continuous delta modulation - philips bound... · continuous delta modulation isavariant ofnormal...

R664 Philips Res. Repts 2.3, 233-246, 1968

CONTINUOUS DELTA MODULATION

by J. A. GREEFKES and F. de JAGER

AbstractIn delta modulation the coding procedure can easily be adapted to theamplitude variations of a speech signal by varying the height of the unitstep which is used in the feedback loop. By deriving a control voltagefrom the transmitted pulse pattern, this control action can be performedin an identical manner at the transmitter and the receiver. This controlaction is introduced in the feedback loop in such manner that with a26-dB variation of the input signal the mean number of positive pulseschanges from 1/3 to 1/2 of its maximum. As a result the amplitude ofthe quantization noise varies almost in proportion to the amplitude ofthe speech signal. High-quality speech reproduetion requires a pulsefrequency of 40 kc/s, whereas speech of lower quality was found to besatisfactory with a pulse frequency of 16 kc/so In the latter case 20-dBvariations of the input signal could easily be tolerated.

1. Introduetion

Continuous delta modulation is a variant of normal delta modulation. Its aimis to encode information signals showing large level fluctuations (about 30 dB)in a more efficient way. This is achieved by an automatic adaption of thequantization step to signal level. The essential features of the system are:(1) the height of the quantization step in the feedback circuit at the transmitter

is varied almost in proportion to the amplitude of the input signal;(2) information about the height of this quantization step is transmitted to the

receiver by changing the mean number of "1" pulses in the binary pulsepattern;

(3) features (1) and (2) are achieved by combining feedback and forward controlat the transmitter;

(4) the height of the quantization step is changed in the same manner at thetransmitter and the receiver, this height being controlled by the binary pulsepattern.

In this way the signal-to-quantizing-noise ratio can be made nearly constantover a wide range of signallevels and the system operates with perfect stability.Before presenting the details of the system a short description of normal deltamodulation will be given.

2. Normal delta modulation

In the transmitter the input signal. a (fig. 1) is converted into a binary pulsepattern p, and in the receiver this pulse pattern is converted again into a closeapproximation af of the original input signal. In delta modulation the pulse

234 J. A. GREEFKES and F. de JAGER

pattern is arranged such that the signal can simply be reconstructed from thepulse pattern by linear filtering, usually by means of an integrator, followed bya low-pass filter, as shown in fig. 1. .

Fig. 1. Transmitter and receiver for normal delta modulation.

To obtain the correct sequence of pulses an auxiliary receiver (I) is used atthe transmitter. If the transmitted pulses are integrated here, a first-approx-imation signal b is obtained, which is compared with the original a by meansof the differential amplifier D. The difference e = a - b is then sampled atequally spaced time intervals and, depending on its polarity, used to generatepulses which are either 1 or O. This sampling and pulse-forming circuit is in-dicated by PM in fig. 1. The transmitter therefore essentially consists of a circuitapplying negative feedback, which differs, however, from a normal feedbackbecause it is quantized in amplitude and in time.

If the transmitted pulses are applied to an identical integrating device at thereceiving end, an identical approximation signal b' will be obtained. As thissignal shows spectrum components of higher frequencies than are present inthe input signal, it is convenient to eliminate these by means of a low-passfilter LP.

The operation can be improved by using a double-integrating network in thefeedback loop 1). The result of this is that not only instantaneous deviationsbut also their cumulative effects are taken into account. Besides, as the differencesignal then has a more irregular form, this results also in a more continuousspectrum of the quantization noise.

