CA1147852A - Noise reduction apparatus - Google Patents

Abstract

IN THE RECEIVING OFFICE OF THE
UNITED STATES PATENT AND TRADEMARK OFFICE

INTERNATIONAL APPLICATION
UNDER THE
PATENT COOPERATION TREATY

NOISE REDUCTION APPARATUS

Abstract of the Disclosure An improved apparatus for reducing noise in a frequency-modulated data stream of the type utilizing a reference stream of predetermined frequency that has been subjected to essentially the same noise. In a preferred embodiment of the apparatus, the data stream is transformed into a first signal of value propor-tional to the frequency of the data stream, and the reference stream is transformed into a second signal that has a value proportional to the product of the reference stream frequency times a feedback value.
The feedback value is derived from a combination of the first and second signals. One of the important uses of the apparatus is in connection with frequency modulation tape recording systems.

Description

8~

IN THE RECEIVING OFFICE OF THE
UNITED STATES PATENT AND TRADEMARK OFFICE

INTERNATIONAL APPLICATION
UNDER THE
PATENT COOPERATION TREATY

NOISE REDUCTION APPARATUS

DESCRIPTION

Technical Field The present invention relates generally to noise reduction, in particular, to noise reduction in systems having a frequency-modulated data stream with undesir-able noise and a reference stream of predetermined fre-quency that has been subjected to essentially the same noise. Such systems are commonly formed in frequency modulation (FM~ tape recording systems.

Background Art Analysis of noise problems in typical prior art for tape recording systems has followed the pattern of noise analysis in communication theory generally. That is, cornmunication theory often views noise reduction as the problem of subtracting a noise component from a stream that is the sum of a signal component and a noise component. See, for example, Y.W. Lee, Statis-tical Theory of Communication (John Wiley & Sons, Inc., N.Y. 1960), p. 396.

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Prior art FM tape recording systems commonly have provided two adjacent channels, one channel for recor-ding and playback of the FM data stream and the other channel for recording and playback of a reference stream. To a great extent both channels are subjected to the same noise, of which tape flutter is usually the major component. If no noise were present in either channel, the data stream would be a pure fre-quency-modulated carrier wave and the reference stream would be a carrier wave itself. The presence of similar noise on both the data and reference streams led to the prior art approach of separately demodula-ting each stream and subtracting the demodulated reference stream from the demodulated data stream.
Thus the prior art technique is to subtract any demo- i dulated noise of the reference stream from the demodu-lated data-plus-noise of the data stream. This tech-nique has caused a substantial improvement over perfor-mance of FM tape recording systems that lack a reference channel. Nevertheless, prior art FM tape recording systems utilizing a reference channel do not remove all of the flutter-induced noise that is common to both the data and reference channels. The flutter-induced noise that remains in such systems can be troublesome in many instances. Further reduction in flutter-reduced noise generally can be accomplished only with expensive tape transport mechanisms or other expensive or complicated approaches.

Disclosure of Invention It is an object of the present invention to provide an improved apparatus for reducing noise in FM tape-recording systems. r It is also an object of the present invention to provide an apparatus for improving dramatically the per-formance of FM tape-recording systems for a yiven cost.

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It is a further object of the present invention to provide an improved apparatus, for reducing noise in an FM data stream, of the type utilizing a reference stream having a predetermined frequency which has been subjec-ted to essentially the same noise.
It is a further object of the present invention to provide an improved apparatus for reducing flutter-induced noise in FM tape-recording systems.
It is a further object of t:he present inver~ion to provide a relatively lcw-cost instrumentation FM tape-recording system.
These and other objects of the invention are achie-ved by providing an improved apparatus, for reducing noise in an FM data stream, of the type utilizing a re-ference stream having a predetermined frequency which has been subjected to essentially the same noise, wherein the improvement includes a data stream frequency-discri-minator to transform the data stream into a first signal of value proportional to the data stream frequency; a reference stream frequency-discriminator to form a second signal of value proportional to the product of the refe-rence stream frequency times a feedback value; a combiner to combine the first and second signals to generate an output value proportional to the feedback value; and a feedback loop to return the feedback value to the refe-rence stream frequency-discriminator. Some embodiments of the invention utilize ratiometric techniques to per-form some of the functions of the preceding embodiment without using a feedback loop. Other embodiments of the invention use a feedback technique such as that just de-scribed to produce a signal which varies as the ratio of the frequency of a first, data stream to a second, refe-rence stream.
Brief Description of the Drawings r These and other objects and features of the inven- ~

~47852 tion will be more readily understood by consideration of the following detailed description taken with the accompan-ying drawings, in which: -FIG. l is a simplified block diagram of a noise-reduction system embodying the principles of the present invention;
FIG. 2 is a mathematical analysis o~ a model of the system shown in FIG. 1, FIG. 3 is a diagrammatic representation of an FM
discrimination section in an embodiment of the present invention;
FIG. 4 is a diagrammatic representation of a data channel discriminator used in an embodiment of the present invention;
FIG. 5 is a diagrammatic representation of a refer- ~r ence channel discriminator used in an embodiment of the present invention;
FIG. 6 is a detailed block diagram of a noise-reduction system embodying the principles of the present invention;
FIG. 7 is a mathematical analysis of a model of the ~ystem of ~'IG. 6;
FIG. 8 is a portion of a schematic diagram of a preferréd embodiment of the noise-reduction system of the present invention, the diagram being connected to FIG. 9 at leads 37 and 38, FIG. 9 is the remainder of the schematic diagram of FIG. 8;
. FIG. 10 is a view of an oscilloscope screen showing the operation of the present invention on a full-scale saw-tooth signal, recorded on an inexpensive tape trans-port;
FIG. 11 i~ a view of an oscilloscope face showing the effect of the present invention on a one percent of r full-scale, saw-tooth signal, recorded on an inexpensive tape transport; and FIG. 12 is a view of an oscilloscope face showing ~478~2 the effect of the present invention on the same one per-cent of full-scale, saw-tooth signal played back with gross amounts of artificially induced flutter noise.

