t) = kyf ' d(q-) d~-,
output) by {(ln}. 3 Using (4) and the sequence {ci.} the signal ¢t(t) can be synthesized and taken in (1) for computing the time instants tk, see Fig. 3.
m-1 fL =
Tfb,
m+l , fn = - - ~ f b
(5)
where fb is a bit-rate and m can be any integer. Using this fact the creation of the sequence x* (k) as well as the reconstruction of s(t) from s*(k) will be substantially simplified. 3 Presence of s(t) in x(t) causes errors in demodulation, i.e., ~, =~a, for some n.
D. Wulich, M. Bukris / Data over voice using time-warping
4.1. Nonuniform sampling by decimation Solution of ( 1 ) for ~ ( t ) which represents the MSK signal gives 2.rr
k
fL: q/(t) =2"rrfLt=-~k fH=qt(t)=2~rfnt =
~ k
k
tk-=Nfm=fs--~' ~
tk-~
k
k
fsn"
(6) (7)
From (6) and ( 7 ) two different uniform sampling rates are obtained, namely fs~ = NfL and fs, = Nfn. We can find a sampling frequency S for which: (i) by taking every Hth sample from x(k/fs) when its instantaneous frequency isfn, samples o f x ( t ) atfs,, i.e., x(k/fs,) are obtained, and (ii) by taking every Lth sample from x(k/fs) when its instantaneous frequency isfL, samples o f x ( t ) at f sL, i.e., x( k /f s~) are obtained. From the above it follows that
fs=Hfs,,
fs=LfsL,
(8)
where H and L are natural numbers. Furthermore from (5) and (8),
H(m+ 1) = L ( m - 1).
(9)
To find the frequencyfs it is needed: (i) for given m to determine pairs (H, L) which satisfy (9); (ii) to choose such H (L) for which, for given fb and N, a suitable (in most cases the lowest possible) frequency fs is determined from (8).
4.2. Reconstruction of s(t) from s*(k) by additional decimation By taking every Lth sample from s*(k) when the instantaneous frequency of r(t) is fH and by taking every Hth sample when the instantaneous frequency is fL a sequence s**(p) is created, s**(p) represents a uniformly sampled, at a rate fs/ (HL), signal s(t). If additionally by appropriate choice of N, fs/(HL) is above the Nyquist frequency of the signal s(t), then s(t) can be easily reconstructed from s** (p).
EXAMPLE. The signal s(t) is limited to 3.4 kHz,
103
fb = 1000 bits/sec (Hz), m--=3, N = 20. For such data f c = 5 0 0 HZ, fH = 1000 Hz, fsL = 10 kHz andfs,,=20 kHz. H = 1, L = 2, therefore fs =fs,, = 20 kHz and fs/ (HL) = 10 kHz is above the Nyquist frequency of s ( t ). Figure 4 shows the signals r(t), s(t), sequences r*(k), s*(k) and s**(p). It should be stated here that in order to implement time-warping in general, as follows from ( 1 ), there is no need to know ~b, the initial phase of the MSK signal. However, for performing time-warping by decimation, as presented above, the value of ~bmust be known, i.e., the system must be coherent.
4.3. Performance of the MSK demodulator with the presence of a voice signal s(t) and a background noise n(t) Consider a case where s(t) = v ( t ) + n(t); v(t) represents a voice signal while n(t) is a background (white) noise. The signal s(t) appears at the MSK demodulator together with the signal r(t) and therefore influences the probability of bit error P~. As is known, the voice signal v(t) is a nonstationary process and therefore it is impossible to use the analytic expression for calculation of Pe obtained for white (stationary) noise. For the purpose of this work the influence of the signal s(t) o n Pe has been checked experimentally on a DEC station 5000/200. For this purpose 12.5 sec of male spoken English text sampled atfs =fs, = 20 kHz by a 12-bit A / D converter was stored in the computer. An MSK signal as well as the background noise was synthesized in the computer and together with the real voice signal it was fed through a 5 kHz low pass filter ( - 2 0 dB/sec) into the MSK demodulator, both software implemented. The long term probability density function of used voice signal fits very well the model given by the/'function [ I ]. The estimate of Pe has been found by the MonteCarlo method by counting the number of errors over 12500 bits, Pe mainly depends on two ratios: that of the energy of the MSK signal to the power density of the background noise - Eb/~ (as commonly used), and the ratio y between the peak value of the voice signal and the amplitude of the MSK signal. Obtained values Vol. 34. No. 1, October 1993
104
D. Wulich, M. Bukris / Data over voice using time-warping
flt
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o , ,~
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(din')
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Fig. 4. The signals r(t), s(t), r*(k), s*(k) and s**(p).