'\3. Continuous delta modulation

If a d.c. component is applied to the input of the transmitter in fig. 1, the ratiobetween the mean number of 1 and 0 pulses ofthe transmitted pulse pattern willchange. In fact, as a consequence of the feedback action, a new point of equi-librium is reached where the mean voltage at the output of the feedback networkhas the same but opposite value to that of the inputsignal, making the differencesignal nearly equal to zero. As the same d.c. component is present at point b'of the receiver, t~is is an easy way of transmitting d.c. voltages by means of

CONTINUOUS DELTA MODULATION 235

delta modulation *). The fact that it is quite easy to change the mean numberof "1". pulses\ in the transmitted pulse pattern, gives a possibility to transmitan additional low-frequency information over the delta-modulation channel.In continuous delta modulation this effect is used to inform the receiver aboutthe varying quantization-step height used at the.transmitting end.The circuit diagram of the transmitter is given in fig. 2. Comparing this with -

fig. 1 we note that a pulse-amplitude modulator PAM has been inserted in the

p

Fig. 2. Circuit diagram of the transmitter for continuous delta modulation.

feedback loop, the transmitted pulses p applied to the integrating network inthe feedback loop being controlled in amplitude in the pulse modulator PA:M;by means of a control voltage c. This control voltage, which represents the meannumber of "1" pulses in the binary pulse pattern, is obtained fromp by applyingit to a low-pass filter LP l' The system is named "continuous" delta modulationfor the reason that the pulses q used for regenerating the approximation signal bcan be varried in an almost continuous way.Let us suppose now that things are arranged such that for very~small input

signals the ratio between the mean number of 1 and 0 pulses in the transmittedpulse pattern is as 1 : 2, and that for high input signals this ratio changes to1 : 1. Then the control voltage c is obviously 1·5 times higher for strong inputsignals than for signals of very small or zero amplitude. This variation by afactor of 1·5 of the control voltage c can be used to vary the amplitude of thepulses q provided by the pulse modulator PAM by a factor of 20. With thisthe height ofthe quantizing step at the integrator also varies by a factor of20.

Observing the change in d.c. voltage at the output b of the integrator we finda change in the ratio 1 to 30 (a factor of 20 resulting from the higher pulseamplitude and a factor of 1·5 resulting from the higher density). It is now asimple matter to use this change in d.c. level for automatically adapting thequantization-step height to the level of the input signal. To this end the signalvoltage a is rectified and smoothed by an RC network to form a d.c. compo-nent d which is added to the originalinput signal. It will be assumed that theinput signal a,which is in most cases a speech signal, does not contain spectrum

*) In the literature it is sometimes erroneously stated that delta modulation is not capableof transmitting d.c. signals 2.3). Applications of delta modulation for the transmission ofVocoder signals or, for instance, for the analog-to-digital conversion in telemetry 4) haveshown, however, that all low frequencies, including the frequency zero, can be handledwith normal delta modulation. .


components of very low frequencies, so that a and d are indeed located in"different parts of the frequency spectrum.It has already been pointed out in the description ofthe diagram offig. 1 that

the system tends to keep the difference signal 8 to a minimum. This applies alsoto signals in different parts of the frequency spectrum. Thus, as the informationsignal a is compensated by the fast :fluctuations in the approximation signal b,the d.c. component d is automatically compensated by the d.c. component atthe point b. This means that, over a large range of signal amplitudes, the d.c.component of the pulse series q is varied proportionally with the signal ampli-tude. From the :fixed relation with the pulse series it then follows that the heightof the quantization step is also varying almost in proportion to the input signal,thus keeping the instantaneous signal-to-noise ratio nearly constant. As a con-sequence of the chosen characteristic of the pulse modulator PAM the meannumber of "1" pulses in the transmitted pulse sequence will thereby vary onlyfrom one third to a half of the applied pulse frequency.

Fig. 3. Circuit diagram of the receiver for continuous delta modulation.

The receiver is represented in fig. 3. It uses an identical combination of a pulsemodulator PAM and a low-pass :filter LP! as at the transmitter. Thus the re-constructed signal b' is essentially the same as the signal b in the transmitter,because both signals are derived from the same (binary) pulse pattern. Even ifa certain delay is present in the low-pass filter LP!, this will affect the pulsemodulators at the transmitting and receiving end in an identical way.

A

.~==1

t~~~I

I'1IIII

Fig. 4. The characteristic of the pulse-amplitude modulator PAM, used in figs 2 and 3.