Description of Specific Embodiments Data transmission or recording using a frequency-modulated carrier is accomplished by deviating the carrier frequency in response to the amplitude of a data signal, and by transmitting or recording this modulated carrier frequency. In a typical FM system, the magnitude and polarity of the data signal determine, respectively, the amount and direction of the frequency r~

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~147852 deviation of the carrier. -A "dc" (n~n-time~
Yarying) si~al, depending on its polarity, either increases or decreaSes the carrier frequency, while an - "ac" (time varying) signal alternately increases and decreases the carrier ab~ve and below its "center", or unmodulated, frequency at a rate equal to that of the data frequency. In the typical (nlinearn) FM system, where fc= the unmodulated carrier frequency, and fD= the carrier frequency modulated by the data, the amplitude of the data signal is expressed by the relative frequency deviation of the carrier. The instantaneous value of the data, AD, is given by ( ) AD K(fD fc) ~ K = a constant fc where the ratio K/fC is the scaling factor for the channel, i.e., in a system where K/fC = ~0.01 Volt/Hz, a positive 100 ~z deviation of the carrier would be equivalent to a data signal of +l volt.
(+0.01 V/Hz x ~fc + 100 ~ fc) Hz = ~1.0 Volt) Because the data information is imparted to the carrier by deviating the carrier frequency, the demodu-lation (data recovery) process must determine, from whatever deviations are present in the carrier, theoriginal form of the data signal. Any external factors which are capable of altering the transmitted and/or received frequencies, hence, will be demodulated and exist as undesirable, erroneous "noise" components in the demodulated data signal. If these noise-inducing factors are not precisely known, then the exact value of the original data signal can never be determined.
For this reason, many FM systems employ a reference frequency, a known frequency which is transmitted or recorded simultaneouslY with the data-modulated carrier frequency. It may be assumed that whatever system perturbations have caused variations in 7~S2 this reference frequency from its known value will also have caused instantaneous related variations in the data-carrier frequency. By accurately knowing how the reference frequency has been affected, one can theore-tically, with sufficient knowledge of how these known influences on the reference signal would have affected the data-~odulated carrier, in effect go "backwards"
and reconstruct the true value of the original data signal. Let fR = the transmitted reference frequency fD = the transmitted carrier freguency modula-ted by the data signal fR = the received reference frequency (system perturbations have changed fR so that f~
no longer equals fR) f~ = the received data-modulated carrier frequency (the sa~e perturbations have also changed fn, ln the transmission process so tha~ f~D ~ fD) Let (2) ER = f~ ~ fR the known transmission , error experienced by the fR and let (3) ED = fD ~ fD the (unknown) transmission ~ error experienced by the fD data channel With sufficient knowledge of the overall system, one can define a term S which expresses the instan-taneous relationship between the transmission error in the data channel, ED, to the error in the reference channel, ER, i.e., let (4) S = ED/ER
If one knows both S and ER, ED can now be found by (5) ED = S x ER
Replacing the now known value for ED into equation (3) results in (6) fD = fD the frequency of the data = carrier with the 1 + ED transmission error removed.
The true frequency deviation and, hence, the true value of the original data signal can now be found by demodulating fD
The overall expression for the amplitude of the data, AD, as a function of the received data and I
I

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- ~147~52 - reference frequencies and the system function S can be found by combining the expressions for S and ER with equation (1) or (7) AD = K - _ 1 + S(f~ - fR J fc - ` fc In any real F~ data-transmission system, it is - never possible to determine exactly the value of the original data signal. Digital systems are limited in accuracy by non-infinite word lenyth which results in quantizing error, the uncertainty resulting from the finite size of the smallest incremental change which the system can express. Analog systems are limited by residual noise which generates output signals even when no input signal is present. Because the presence of noise limits the accuracy of an information system, it has become common practice to express the accuracy of a system as a ratio of the maximum amolitude of a transmitted siqnal to the amPlitude of the svstem noise.
The signal to noise ratio, or S/N, is usually expressed in decibels, or db.
S/N ~db) = 20 log10 Amplitude of max signal Amplitude of noise Thus a S/N of 40 db would indicate a 100:1 ratio, or a system uncertainty of one percent of the value of a maximum amplitude signal. When the noise is not uniform, but varies with the amplitude of the recorded signal, then a S/N figure would include this "gain" noise or "percent of signal amplitude" noise as a separate, spe-cified term. Because of the often complex waveforms associated with noise signals, care must be taken in interpreting S/N figures regarding the units of noise measurement, bandwidths involved, and other related variables.
The frequency modulation technique is usually selected for its ability to transmit "dc" information, and for such a system's relative insensitivity to ampli-~4~352 g tude variations in the transmitted and received carrier waveforms. But because the information is contained in - the frequency rather than the amplitude of the modulated carrier, an FM system is extremely sensitive to unwanted frequency variations. In a magnetic tape recording/
playback system, flutter (unwanted variations in tape speed) is unavoidable, both during recording and playback. These velocity variations in the tape speed frequency modulate the already modulated carrier. The effect of flutter on the FM carrier is instantaneous - multiplication of the recorded frequency by the instan-taneous value of the cumulative record/playback tape velocity, which equals (1 + F) where F is the cumulative instantaneous record/playback flutter, or velocity error.
Thus F becomes a mathematical factor common to all signals simultaneously exposed to the speed variation. A
+1 percent flutter (i.e., F = +0.01) would cause a 3 KHz carrier to appear as 3030 Hz, a 5 KHz carrier as 5050 Hz, etc. [Errors such as these in the time-base (absolute frequency) accuracy of the data can be eliminated only through use of a buffer system, where data is input at a rate modulated by the system flutter, but output at a corrected rate determined by the original sampling rate or some other reference rate. Fortunately, these flutter-generated time-base errors are usually insignifi-cant compared to the corresponding flutter-generated amDlitude errors in an FM recording system (as evident in FIGS. 10, 11, 12). All references to nnoise" will refer, as is customary, to amplitude error rather than to time-base error, unless otherwise indicated.]
If one lets F = the cumulative (for both recording and playback) instantaneous flutter, or speed error, in the velocity of the ~agnetic tape, f = the frequency of the unmodulated data c carrler, m = the amount of modulation of the carrier due to the data signal, i.e., m - +.5 for +50 percent modulatlon , ; '''^~
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~ then in a typical (~linear") Fr~ system (8) fD = f (1 + m) = the frequency of the re-c corded, data-modulated carrler, and 5(9) fD = f (l + m~ (1 + F) = the instantaneous c frequency of the same signal, fc ~l + m), upon playbac~, with - an lnstantaneou~
cumulatlve flut-ter of value F.
-If the reference carrier, wnich by definition has a known modulation (usually zero), has been recorded simultaneously with the data carrier, then if fR = the frequency of the recorded reference carrier, then (lO) f' = f (1 + F) = the instantaneous fre-R R ~uençy of the reference carrler, fR, upon play-back, with an instanta-neous cumulatlve flutter equal to F.
Equation (9) demonstrates the non-uniform effect of the flutter, in that the frequency error caused by the flutter is multiplied by (1 + m), or by the data modula-tion itself. Thus a one percent flutter will cause a one percent change in the carrier only when m = O, or when no data is present. In a s~stem where the modulation is symmetrical about the carrier frequency, the absolute value of m must be less than one to prevent the carrier frequency from going to zero at m = -l, so that the effect of the flutter is nearly doubled as m approaches +1, and approaches O as m approaches -1.
In the most widely used method for reducing flutter nolse in FM recordings a reference carrier with no modu-lation is recorded simultaneously with the data-modulated carrier, either on the same channel (or track), or on a separate channel. Each channel is demodulated via a limiter ~to lessen the effects of amplitude modulation), an FM discriminator such as a phase-locked loop, or the more common constant-energy pulse generator (a mono-stable multivibrator), and a low-pass filter. The output of the reference channel is then subtracted from the out-.