Signal Processing
tra~sformed time
* reai~ime
D. Wulich, M. Bukris / Data over voice using time-warping
of ee a s a function of Eb/"0 for T and different pairs (m, fb) as parameters are presented in Fig. 5. There are three types of lines in this figure: dotted, broken and solid. The dotted line represents the performance of the MSK demodulator in the background noise only (without the voice signal) as obtained from analytical considerations [3, 4]. The broken and solid lines represent the performance of the MSK demodulator when both the background noise and the voice signal act at the input of the MSK demodulator. Two different configurations of the MSK signal are considered (m = 6,fb = 600 bits/sec) represented by the broken line and (m = 3,fb = 1000 bits/sec) represented by the solid line. Three curves of each type for T = 0, 0.5 and 1.5 are presented in this figure. For T = 0 and for any of two considered pairs (m, fb) the obtained value of Pe is very close to the analytical results obtained in the presence of white noise only (dotted line). When T increases Pe alSO increases as
105
expected. The influence of the voice signal on Pe is not the same for the cases considered. From Fig. 5 it is clearly seen that for ( m = 3, fb = 1000 bits/sec) the presence of the voice signal increases Pe more than for (m = 6,fb = 600 bits/sec). The reason for such behaviour lies in the fact that the voice signal, during a short observation interval ( Tb = 1/fb), can be considered as a stationary process [ 1, 3], and therefore for lowerfb the energy of a bit is higher and consequently the ratio of the MSK signal to the voice signal increases. It is clearly seen that for T = 0.5 and T = 0 the Pe curves are very close. The difference in Eb/rl is only fractions of a dB. This result means that it is possible to transmit a voice signal with peak value slightly lower than the amplitude of the MSK signal ( ,/= 0.5) without significant degradation of the performance of the MSK demodulator. Because of that it is possible to take advantage of the output of the MSK demodulator to reconstruct the instantaneous phase of the MSK.
10 e
peak value of the voice signal ¥= ..... MSK signal amplitude , lO .4
10 "~
Pe le -)
10 -4
l e "~ -2
\ \÷=o.s f •
i 2
f 4
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I 6
I $
16
12
[dB]
Fig. 5. Pe as a function o f Eb/71 with y a n d (m, fb) as parameters; dotted line: c o m p u t e d f r o m the analytic f o r m u l a ( w i t h o u t the voice signal) ; broken line: simulation forfb = 6 0 0 b i t s / s e c and m = 6; solid line: simulation f o r f b = lO00 b i t s / s e c a n d m = 3. Vol. 34, No. I, October 1993
106
D. Wulich, M. Bukris / Data over voice using time-warping data out
MSK DEMODULATOR
DECISION SYSTEM
i
x(t) -- r(t) + s(t) "~,--
fs
I I ,1_I ,,oiout DELAY
Tb i
SAMPLES [X*(k) =r*(k) + $*(k).._lCONSTRAINEDNoTCH "- I FILTER
,REMOVING
Fig. 6. Block diagram of the entire system.
4.4. The entire system The entire system is presented in Fig. 6. The output of the MSK demodulator d, is used to determine which one of the two frequencies fn or fL is currently at the input to the system. According to that, the samples at the appropriate time instants are removed as it was explained in Subsections 4.1 and 4.2. Thus r*(k) is obtained as a harmonic sequence and can be rejected by the CNF leaving s*(k) as its output. Removing appropriate samples from s*(k) yields s**(p) which represents uniformly sampled voice signal (with a background noise) which can be reconstructed by using a D / A converter and a low-pass filter.
(MOS). A score of 5.0 implies perfect quality, while a score of 4.5 is regarded as a necessary condition for tool quality, the quality of commercial telephony [ 1]. The parameters of the MSK signal are m = 3 , f b = 1 0 0 0 bits/sec, fs=fsn=20 kHz, fsL=10 kHz. The speech signal is fed into the computer through 12bit A/D.
EXPERIMENT NO. 1. The mixture of the voice signal with the MSK signal, 7 = 1, no background noise, is presented to the listeners (the MSK signal is not rejected here by the CNF). The intelligibility in this case is very poor and the quality is practically 0.
EXPERIMENT NO. 2. Only the voice signal, sampled 5. Experimental results The aim of the experiment is to check the quality and intelligibility of the voice at the output of the system when there are errors at the MSK demodulator. For this we assume that there is no noise, i.e. Eb/~ = ~, and that the errors are caused by the high level of the voice signal ( T > 1). The quality and intelligibility is determined by subjecting 12.5 sec of the reconstructed voice signal g(t) to the judgement of 11 independent listeners. The quality of the reconstructed voice signal is measured by formal subjective testing based on mean opinion score SignalProcessing
atfs = 20 kHz and reconstructed by a D / A converter plus low-pass filter is presented to the listeners. The intelligibility is practically equal to that of the original, while the MOS quality is 4.67 with a standard deviation of 0.39.