The characteristic of the pulse modulator PAM is illustrated in fig. 4. Withthe input signal a at a very low level the low density of the pulses produces acontrol voltage c corresponding to the interval AB. In this case the pulses qgenerated at the output of this modulator have only 5% of the maximumamplitude. With signals of maximum amplitude the control voltage c corre-sponds to the interval AO, providing pulses of maximum amplitude.In delta modulation, overloading is connected with excessive values in slope

and not in amplitude of the signal. For this reason the process of rectificationshown in fig. 2 is not directly applied to the input signal a but to its derivative.The height of the quantization step is thus adapted to the mean value of theslope and not to the amplitude of the input signal. The RC network used forsmoothing the rectified output may have a cut-off frequency of 100 cis whenspeech signals are coded. Simple RC low-pass filters with similar cut-off fre-quencies are used for the filters LP1 in figs 2 and 3. Owing to these narrowbandwidths a discrepancy between the modulator characteristics of the circuitsPAM in figs2 and 3 does not produce non-linear distortion in the output signal,but results only in level fluctuations. Further it may be remarked that a feedbacknetwork with double integration mayalso be used in combination with con-tinuous delta modulation, reducing the quantization noise in the usual way.In the diagram of fig. 2 the generated pulse pattern represents two different

information signals. One is the information on the instantaneous value of thespeech signal, the other that on the height of the quantization step. The firstis obtained with a rapid-response-feedback mechanism which is essentially thesame as for normal delta modulation. The second is obtained from a combi-nation of forward control and feedback control, operating at slow speed. Infactthe same feedback circuit is used for both. mechanisms, the polarity of thedifference signal being the only quantity determining whether a "1" or a "0"pulse must be transmitted. Consequently the additional circuitry required tochange from normal to continuous delta modulation is kept to a minimum.

4. Mathematical analysis

We define x as the relative number of "1" pulses in the transmitted pulsepattern (0 ~ x ~ 1). Since the control voltage c is a function of x, the pulseamplitude q can also be expressed as a function of x, so we can generally write

q = q(x). ' (1)

Itwill be supposed that x varies from Xl to X2 when the amplitude ofthe inputsignal varies from a '= 0 to a = a.;Writing q", for the maximum pulse amplitude present with large input signals

and (J for the ratio in which these pulses are decreased for input signals of zeroamplitude, we have /

238 J. A. GREBFKES and F. de JAGER

forfor (2)

Thè d.c. component found at point b in fig. 2 is proportional to the productof the pulse amplitude q(x) and the pulse density x. By means of the feedbackaction this d.c. component is made equal to the rectified signal d, which isproportional to the input signal a. Adding a constant voltage E for obtainingthe desired characteristic we thus have the relation

a(x) = Kx q(x) - E. (3)

The constants K and E must be chosen so that they satisfy the initial con-ditions

a '0 forfor (4)

a =alll

Equations (2), (3) and (4) thus lead to a general relation between a and x,depending on the (arbitrary) control characteristic q(x):

am [X q(x) - (Jxlqrn]a(x) = - .

qm X2-{JXI(5)

We now have to specify the characteristic q(x) introduced in eq. (1). If thelinear characteristic of fig. 4 is used, q and X are connected by a linear relationin the form

q(x) = ClX + C2'From condition (2) we thus find:

q(x) = qm {(I - {J)x - (Xl - (Jx2)}.X2-XI

(6)

(7)

1.--,---,---,---,--=·q/qm

t~r-'_-+--~~~

Fig. 5. Amplitude of pulses applied in the feedback loop as a function of signal amplitude.


Equations (5) and (7) determine the relation between the pulse amplitude qand the input signal a. With Xl = 1/3, X2 = 1/2, the value of q is given infig. Sas a function of a, with different values of the parameter (J. It is seenthat, except for very small input signals, the pulse amplitude q varies nearlyproportionally with the amplitude a of the input signal. 'Let A be defined as the signal-to-noise ratio for a full-modulated signal

(x = X2). For other modulation depths we have to keep in mind that the signalamplitude Sex) is equal to a(x), and the quantization-noise amplitude N(x) isproportional to q(x), say N(x) = rq(x).From A = a(x2)/rq(x2) and S/N = a(x)/rq(x) it follows then that the signal-

to-noise ratio can generally be expressed by the relation

Sex) a(x) q(X2)-=A----"-.N(x) a(x2) q(x)