~1~7852 put of the data channel. As previously stated, in a typical FM system the output signal or voltage is linearly proportional to the deviation of the carrier, Vout = K ~ ~

Substituting the expression for the played-back fre-quency of the data channel (equa~ion 9) for fD in the above equation, and letting K = 1 for the sake of simpli-city, yields tll) VOUt [Data Channel] = fc(l + m)(l + F) ~ fc = (1 + m)(l + F~ - 1 = 1 + m + F + mF - 1 = m + F (1 + m) Substituting in like manner the expression for the reference channel playback frequency (equation 10) results in (12) VOut[Ref. Channel~ fR(l R
fR
= 1 + F - 1 = F
Subtracting the output of the reference channel from that of the data channel indicates that (13) V [Data Channel -out Ref. Channel] = (m I F + mF) - (F) = m[data] + mF[noise]
or that the output signal consists of the desired data term, m, and a data-modulated flutter-generated term, mF.
It is lmmediately apparent that thls flutter correc-tion method is far from perfect, in that a noise term is present except when m = 0, i.e., the effect of the flutter is only removed when there is no data beinq recorded.
Equation 11 shows that without a reference channel, the ratio of noise to maximum signal output for the data channel would be (14) N/Smax[Data Channel] = F(l + m) Because practical considerations limit the allowable modulation to less than 100 percent (i.e., mm~X must be .. ..
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7~352 - less than 1), equation 14 expresses the "flutter multiplication" effect on S/N, in that a certain percen-tage of flutter will result in a qreater percentage of noise relative to the maximum possible signal.
For a modulation equivalent to +Full Scale of +50 percent, the corresponding N/Smax figures would be m N/SmaX
- nPositive Full Scalen +.5 F(1.5/.5) = 3F
"Baseline" O F(1/.5) = 2F
nNegative Full Scalen -.5 F(.5/.5) = lF
i.e., the effect of the flutter is doubled at m = O, tripled at +Full Scale, and in a one-to-one ratio at -Full Scale.
Because subtracting the output of the reference channel results in an output expressed by m + mF, the noise to signal ratio is improved, and expressed by (15) N/Smax[Data Channel - Ref. Channel] = mF/mmax The corresponding N/S figures for the same +50 per-cent modulation are m N/S
- max +.5 F
O O
-.5 -F
It is apparent that this technique for flutter com-pensation is only effective for small amplit~de signals (m near 0), and that the effect of the flutter is still 100 percent for signals of maximum amplitude.
The preceeding calculations express, of course, theoretical performance. In a real system using this technique there will always be some flutter noise present even when no siqnal is present (m = O), primarily because of slight variations in the gain and phase responses of the two low-pass filters necessary for the demodulation of the two channels.
It follows from my preceeding expressions for the frequency outputs of the data and reference channels that ~4173852 ..
to perform perfect compensation (i.e., remove all flutter--generated noise for anY modulation value), a theoretically perfect demodulator would have to perform division of the data channel playback frequency by the reference channel playback frequency, i.e., (15) f [Data channel] = fc(l ~ m) (1 + F) f [Ref. channel~ fR(l + F) = l + m when fc = fR
which results in a constant (l) and the desired data signal (m). Subtracting the constant leaves only the data signal with all am~litude noise caused by the flutter completelY eliminated.
One possible system to accomplish this involves an analog divider circuit. ~owever, highly accurate and stable division is a relatively difficult function to perform with analog circuitry. Devices which are currently available to perform such functions are not only expensive, but fall short of the ideal device in their operation, being prone to such phenomena as tem-perature instability, "dc" drift, non-linearity, limited irequency response, and Lnternelly generated noise.

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. ' Another possible system attempts flutter removal utilizing computer-based digital techniques. The system measures the frequencies of the reference and data chan-nels and stores this information in the computer, where the mathematical process of division is performed upon the frequencies, resulting in the "true" value for fD which can then be mathematically demodulated to yield the information transmitted. Besides requiring a com-puter and associated peripheral equipment, the overall result falls short of the theoretical values, due pri-marily to the fact that:
a. the measurement of frequency requires sampling over a time interval. The more accurate the desired measurement, the longer must be the time over which the sample is taken. Because the frequencies are usually changing during the sampling period, the figures which are later operated upon may not be of sufficient accuracy, and b. overall accuracy is limited by the finite word length used in the calculations.
Another possibility is a system where the input data signal is digitalized via an analog-to-digital converter, the resulting samples being recorded in digital form.