EXPERIMENTNO. 3. No noise (Eb/r/= oo). The value of bit error rate (BER) is set to be 0/12500, 20/12500, 60/12500 = 0 and 100/12500. The value of the CNF parameter a is set to be 0.95, 0.999, 0.9999. For all cases of BER and a the intelligibility is practically equal to that of the original. The quality however is affected by the value of BER and the value of a. The results are presented in Table 1, where for each value
D. Wulich, M. Bukris / Data over voice using time-warping Table I Quality of reconstructed voice,
Eb/"r I =
~, male speaker
BER
0/12500
20/12500
60/12500
100/12500
y VSR [dB]
1.65 - 12.94
3 -7.78
3.85 -5.66
4.6 -4.16
3.06
2.45
2.37
2.55
0.74
0.63
0.51
0.43
4.38
3.81
3.23
3.16
0.62
0.84
0.74
0.60
4.40
3.99
3.35
3.30
0.52
0.57
0.69
0.64
ot = 0.95 Mean Standard deviation a = 0.999 Mean Standard deviation ot = 0.9999 Mean Standard deviation
of BER the value of Y (which ensures such a BER), the voice to MSK signal ratio: V S R = 10 log P i P , (Ps, P, are average powers of the voice signal and MSK signal, respectively), mean and standard deviation of quality are shown. Analyzing the results obtained it is possible to reach two conclusions: (a) When a increases the quality increases too, as expected. It is observed however that the quality remains almost the same for a = 0 . 9 9 9 and ce = 0.9999. This observation helps us to choose an optimal value of a. (b) When BER increases the quality decreases. The influence of BER on the quality however is not significant. For example for a = 0.999 the quality degrades from 4.38 (for zero errors) to 3.16 (at Pe = 10-2!), a value which is quite acceptable in medium-complexity coders at 16 kbits/sec. On the other hand for the case of zero errors the tool quality, i.e., ~ 4.5, is obtained [ 1 ].
6. Conclusion and discussion A new method of data over voice is considered where
107
the digitally modulated signal belongs to the CPFSK family. In particular the MSK modulation format is used, which significantly simplifies the time-warping procedure as well as the reconstruction of the voice signal. The most important question which should be asked in the DOV system is: What is the influence of the voice on data signals and vice versa? In our case it was found that if the peak value of voice signal is below the amplitude of the MSK signal, then the influence of the voice signal on the performance of the MSK demodulator is negligible. On the other hand, the ability of the CNF to reject the MSK signal depends on the error rate at the MSK receiver. Occurrence of error(s) causes a loss of 'nonuniform sampling' synchronization, and consequently the CNF, during the time interval of a bit, is unable to reject the MSK signal. As a result one or more spikes, with time duration equal to the time of one bit, will appear together with the reconstructed voice signal. As follows from Table 1, the quality however is very weakly influenced by that: the appearance of 100 errors in 12.5 sec degrades the quality from 4.38 to only 3.16 for c~= 0.999. In the presented analysis of the DOV system, it was assumed that the channel is noisy but with a flat and unlimited transfer function. As is well-known, real systems are always bandlimited. If the bandwidth is comparable with that of the MSK signal, the MSK signal will be distorted and as a consequence its envelope will vary. In such a situation, even if there are no decision errors, the MSK signal will not be rejected in full by the CNF and some part of it will appear at the voice output as a residual MSK signal. At the present stage of investigation the problem of residual MSK seems to be a serious one and its solution will be presented in future publications.
References [ 1 ] N.S. Jayant and P. Noll, Digital Coding of Waveforms, Prentice Hall, Englewood Cliffs, NJ, 1984. [2] A. Nehorai, " A m i n i m u m parameter adaptive notch filter with constrained poles and zeroes", IEEE Trans. Acoust. Speech Signal Process., Vol. ASSP-33, 1985, pp. 983-996. Vol. 34, No. I, October 1993
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[3] J.G. Proakis, Digital Communications, McGraw-Hill, New York, 1989. [ 4] H. Taub and D.L. Schilling, Principles of Communication Systems, McGraw-Hill, New York, 1986. [5] D. Wulich, E.L Plotkin, M.N.S. Swamy and Wen Tong, "PLL based discrete time varying filter for estimation of parameters of a sine signal corrupted by a closely spaced FM interference", 1990 IEEE lnternat. Symposium on Circuits and Systems, New Orleans, LA, 1-3 May 1990.
SignalProcessing
[6] D. Wulich, E.I. Plotkin and M.N.S. Swamy, "Synthesis of discrete time-varying null filters for frequency-varying signals using the time-warping technique", IEEE Trans. Circuits and Systems, Vol. 37, 1990, pp. 977-990. [ 7 ] D. Wulich, E.I. Plotkin and M.N.S. Swamy, "Constrained notch filtering of nonuniformly spaced samples for enhancement of an arbitrary signal corrupted by a strong FM interference", IEEE Trans. Signal Process., Vol. 39, 1991, pp. 2359-2363.