(8)

This is the "instantaneous" signal-to-noise ratio such as would be measuredwith a sine wave of constant amplitude. The decrease in signal-to-noise ratiosfdr lower levels of the input signal can now be found from eqs (5) and (7) andthe results are demonstrated in fig. 6, for various values of (J. The dashed line

odB

j-s~ ~" ~ t=::::- r--,, <,F::: --.;;;

~-r, I'---. ~()'O2,,,

"'" "0.05 ~,,, 1'-..1'-... ,

,, ().f()-""'" -. '", '" r-,,, ."" r-, "-',MiO ",,~ -,,,,

,~

,,

-15

-20

-25

-35o 5 ~ ~ 20 ~ ~ ~ ~ ~ ~ D-.-aja""dB

Fig. 6. Decrease in signal-to-noise ratio, caused by a decrease in signallevel.

represents the decrease in S/N ratio in the uncontrolled version (correspondingto (J = 1). The smaller the value of (J the longer the S/N ratio is maintainedat a nearly constant value (corresponding to the ratio A) over a large rangeof signal levels. '

5. The signal-to-noise ratio A

As regards the above-mentioned S/N ratio A, it has been shown 1) that witha pulse frequency fp, and a cut-off frequency fo of the low-pass filter used, theamplitude relation between .signal and quantization noise is given by

240------------~----------------------------------J. A. GREEFKES and F. de JAGER

S ( J. 5 )1/2-=0,026 _p_ •

N f2f03(9)

This is the SIN ratio for a signalof frequency fwhich is quantized in a systemusing double integration. The quantization noise has an almost uniform spec-trum (if the pulse frequency is not too low) and the maximum amplitude of thesignal is inversely proportional to its frequency. In this case it is assumed thatdouble integration in the feedback network starts at the frequency fo ..

However, the amplitude-frequency distribution of speech signals is found todecrease at a somewhat higher rate than 6 dB per octave, especially at thehigher end ofthe frequency spectrum. For this reason, in many practical appli-cations, double integration may start at a frequencyj., which is somewhat lowerthan the cut-off frequency fo of the low-pass filter. Then the amplitude of thequantization noise is decreased in the ratio fm/1o, because the amplitude of thedifference signal (which in fact constitutes the quantization noise) is mainlydetermined by the frequency response of the network in the feedback loop forfrequencies beyond fo and these components are all reduced in amplitude inthe ratio fm/fo.

Thus, using a similar network at the receiving end followed by a low-passfilter with cut-off frequency fo, we obtain, for frequenciesf <1,,,, the SIN ratio:

S ( f/ )1/2-=0,026 -- .N f2J,,,2/0

The attenuation characteristic ofthe network to be used in the feedback loopis shown in fig. 7. Since the band of the speech signals to be transmitted rangesfromia to fo, wherej, may be 200cis, frequencies below ia need to be integrated.

(10)

60dB

lso

JO

IT I IT 11/ ....1.-'

I-- nn- ,,:/.~y

I)/'-

lt~ ."'",

0

0 l--' ~~.1 J +

20

02510251025025_fr,c/,

Fig. 7. Attenuation characteristic of the network I in the feedback loop, with fa = 0'2, fm =1·8 and fp = 32 kc/so For pulses of 50% duty cycle we have then f1 = 8 kc/so

Double integration starts at the frequency 1,,, which may be taken at 1·8kc/s inpractical cases and this value can conveniently be combined with a cut-off fre-quency fo = 3·4 kc/so For reasons of stability arechange from double to single

241.--------------------------------------CONTINUOUS DELTA MODULATION

integration is required at a frequency f1> which is determined by the pulsefrequency fp. Itwas found experimentally 1) that the most suitable value of 11

. is given by the relation f1 = fpl2n, in accordance with a "prediction time"equal to one pulse interval. This agrees with the theoretical derivation givenby Nakamaru and Kaneko 5). In practical cases, using pulses with a 50% dutycycle, it was found tbat f1 = fpl4 is a suitable value iffpl!'" is in the range7 < fpl!'" < 30.The equation (9) for the signal-to-noise ratio in a system using double inte-

gration has been derived by assuming that the pulse frequency fp is high withrespect to the cut-off frequency fo. If this is not the case a more detailed analysisshows that the right-hand side of eq. (9) has to be multiplied by a factor k,where, approximately,

k = 0·8 + 4folfp· (ll)