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1~7b~52 The playback process then consists of passing each sample through a digital-to-analog converter to reconstruct the original data signal. The only effect of flutter in such a system is inaccuracy in the time base in the reproduced data, i.e., no amplitude noise is added to the output signal by the flutter. The system is limited in accuracy only by the number of bits used in the digitizing pro-cess. The sampling rate must be at least twice the fre-quency of the highest data frequency, and requires a fairly sophisticated digital recorder, as well as the required analog-to-digital and digital-to-analog conver-ters. Such a system would be inherently quite expensive and would very likely require higher bandwidth capabili-ties in the recording process than would a comparable FM
system. Although such a system would be many times more expensive than a similar FM system, its improved perfor-mance over currently existing FM systems would justify the expense in many situations requiring a low-noise, high-performance recorder.
As previously stated, the effect of flutter (unwanted variations in tape speed) on a recorded frequency is instantaneous multiplication of the recorded frequency by the instantaneous value of the cumulative record-playback tape velocity, which equals (1 + F) where F is the cumu-lative instantaneous record-playback flutter, or accumu-lated velocity error, and exists as a mathematical factor common to every signal which is simultaneously exposed to the noise generating operation.
Where f = the frequency of the unmodulated data ' carrier, and m = f - f = the amount of modulation imparted c to the data carrier frequencY bY
fc the data siqnal (i.e., m = +~
for +50 percent modulation) then in a typical FM information transmission system f = f (l ~ m) = the frequency of the recorded, D c data-modulated carrier fre-quency ~ If one lets F = the cumulative instantaneous flutter, or speed error, in the velocity of the magnetic tape then 1 + F = the effective playback velocity of the magnetic tape - and, therefore, f' = f (1 + m)(l + F ) = the instantaneous fre-D c D quencv of the recorded signal, f (1 + m), upon c playback, with an lns~antaneous cumula-tive data channel flutter equal to FD.
In similar fashion, where fR = the frequency of the unmodulated recorded reference carrler then f' = f (1 + F ) = the instantaneous frequency of R R R the reference carrier, fR, upon playback, with an instan-taneous cumulative reference channel flutter equal to FR.
Due to the fact that the data-modulated carrier and the reference carrier are simultaneously recorded onto (and played back from) the same magnetic tape, tape speed variations during the record or playback process are essentially identical for each channel at any instant in time. Although such factors as dynamic skewing and non-uniform dynamic stretching of the tape can result in slightly different instantaneous flutter values between two different tracks on the tape, these mechanical effects are relatively minute and the analysis will make the excellent assumption that the F values in the expressions for the playback frequencies are the same, i.e., that FD = FR = F.
Because the effect of flutter is "common-mode multiplication" of the two frequencies (i.e., each fre-quency by the same amount), the circuitry of the inven-tion reiects as data any frequency modulation which has a common multiplier between the data and reference chan-nels, since such frequency modulation could only have 1~47852 been the result of flutter. This ~ocess is performed by multiplying the reference channel playback signal by (1 ~ m) utilizing a feedback configuration, and by subtracting the resulting value from the data channel S signal. Mathematically, the simplified expression for the overall operation performed is (23) f (1 + m) (1 + F) ~ fc ~ rfR(l + F) fRl( rc L R
where the m in the (1 + m) term is provided by feeding bac~ the output to the reference channel discriminator, where the necessary multiplication by (1 + m) is performed.
FIG. 1 is a simplified block diagram of an embodi-ment of the invention, which shows the basic signal flow and, more importantly, FIG. 2 shows the analogous mathe-matical model which demonstrates the feedback technique whereby the output signal is used to generate itself.
As will be shown below, there are no low-pass filters between the FM discriminators and the summation circuit.
The summation of the data channel signal with the inverted flutter channel is, therefore, performed essen-tially instantaneouslY as the freauencies come off the tape, by summing the voltage pulses representing the values of each channel without either signal having to first pass through a low-pass filter. This predemod~la-tion pulse summation eliminates the gain, phase, offset, temperature coefficient, and transient-response differen-ces inherent between two low-pass filters, and renders the flutter noise cancellation virtually perfect. The invention in fact eliminates complete demodulation of the reference channel, in that no low-pass filter is required for the reference channel but only a single pulse-generating discriminator which can supply any number of data channels, with the proper reference channel signal.
The overall system characteristic is one of translating the accuracy of the flutter removal from the flutter fre-quency domain to the data frequency domain; i.e., with 1~47852 - this system the removal of the flutter noise is essen-tially independent of the flutter frequency.
A figurative representation of the FM discrimination section of an embodiment of the present invention is shown in FIG. 3 (in general), FIG. 4 ~specifically for data channel) and FIG. 5 (specifically for reference channel). The data channel uses the simple but very accurate constant-energy-pulse generator (known as a - monostable multivi~rator) as the FM discriminator. This device produces a rectangular pulse of constant amplitude (V) and constant width (r) for every cycle of the input frequency signal. The average or "DC" value of such a series of pulses is given by (see FIG. 3) ( ) average ~ f(t) dt = Vr 3 Vrfin where f(t) = V for t = O to r, and 0 for t = r to T, and where T = l/input frequency. Usually r is set such that when the input frequency eauals fc (i.e., no modulation is present), r = .5T and the waveform has a 50 percent t Vaverage = U5T = V Variations in the input frequency change T and, therefore, the average value. As the frequency approaches 0, the pulses become so widely spaced that Vaverage approaches 0, and as the frequency approaches 2 fc the spacing decreases and Vaverage approaches V. Thus the relative change in VaVera9e is directly proportional the frequency deviation of the input signal from fc. The overall effect of a changing input frequency on the average value is that the average value is equal to the mid peak-to-peak voltage plus half the peak-to-peak amplitude times the ratio of the frequency deviation to the center fre-quency or, (25) Vaverage Vl + V2 + V~ V2~ ¦~;A tc~

when r = .5T for fin = fc This is because the integral in the expression for ' '~

' 1~785Z

~ne average value (Equation 24) is equal to the area under the wave-form from 0 to T, and may be easily deter-mined as equal to the sum of the shaded areas I and II
indicated in FIG. 3. Since the area of I equals (Vl -V2)r and that of II equals V2T, then ( ) average T ~ flt, dt = 1 [area I + area II]

= 1 [V2T + (Vl - V2)r] = V2 + (Vl - V2)r This may also be expressed as (27) V = V2 + (Vl ~ V2)r T
Tc T
Because we know from the defined terms that c / c fin T l/fin fc equation 27 may be expressed as ( ) Vaverage = V2 + (Vl - V2)r fi T f c c This may be correctly rewritten as (29) V = V2 + (Vl ~ V2)r fin -1 + (Vl - V2)r 'l'C ~ - 'l'c Combining and simplifying terms, ~then ( ) average ' V2 ~ V2r + Vlr +rr (Vl - V2~¦ fi ~ f ~ ~ L~ ~ fc If we set r equal to 5Tc in equation 30, the expression further simplifies to that indicated in FIG.
3, namely (31) Vaverage = V2 ~ V22 + 2l + Vk - V2] [~n ~ e.]

= Vl + V2 +[Vl - V2~ o]
For the data channel, V2 = 0 and fin equals fc(l +
m) (1 + F) when flutter is present, so that (32) VD = Vaverage = V + _ ~c(l + m)(l + F) - f [Data Channel] c = V[l + (1 + m)(l + F) - 1]
= V(l + m)(l + F~

1~7852 Thus, the amplitude of the pulses is multiplied by the factor which causes spacing deviations in the output pulses (i.e., the input frequency); thus it might prove feasible to perform effective multiplication of a fre-quency by using the amPlitude of the pulse train as oneof the terms to be multiplied. This is precisely how the FM discriminator in the reference channel performs the multiplication indicated in the system block diagram. In the reference discriminator, Vl is the feedback voltage from the output before the offset voltage is removed, namely z(l + m), and V2 is this same voltage inverted, or V2 = ~ V(l + m). The r-width pulses are inverted to change the sign of the output signal so that the addition performed is in reality subtraction.
In like manner, therefore, R average = ~ (V/2)(l + m) - (V/2)~1 ~ m) [Ref. channel] [(V/21(l + m) 1(-V/2)(1 + m) rfR(l + F) L fR J~
- 0 - (V/2) (1 + m) (1 + F ' 1) = -(V/2)~1 + m) F
which is a signal proportional to the tape flutter multiplied by the data modulation.
FIG. 6 is a detailed block diagram of a preferred embodiment of the invention and FIG. 7 is the mathemati-cal eqùivalent of the operations performed by the cir-cuitry. The data and reference fre~uencies are dividedby 2, recorded, and then doubled upon playback to both conserve tape bandwidth an gain an octave of frequency separation for simpler output filtering. The resistive adder 44 attenuates the signals by a factor of 2 and is, therefore, followed by a gain-of-2 amplifier 30, which is adjustable over a small range and is used to set the flutter noise precisely to zero. The ndc~ offset of ' .

