US3819861A - Sound enhancing system for musical instruments - Google Patents

Abstract

Apparatus for enhancing the sound quality of musical instruments and of electronic sound sources is disclosed. Electrical signals representative of sound are modulated in a predetermined manner to increase their spectral content and are then processed by a resonance network which alters the amplitude and phase relationships of the various harmonic signal components. The processed signals are then demodulated in accordance with the modulation method used, thereby recreating a distorted replica of the original tone which is rich in harmonics that are uncorrelated in amplitude and in phase with each other. Upon conversion to sound this demodulated signal results in a pleasing tone.

Description

Patent 1 1 SOUND ENHANCING SYSTEM FOR MUSICAL INSTRUMENTS [4 June 25, 1974 3,688,010 8/1972 Freeman 84/111 Primary ExaminerKathleen H. Claffy [75] Inventor: g x g f Ngw Assistant Examiner.lon Bradford Leaheey row ence Attorney, Agent, or Firm-G. E. Murphy [73] Assignee: Bell Telephone Laboratories,

Incorporated, Murray Hill, NJ. [57] ABSTRACT [22] Filed: No 24, 1972 Apparatus for enhancing the sound quality of musical instruments and of electronic sound sources is dis- PP -Z 309,203 closed. Electrical signals representative of sound are modulated in a predetermined manner to increase [52 us. (:1. 179/1 M, 179/1 D 84/1.04 their Spectral Content and are Processed by 9 [51] Int. Cl. G10h 5/00 onance network which alters the amplitude and Phase [58 Field of Search 179/1 M 1 D 1 SA' relationships of the various harmonic Signal compo- 84/H6 L04 1 nentsv The processed signals are then demodulated in accordance with the modulation method used, thereby [56] References Cited recreating a distorted replica of the original tone which is rich in harmonics that are uncorrelated in UNITED STATES PATENTS amplitude and in phase with each other. Upon converg i 67 sion to sound this demodulated signal results in a 1'00 5.... 3,667,047 5/1972 lwasaki 179/1 SA Pleasmg tone 3,668,294 6/1972 Kameoka 179/1 SA 15 Claims, 8 Drawing Figures 20 RESONANCE l0 NETWORK r 3 SIGNAL AUDIO SOURCE CONVERTOR PATENTEDJUHZS 1914 3.8193361 sum 1 or 3 FIG.

'RESONANCE' NETWORK SIGNAL AUDIO SOURCE T CONVERTOR u. 0 5 Z 5 2000- O E A IOOO P .IX

1 1 I I I 1 I I o 4 8 l2 I6 20 x= PEAK NUMBER so 70 7 so I I I PATENTEDJUHZS I974 3L81 9.861

SHEET 2 0F 3 FIG. 4

L20 RESONANCE NETWORK f F/G. .5

BASIC fi BASIC I NETWORK I WY I, J 72 ::13 ;1 m 1 \BASIC NETWORK y {l5 {l6 7 {l7 (l8 rlg SIGNAL RESONANCE AUDIO SOURCE EXPANDER NETWORK CMPRESSR CONVERTOR PAIENTEUJUII 25 I874 SHEET 3 IIF 3 SIGNAL FREQUENCY SIGNAL FREQUENCY FM MODULATION SIGNAL *c FREQUENCY MODIFIED FM MODULATED SIGNAL c FREQUENCY DEMODULATED SIGNAL MEDE ESE FREQUENCY SOUND ENHANCING SYSTEM FOR MUSICAL INSTRUMENTS BACKGROUND OF THE INVENTION This invention relates to signal processing and, in particular, to processing systems for modifying the sound quality of musical instruments.

Electronic means are used extensively to enhance the quality and richness of sound that is generated by musical instruments. This is done by obtaining an electrical signal representation of the sound to be produced, modifying it according to some method, and converting the modified signal to sound.