The effect of tbis correction is shown by the dashed curve of fig. 8, wbichshows that the correction is oflittle importance for the higher pulse frequencies,

8sIN,dBro

6

5

0

/

0V

0/

~fJlI-\P/.;~/

0

JO

20

10

10 20 50 100 200~fp,"c/s

Fig. 8. The SIN ratio of normal delta modulation as a function of the sampling frequency,for I= 0·8,lnI = 1·8 and 10= 3·4 kc/so

but amounts to about 6 dB for a pulse frequency of 10 kc/s. In using continuousdelta modulation with these lower pulse frequencies the value A should be takenfrom the dashed curve in fig. 8. For a normalized system with f = 800 cis,fnl = 1800 cis andfo = 3400 cis, an approximate value of the SIN ratio A canbe found from the simple relation

(SIN)dB = 4310gfp - 28, (12)

with fp expressed in kc/s.As can be seen from fig. 9 the measured values of this SIN ratio are very close

to the theoretical values as given by eq. (12). For a comparison the theoreticalSIN ratio for PCM, with a sampling rate of 8 kcls and a code of n bits is also


sjN,dB

1:5

40

30

20

h1-

.1!: a-slY.0

k'11r/v~

/ 4

J

~0

na'l5 10 2 5 Ier . 2

10

-fp,kc/s

Fig. 9. Measured SIN ratios in a system of normal delta modulation with parameters as infig. 8, as a function of bit rate. Curve a corresponds to eq. (12). Curve b shows the theoreticalSIN ratio in the case of PCM, with n-blt coding and 8-kc/s sampling rate. In the latter casethe SIN ratio is expressed by the relation (SIN)dB = 0·75 Jp + 3.,

shown. The. cross-over point between normal PCM and normal delta modu-lation is found at a signal-to-noise ratio of about 50dB, corresponding to an8-bit PCM code.The signal-to-noise ratio A obtained from eq. (12) can now be introduced

into fig. 6. This gives the diagram of fig. 10, where the SIN ratio is given as afunction of the input level for the sampling frequencies fp, having values of56 kc/s, 32 kc/s, 24 kc/s and 16 kc/s respectively, with c5 as a parameter. Theexperimental verifications of these curves are shown in fig. 11.

Fig. 10. The theoretical SIN ratio of continuous delta modulation as a function of the inputlevel for different values of the sampling frequency Jp and the compression parameter o.


Fig. 11. The measured SIN ratios of continuous delta modulation for Ö = 0·02.

6. Description of the equipment

The basic circuit of fig. 2 consists essentially of three parts which will bedescribed separately. They are:(1) the pulse-forming circuit, used to convert the small difference signal B into

a sequence of well-defined identical pulses p, the presence or absence ofwhich is solely determined by the polarity of B at the moment of scanning;

(2) the pulse modulator which, together with the circuit for deriving the controlvoltage and the network in the feedback loop, converts the pulse sequence pinto an approximation signal b;

(3) the combining circuit which adds the input signal a, its rectified envelope dand the above-mentioned approximation signal b.

6.1. The pulse-forming circuit

This consists primarily of two transistors Tl and T2 (fig. 12a), which areconnected ~s in a flip-flop. However, the supply voltage is not constant here,but is switched on and off by means of the square pulse P applied periodicallywith the pulse frequency lp (a duty cycle of 50% is a convenient value for thesepulses).

Before the leading edge of each pulse both transistors are in the non-conduct-ing state. By applying the pulse P the circuit is always forced into a state whereone transistor is conducting and the other is not. The question which of thetwo transistors will become conducting depends entirely on the current enteringfrom B during the leading edge of the pulse P. Once the circuit has made a .decision it remains in this state during the rest of the pulse interval. The formof the outgoing pulse is therefore independent of any subsequent change in thecurrent B.