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-21-_ amplitude V/2 is not removed until the output stage because it is circulated through the feedback network to provide the proper switching bias voltage level for the bipolar reference channel switch 46. The entire demodu-lation system uses only a single positive voltagereference denoted at +V (+V equals +5 vdc in the actual circuitry) to generate a bipolar output of +2.5 volts for +50 percent modulation. Changes which might occur in the +5 v reference have no effect on the output offset voltage and no effect on the accuracy of the flutter-noise removal. The only effect is on the gain since the output signal is Vm.
A schematic diagram of a preferred embodiment of the invention is shown in FIGS. 8 and 9. Each heavy square or triangle represents a tiny integrated circuit. In the diagram, all of the triangular operational amplifiers have +12 volts connected to their number 7 pin and -12 volts connected to their number 4 pin. Q4, Q5, Q6 and Q7 represent 50 ohm "N" channel field-effect transistors.
All resistors are one percent, 1/8 watt, m~tal film unless specified. Zl and Z2 represent Fairchild yA709C
operational amplifiers, Z3 is a National Semiconductor Corp. LM339 Quad Comparator, Z4 is a SN74L86 Quad Exclusive-Or Gate, and Z5 and Z6 are Signetics 555T
Timer8. Z7 and Z8 are RCA 4007 cos/mos "Dual Complementry Pair Plus Invertern, and Z9, Z10, Zll, Z12 and Z13 are LM307 Type operational amplifiers. 20T and S.T. mean "20 turns" and "single turn" respctively, and , w.w. means wire-wound. The frequency signals for each channel are recovered from the moving magnetic tape 20 by the data channel playback head 34 and reference channel playback head 35 (both physically in the same "playback head~) at the millivolt level and are boosted by a gain of approximately 2000 in the playback amplifiers 21 and 22 over a 3 db bandwidth of from 900 Hz to 5000 Hz. The center fre~uency fc of the data channel was arbitrarily chosen at 3000 Hz, with a maximum data-modulated ,, .
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~j ., ~78S2 deviation of +1500 Hz (+50 percent). The recorded reference frequency can also be 3000 Hz, or it may be varied from this value since it isn't modulated. The sinewave outputs of the playback amplifiers are fed into S Z3, an "LM339 Quad Comparatorn, a device which contains four high-gain open-loop amplifiers which serve as zero-crossing detectors 23 (two are left over and can be uti-lized for two more data channels). Each of the two square-wave outputs from Z3 (one at the data frequency, one at the reference frequency) drives the frequency doubler and pulse generator 24 including Z4, a Transistor-Transistor-Logic (T2L) "Quad Exclusive-Or"
circuit, each input driving a gate with a resistor-capacitor network on the input which causes each gate to output a single positive pulse for each transition of the square-wave input. This doubles the frequency of each channel, with the pulses approximately 5 micro-seconds wide. These narrow pulses are inverted by the remaining

2 gates in Z4 to provide the proper negative-pulse input , 20 trigger signals for the monostable multivibrators 25 and i 26, Z5 and Z6. These are Signetics Model NE555 Timers which produce a single-positive output pulse (of adjustable width) for each trigger pulse. ~ach output is then level-shifted and inverted through a high-speed 25 transistor switch 27 and 28 tQl and Q2) to provide the optimum input signal for Z7 and Z8, each of which is an ~CA CMOS "Dual Complementary Pair plus ~nverter~. These devices are normally used for digital logic applications, but they are utilized in this invention to ' 30 1. provide the optimum voltages to drive the gates of the field-effect-transistors tF.E.T. 'S) in the pulse-summation circuit, and 2. to provide the inversion required so that only a single F.E.T. in a pair is on at any one time-i.e., to drive them out of phase with each other.
Z7 drives the gate of Q3 between -12 vdc (Q3 "off~) ,"

~147852 and +5 vdc (Q3 "on") and the gate of Q4 between zero volts (Q4 ~onn) and -12 vdc (Q4 "offn). Z8 drives the ~ gates of Q5 between the feedback voltage (V/2) (1 + m) (Q5 "onn) and -12 vdc (Q5 "offn), and the gate of Q6 be-tween (-V/2)(1 + m) (Q6 "onn) and -12 vdc (Q6 ~off~).
The net result of this switching is that VD is an extremely accurate square wave driven between +5 vdc (Q3 on, Q4 off) and zero volts (Q3 off, Q4 on), with rise and fall times on the order of 100 nanoseconds, and with a pulsewidth determined by the data channel monostable multivibrator 2~. As demonstrated previously, the "dc"
value of VD is (V/2)(1 + m)(l + F). The reference output voltage VR is also an extremely accurate rectangular pulse which is switched between (V/2)(1 + m) when Q5 is on and Q6 is off, and (-V/2)(1 + m) when Q5 is off and Q6 is on. The average value of VR has been shown to equal (-V/2)(1 + m) F. This minus sign is created in Z8 by reversing the driver arrangement of Z7 so that the pulses are negative instead of positive. Thus the summation circuit 44 can perform subtraction by adding the two signals.
One reason for the simplicity and extreme accuracy of this invention is the capability to eliminate the two low-pass filters which would normally be used to demodulate these data and reference channel pulses prior to their addition.
Because the process of low-pass filtering is mathemati-cally a linear process, theoreticallY there should be no difference between 1. filtering two signals and then adding them to form the sum, or 2. adding two signals and then filtering the sum.
If one denotes the filtering process by X, then the equivalent mathematical statement would simply be KA + KB = K(A + B) The summation expressed by the KA + KB term need not be highly linear outside of the bandwidth represented by the ~; , .

~:~L47852 filtering process K. However, to accurately perform the ~(A + B) summation requires that the process be extremely linear essentially over the frequency spectrum of the signals to be added. Any non-linearity will generate intermodulation distortion products which will appear as unwanted noise signals at the sum and difference frequen-cies of the added signals, if the sum and difference fre-quencies fall within the bandwidth of the filter.
Because A and B are in reality ultra-accurate, fast rise-and-fall time pulse waveforms containing harmonics from the fundamental frequency of a few thousand ~ertz up into the megahertz region, the summation of these signals must be of exceptional linearity over a comparable bandwidth.
Any attempt to perform this summation with active cir-lS cuitry (such as with operational amplifiers) prior to anyfiltering of the waveforms would fail dismally due to the gross non-linearities encountered at increasing frequen-cies. For this reason the actual summation is performed by two simple resistors, which are inherently highly linear over an extremely wide bandwidth.
The effective source impedance of such "switch" with respect to the summing node (denoted as 50) is 15 k ohms (+l percent) plus the resistance of the particular field-effect-transistor which is conducting at the time.
Field-effect transistors of maximum-on-resistance equal to 50 ohms were chosen because variations in their on-resistances would be small compared to 15 k ohms. The actual resistances of the transistors is relatively unim-portant. The only requirement for a high degree of linearity is that the transistors driving the summing junction be 1. matched on a "side" ~i.e., Q3 to Q4, QS to Q6), or 2. symetrically mismatched.
The linearity of the summation network can be observed by supplying to the frequency inputs a data and reference frequency separated in frequency by a number of ~ ,., ,.-~j7852 Hertz less than the bandwidth of the output filter sothat whatever intermodulation noise is generated at the difference fre~uency may be observed at the output with a high-gain oscilloscope. For example, a 3000 Hz and a 3010 ~z signal will cause residual circuit non-linearities to generate a 10 Hz intermodulation noise signal of very small amplitude, typically about -66 db peak-to-peak (all "db" figures mentioned are with respect to a maximum peak-to-peak output signal for + 50 percent modulation). Although this figure is exceedingly small - (1 part in 2000) it was desired to obtain a residual-system-noise figure well below this level. For this reason, R47 and potentiometer R48 were added. R48 is adjusted for minimum intermodulation noise at the output, in effect creating a symmetrical mismatch of the driving impedances. This simple adjustment reduces the intermodulation-distortion products generated by residual non-linearities in the summation circuitry to the insignificant level of -80 db, or 1 part in 10,000. This adjustment would be unnecessary in all but the most cri-tical of applications.
The feedback filter 29 is a 4 pole filter; a 3-pole Chebyshev active filter ~Z9) followed by a single pole, R35 and C20. (The single pole permits simple, predic-table modiication8 of the filter response, if desired, by merely changing R35.) The primary purpose of this fllter is to attenuate the frequencies generated at the summing node. Any residual data carrier or reference carrier frequencies at the output are circulated in the feedback network as noise on the two switchi,ng voltages [(+V/2)(1 + m)l used by the reference channel, and will be demodulated by the sampling action of the reference bipolar switch formed of transistors QS and Q6. The net effect is similar to that produced by non-linearities in the summing circuitry in that a small residual difference-frequency signal will exist on the output signal. The amplitude of this noise signal is approxima-, ~1478S2 - tely equal to the amount o~ attenuation provided by the feedback filter to the data and reference channel fre-quencies. This filter, therefore, exhibits better than 70 db of attenuation at 6 k~z to maintain the residual 5 system noise at an insignificant level. It is, of course, possible to filter one or both of the signals to be added before the adder network. However, to do so would be unwise from an economic standpoint, since each signal would require a separate filter, whereas both signals benefit from the action of the feedback filter.
The effect of phase shift (time delay) in the feed-back filter is to generate a small instantaneous ampli-tude error in the switching voltages of the reference bipolar switch. The overall effect is the generation of a small qain error in the data output which is a function of the data frequency and the cumulative record-playback flutter. Even with a feedback filter 29 bandwidth as low as the output filter 32 bandwidth (typically 100 Hz), this effect is small in that it requires a 30 percent flutter to generate a few percent peak-to-peak gain error in the amplitude of a +full scale 100 Hz signal. This effect can be made insignificant by increasing the band-width of the feedback filter and thereby decreasing its phase shift for any particular frequency, retaining of course, the necessary attenuation required for the data and reference carriers. For this reason, the feedback filter shown has a wider bandwidth than the output filter, with appreciable attenuation starting for fre-quencies approaching lRHz. The Chebyshev section pro-vides a small peak in the filter response to improve thephase-shift characteristic. This reduced phase-shift ~- (compared to the output filter phase-shift) reduces the gain error in a +full scale 100 Hz data signal to well below 1 percent for a flutter of 30 percent, which ls approximately 30 times the flutter that would be expected in normal situations. (Phase correction circuitry could be incorporated here but its use would be unwarranted in i all but the most critical applications.) ,, .~
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~7852 The low-pass output filter 32 indicated on the sche-matic is also a 3-pole Chebyshev filter due to the more effective filtering provided over a standard 3 pole Butterworth filter, at the expense of absolute flatness in the frequency response characteristic. The actual number of poles, filter flatness, type, and bandwidth is dependent on the requirements of the application. In this circuit a filter bandwidth of from 0 to 100 Hz with an accuracy of f.l db was typical. It must be remembered that non-linearities in the filter response will, of course, demodulate flutter-modulated input signals, resulting in amplitude modulation of the output. This is a consideration when determining output filter requirements and overall system gain accuracy.
Z13, the offset subtractor, and X2 data amplifier 33, is an operational amplifier configured for a positive gain of 2 with respect to the data signal, and a negative gain of one with respect to the voltage reference V.
This circuit subtracts the "dc" offset of V/2 from the data signal and multiplies the data by two so that the final output signal is Vm. An adjustment is provided so that the ~dc" offset of the output may be precisely set to 0.000 Yolts. This circuit could be followed by a variable-gain stage to vary the output amplitude, if such a feature is desired.
One technique to initially set up the noise-reducing circuitry for proper operation is as follows:
1. Ground the signal input to the recorder and adjust the center frequency of the data oscillator and the reference oscillator for the desired frequencies.
2. Switch the ci~cuitry to a "Monitor" mode which connects the recording frequencies to the inputs of the demodulation circuitry, and switch on the flutter noise reduction system.

3. Using R18, adjust the pulse width of the data monostable multivibrator so that the Vd test point equals 2.500 volts as measured with a Digital : ,. ~,r~

,, ~147852 - voltmeter. (It is assumed that the +v voltage - reference equals +5 volts).

4. Similarly adjust R25 so that the voltage at the VR test point measures 0.000 volts. ~There adjustments insure that the pulse generators have about a 50 percent duty cycle at the center frequencies.)

5. Record 20 seconds of tape leaving the input to the data channel grounded--this is a "baseline~
signal which should generate a 0.000 volt out-put.

6. Playback this signal while monitoring the voltage at the output of the feedback filter which will be approximately 2.5 V (2.500 V ~ a few millivolts).

7. Introduce gross amounts of flutter (by either ; physically slowing down the recorderis capstan, or by turning on and off the power to the tape-drive motor) and adjust R37, the flutter noise adjustment, so that the voltage at the loop filter output does not chanqe while the tape is experie~cing these speed variations.