~----------------------~~------------------~------- ----


..

Fig. 12. Schematic diagram of a transmitter for continuous delta modulation.

It càn easily be seen that in this way a very narrow decision level must exist,which in fact corresponds to an infinite amplification at the moment of scanning.Due to this high amplification just at the moment when it is required, it ispossible to detect the polarity of very small input signals 8. In order to avoidmemoryeffects in this decision circuit, it is advisable to use it in an unloadedversion and therefore the outgoing pulses are taken off via transistor T 3' Thistransistor is thus switched on or off (without entering into saturation) duringthe whole time interval of the pulse P and it delivers the pulses p for applicationto th~ feedback loop and the pulses p' for transmission.

6.2. The pulse modulator

In the absence of a pulse p the transistor T4 in fig. 12b is cut off, in thepresence of a pulse it delivers a current pulse q, which is determined by theconstant pulse height of the pulses p and the variable control voltage c. Thelatter one is proportional to the mean number of the pulses p. Thus the currentpulses q in the collector of this transistor are modulated in amplitude accordingto the characteristic of fig. 4. They are integrated in the well-known circuit usedfor double integration and thus deliver the approximation signal b. The diode dlis introduced for compensating temperature effects in the transistor T4, thuspermitting a high compression ratio (34 dB) over a wide range of temperatures(0 to 40°C).

6.3. The combining circuit

This is shown in fig. 12c. The input signal a is differentiated in R, Cl> thenrectified in d and added to the afore-mentioned approximation signal b. Theaddition of band d is performed before the following differential amplifier T 6

and this has the advantage that the high d.c. voltages of band dare compensatedbefore addition so that transistor T 6 has to handle only a slight signalvariation.

/

CONTINUOUS DELTA MODULATION

The input signal a is applied to this differential amplifier via the high-pass filterC2R2 in order to suppress d.c. components or very low frequencies which mayoccasionally occur in the speech signal and which might interfere with the d.c.component of d and b. The difference signal e, which formed the starting pointin the description of fig. 12a, is thus obtained.

Because the circuit of fig. 12a can also be used as a pulse-sampling circuit,the receiver can be constructed from the circuits of fig. 12a and b. However,if it is desired to keep the quantization noise to a minimum for frequencies~bove the speech band, it is advisable to add a simple low-pass filter at theoutput of the receiver. The entire circuit is shown in fig. 13a, band c.

Fig. 13. Schematic diagram of a receiver for continuous delta modulation.

7. Conclusion

It has been shown that high-quality speech transmission by means of deltamodulation is possible with-favourable pulse frequencies, thereby permittingthe transmission of speech with great dynamic variations. The system has thefunction of a coder with a digitalized compander, applied per channel. In spiteof the many functions that have to be performed the number of required com-ponents is relatively small (6 transistors per transmitter, 5 per receiver). Withthe gradually decreasing price of transistors it may be more economic now tohave coding per channel rather than a coder which is used for several channelssimultaneously.With a coding per channel, multiplexing can be performed by digital circuits

without any fear of cross-talk, whereas a coder that is used simultaneouslyalways requires a concentration and distribution circuit handling analog signalsand thus has to fulfil rather severe cross-talk requirements. Further, because thesampling frequency is always high in delta modulation, the required low-passfilter can be made simpler with less phase distortion than with the 8-kc/ssampling frequency used for PCM. The latter point is of special interest in thetransmission of data signals.

245


Acknowledgement

We should like to thank Mr K. Riemens for his assistance in designing theequipment and executing the measurements.

Eindhoven, April 1967

REFERENCES1) F. de Jager, Philips Res. Repts 7, 442-466, 1952.2) H. Irio se, Y. Yasuda and J. Murakami, IRE Trans. Space Electronics Telemetry

SET-S, 204-209, 1962.3) H. Inose and Y. Yasuda, Proc. IEEE 51, 1524-1535, 1963.4) J. C. Balder and C. Kramer, IEEE Trans. Space Electronics Telemetry SET-10, 87-90,

1964.5) Y. Nakamaru and H. Kaneko, N.E.C. Res. Dev. 1, 46-54, Oct. 1960.

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