8. Adjust the ZE~O potentiometer ~R45) so that the output signal is 0.000 volts while playing back the "baseline" signal.
Recorders in use today which are capable of peak-to-peak signal-to-noise ratios approaching 50 db are in the several thousand dollar price range, and are sorely pressed to attain even the 50 db mark, with or without present forms of flutter compensation. Use of this invention enables a $50 audio cassette recorder operating at 1 7/8 inches per second, to reproduce frequency modu-lated data with a peak-to-peak signal-to-noise ratio of better than 60 db over a flat bandwidth of from 0 to 100 Hz. This is several times better than can be presently obtained by any recorder regardless of cost operating at twice the tape speed.

~785Z

The invention works so well in eliminating the effects of tape speed variation, that if one is willing to accept gross variations in the time base accuracy of the data, the 60 db figure can be reached even by turning 5 the recorder motor ~y hand.
As previously mentioned, the flutter removal is essentially independent of the flutter fre~uency, and is virtually unaffected by temperature variations, etc., which might cause small variations in the recorded fre-quencies or in the width of the monostable pulses. Sucheffects result primarily in minute changes in gain accuracy, and in small output offset voltages.
The fact that this invention eliminates complete demodulation of the reference channel results in the total demodulation system requiring little additional circuitry over what would have been required to demodu-late the FM data signal without any flutter-reduction system.
Variations in the characteristics of the feedback fllter make little overall difference because the filter is, in fact, _mmon to both the data and reference chan-nels, In fact, the output filter can be moved to the pos~tlon of the feedback filter, and the feedback filter discarded, with no "baseline" signal-to-noise ratio degradation and with only a slight degradation of system gain accuracy, and only at high data frequencies and amplitudes.
~f interest is the effect generated when the reference frequency is offset from the data center fre-quency, say from 3000 Hz to 3500 Hz. In such a situation the system would be capable of producing extremely high ~baseline~ signal-to-noise ratios even with inadequate filtering of the summation signal by the feedback filter, say only 45 or 50 db. This is because the inter-modulation noise products generated at the difference frequency would fall outside of the bandwidth of a 100 ~z output filter, and be further attenuated by the output filter.
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~47852 .
The only flutter noise which this system cannot remove is non-coherent flutter, i.e., tape speed variations not common to both the data and reference channels. Such flutter is generated by two factors, 5 namely, a. dynamic skewing of the tape, b. non-uniform dynamic stretching of the tape.
This system is insensitive to tape skew, so long as 1 it doesn't adversely affect playback voltages, because a - deviation in the angle of the tape as it moves past the playback head doesn't affect the frequencies of the signals. Only dYnamic skewing which is proportional to the rate of change of the skew angle will generate an lS instantaneous relative frequency error between two tracks. This factor accounts for over half the residual flutter noise and is caused by relatively low frequency (less than 10 Hz) dynamic skewing of the .150 inch wide cassette tape as it crosses the playback head, since the simple cassette recorder that was used had but a single and rather ineffective metal guide at the side of the head. This effect could be reduced by providing better guiding of the tape. A small portion of the residual flutter noise is due to minute amounts of non-coherent ctretching of the magnetic tape, since it is a non-homogeneous elastic medium under varying degrees of ten-sion, The effect generates higher frequency flutter noise than does dynamic skewing, but even with the thin and narrow tapes in Philips' cassettes this effect is still essentially negligible. Of course, residual noise due to non-coherent flutter could be eliminated by multiplexing the reference frequency onto the same physi-cal track as the data channel. However, it would appear that the minute relative improvement would rarely justify the increase in circuit complexity and cost.
The removal of flutter with this system is in fact so complete that the invention can also be used as a means to test and evaluate the dynamic skewing charac-~.....
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1~4785Z-31-teristics of various tape transports with an extreme degree of accuracy.
Of special importance is the fact that this inven-tion requires no special amplitude or frequency-dependent contouring of the recorded or reproduced signals, i.e., that no pre-emphasis/de-emphasis or similar compression/expansion techniques are employed in the flutter elimination process. Thus the recorder using this system is capable of reproducing data with a flat frequency/amplitude transfer characteristic, and is thereby classified as an instrumentation recorder and not j as a special purpose, limited-use device.
For this reason, the technique described in this invention may be applied to virtually any existing recorded FM data in the world which has been recorded with a reference channel, to remove flutter amplitude ' noise from old recordings with a degree of accuracy thought impossible to obtain until now. This invention will be of vital importance to applications employing ,~ 20 extremely low tape speeds, as the relative effect of the ' flutter becomes very large as the velocity of the tape approaches zero.
' It is highly probable that the basic circuitry of ~ the invention will eventually be incorporated into a ;~ 25 single integrated circuit, with pins for the external connection of the input frequencies and the appropriate filtering and adjustments.
The efficacy of the present invention in reducing amplitude flutter noise is shown in FIGS. 10, 11 and 12.
' 30 FIG. 10 shows the face of a cathode ray-tube oscilloscope ~` displaying the output signal generated from an inexpen-sive tape transport recording of a 4 Hz saw-tooth signal of full-scale amplitude. To the left, is the noticably distorted output before the above embodiment of the invention is switched into the system. To the right, the flutter noise is eliminated.
More important, however, is the output of a tiny ;~

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saw-tooth signal of only one percent of full-scale ampli-tude as shown in FIG. 11. To the left, the signal is virtually obliterated by the normal flutter noise inherent in the tape moving mechanisms. Switching in the noise reducer in accordance with the above embodiment eliminates nearly all of the flutter noise as shown to the right.
!,' , FIG. 12 shows the output of the same signal as in FIG. 11 but with massive flutter introduced by physical , 10 interference with the tape transport. Between the two dashed lines, the invention is switched in, thereby eli-minating nearly all of the flutter noise even in this grotesque situation. From this example it should be clear that even extreme low quality of the tape transport will have little effect on the quality of the output signal, other than the effect gross deviations in tape speed have on the time base accuracy of the output, visible in FIG. 12 as variations in the frequency of the saw-tooth waveform.
Acco~dingly, while the invention has been described with particular reference to specific embodiments thereof in the interest of complete definiteness, it will be understood that it may be emobodied in a variety of forms diverse from those shown and described without departing from the spirit and scope of the invention as defined by the following ~laims.

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Claims (12)

The embodiments of the invention in which an exclusive property or privilege is claimed are defined as follows:

1. An improved apparatus, for reducing noise in a frequency-modulated data stream, which stream is modulated in frequency in accordance with variations in the amplitude of an information signal, such appara-tus being of the type utilizing a reference stream having a predetermined frequency which has been sub-jected to essentially the same noise, such noise being that additional frequency modulation which has simultaneously affected both the data stream frequency and the reference stream frequency, wherein such noise may include noise produced by variations in the velocity of a recording medium used for recording and reproducing the data stream frequency and the reference stream frequency, wherein the improvement comprises:
(a) a data stream frequency-discriminating means which transforms the data stream into a first signal of value proportional to the frequency of the data stream;
(b) a reference stream frequency-discriminating means which effectively performs both frequency discrimination and multiplication, and which essentially multiplies the incompletely demodulated reference stream by a feedback value to form a second signal of value proportional to the product of the reference stream frequency times the feedback value;
(c) a combining means which combines the first and second signals and generates an output value proportional to the feedback value; and (d) a feedback loop which returns the feedback value to the reference stream frequency-discriminating means, so that the feedback loop in the apparatus causes the output value (i) to vary in a manner which is proportional to the ratio of the data stream frequency divided by the reference stream frequency and (ii) to be equivalent to the original information signal with all frequency modulation noise effectively removed.

2. The apparatus of claim 1, wherein, in the reference stream frequency-discriminating means, the frequency discrimination is accomplished by switching an input signal to the reference stream frequency discriminating means at a rate proportional to the reference stream frequency, and the multiplication is accomplished by varying the amplitude of the input signal in accordance with the amplitude of the feed-back value.

3. The apparatus of claim 2, wherein (a) the data stream frequency discriminating means includes a device that transfers the data stream into a first signal that is a first stream of pulses, having constant amplitude and of frequency proportional to the frequency of the data stream;
(b) the references stream frequency-discriminating means includes a reference stream frequency-discriminating device that transforms the reference stream into a second signal that is a second stream of pulses having an amplitude proportional to a feedback value, and a frequency proportional to the frequency of the reference stream.

4. The apparatus of claim 3, further comprising a low-pass filter between the combining means and the input of the feedback value to the reference stream frequency-discriminating means.

5. The apparatus of claim 4, wherein the reference stream frequency-discriminating device includes a monostable multivibrator, having an input that is an input of the reference stream frequency discriminating device and an output.

6. The apparatus of claim 5, wherein the refer-ence stream frequency-discriminating device further includes a transistor switch, connected so as to switch the monostable-multivibrator's output between the feedback value and the inverted feedback value.

7. An improved apparatus, for reducing common-factor noise in a frequency-modulated data stream, of the type utilizing a reference stream, wherein the improve-ment comprises:
(a) a first means for transforming a frequency-modulated first data stream represented by fc(l + m) (1 + F) where fc equals a pure carrier frequency, m equals a pure data modulation, and F is the noise factor, into a second data stream representing the value m + F(1 + m), (b) second means, for transforming a third reference stream representing the value fR(1 + F), where fR is a reference frequency, and a fourth feedback stream, representing the value m, into a fifth stream representing the value -F (1 + m), (c) third means, for a combiner combining the second and fifth streams to generate a signal proportional to the value m, and (d) a feedback loop which feeds the signal back to the reference-stream device.

8. An improved apparatus, for reducing common-factor noise in a frequency-modulated data stream, of the type utilizing a reference stream, wherein the improvement comprises:
(a) a first means for transforming a frequency-modulated first data stream represented by fc(1 + m) (1 + F) where fc equals a pure carrier frequency, m equals a pure data modulation, and F is the noise factor, into a second data stream representing the value m + F(1 + m), (b) second means, for transforming a third reference stream representing the value fR(1 + F), where fR is a reference frequency, and a fourth feed-back stream, representing the value m, into a fifth stream representing the value -F (1 + m), (c) third means, for a combiner combining the second and fifth streams to generate a signal propor-tional to the value 1 + m, and (d) a feedback loop which feeds the signal back to the reference-stream device.

9. An improved apparatus, for reducing noise in a frequency-modulated data stream, which stream is modulated in frequency in accordance with variations in the amplitude of an information signal, of the type utilizing a reference stream having a predeter-mined frequency which has been subjected to essentially the same noise, such noise being that additional frequency modulation which has simultaneously affected both the data stream frequency and the reference stream frequency, wherein such noise may include noise produced by variations in the velocity of a recording medium used for recording and reproducing the data stream frequency and the reference stream frequency, wherein the improvement comprises:
(a) a data stream frequency-discriminating means which transforms the data stream into a first signal of value proportional to the frequency of the data stream;
(b) a reference stream frequency-discriminating means which transforms the reference stream into a second signal of value proportional to the frequency of the reference stream; and (c) a combining means which combines the first and second signals to generate an output signal, the combining means being so configured as to cause said output signal to vary in direct proportion to the first signal and in inverse proportion to the second signal, so that the combining means causes the output signal (i) to vary as the ratio of the data-stream frequency to the reference stream frequency, and (ii) to be equivalent to the original information signal, with all the frequency-modulation noise effectively removed.

10. The apparatus of claim 9, wherein the im-provement comprises:
(a) a data-stream frequency-discriminating means which transforms the data stream into a first digital signal of value proportional to the frequency of the data stream;
(b) a reference-stream frequency-discriminating means which transforms the reference stream into a second digital signal of value proportional to the frequency of the reference stream; and (c) a digital combining means which combines said first and second signals to generate a digital output signal, said digital combining means being so configured as to cause said output signal to vary in direct pro-portion to said first signal and in inverse proportion to said second signal, so that the combining means causes the output signal (i) to vary as the ratio of the data-stream frequency to the reference-stream frequency, and output-signal (ii) to be equivalent to the original infor-mation signal, with all the frequency-modulation noise and reproducing medium effectively removed.

11. Apparatus for producing a signal which varies as the ratio of the frequency of a first stream to a second stream, the apparatus comprising:
(a) a first stream frequency-discriminating means which transforms the first stream into a first signal of value proportional to the frequency of the first stream;
(b) a second stream frequency-discriminating means which effectively performs both frequency discrimina-tion and multiplication, and which essentially multi-plies the incompletely demodulated second stream by a feedback value to form a second signal of value proportional to the product of the second stream fre-quency times the feedback value;
(c) a combining means which combines the first and second signals and generates an output value pro-portional to the feedback value; and (d) a feedback loop which returns the feedback value to the second stream frequency-discriminating means, so that the feedback loop in the apparatus causes the output value to vary in a manner which is propor-tional to the ratio of the first stream frequency divided by the second stream frequency.

12. The apparatus of claim 11, wherein, in the second stream frequency-discriminating means, the discrimination is accomplished by switching an input signal to the reference stream frequency discriminating means at a rate proportional to the reference stream frequency, and the multiplication is accomplished by varying the amplitude of the input signal in accor-dance with the amplitude of the feedback value.