Filters are commonly used as signal modifiers to achieve sound enhancement, as for example, bass boost, treble boost, loudness control, etc. More sophisticated approaches use nonlinear devices as the signal modifiers to increase the harmonic content of the basic signal. For example, U.S. Pat. No. 3,213,180, issued to .I. C. Cookerly on Oct. 19, 1965 discloses one system for generating signals, responsive to musical instruments, having a qiven waveform and frequency response. In this system, as in other systems where enrichment of sound is achieved through nonlinearities, care must be taken to choose the proper approach because some nonlinearities (i.e., distortions) produce a less pleasing sound rather than a more pleasing sound. One reason for this is that discordant sound includes harmonics that are phase correlated'to their fundamentals, while pleasing sound generally has uncorrelated harmonics. This characteristic of sounds is described in an article entitled Regarding the Sound Quality of Violins and a Scientific Basis for Violin Construction," Journal of the Acoustical Society of America Vol. 29, July 1957, page 817, by H. Meinel, where it is pointed out that a violin exhibits a plurality of resonances that are not harmonically related to each other and that the position and height of these resonances are important parameters with respect to the instruments tone quality.

Therefore, a need exists to rigorously classify and characterize these parameters, and to develop apparatus which takes advantage of the sound improvements made possible by the manipulation of said parameters.

SUMMARY OF THE INVENTION It is therefore an object of this invention to enrich and to enhance the quality of sound emitted by musical instruments by providing apparatus for affecting the pertinent parameters of sound.

It is another object of this invention to provide a network that exhibits resonances at various points in the frequency spectrum at such locations and of such magnitude as to enhance the sound quality of musical instruments that are used in conjunction with the invention.

Therefore, in accordance with this invention, enrichment and enhancement of sound are achieved through alterations of the pertinent parameters of sound. One embodiment of this invention comprises a signal source, a spectrum expander coupled to the signal source, a resonance network coupled to the spectrum expander, a spectrum compressor coupled to the resonance network, and an audio convertor coupled to the spectrum compressor.

It has been discovered that a musical instrument possesses a pleasant sound if it exhibits a plurality of peaks in its frequency response. Accordingly, the resonance network of this invention exhibits peaks and valleys in its frequency response where the peaks have the following property;

a. The frequencies of peak response occurrences must be spaced in a nonuniform manner with respect to the harmonic frequencies of any tone. The nonuniform peak spacing must insure that each harmonic of a given tone is on an up slope, down slope, peak, or valley of the frequency response curve, without any strong correlation in amplitude or phase of each harmonic.

b. Theattenuated response away from the peak must be sufficiently large so that the response curve is steep almost everywhere; that is to say, the magnitude of the derivative of the response curve must be large almost everywhere.

c. The peaks must be approximately at one uniform level and the intervening valleys must be approximately at another unifonn level such that the ratio of the peak level to the valley level is between 10 db to 15 db.

The spectum compressor of this invention is such that if connected to the spectrum expander, the output signal developed in a recreation of the spectrum expanders input signal. For example the spectrum expander may be an AM modulator of carrier frequency F and the spectrum compressor may be an AM demodulator of the same carrier frequency.

Operation of the system proceeds in the following manner. A signal emanating from the signal source is modified in a predetermined manner by the spectrum expander, thereby adding spectral lines to the original spectrum. The signal thus modified then passes through the resonance network, wherein the signals various frequency components are changed in amplitude, and in phase, in an uncorrelated fashion from each other (because of the nonuniform spacings of the resonance networks peaks). The spectrum compressor subsequently modifies the signal from the resonance network and recreates a distorted replica of the original tone that contains harmonics and subharmonics of the tones fundamental frequency. This signal is then transformed to sound by the audio convertor, such as a loud speaker resulting in a pleasing sound.

One feature of this invention is the complete latitude available in the selection of the spectrum expander and of the spectrum compressor. In fact, both may be omitted from the sound enhancing system, particularly when the original tones to be enhanced contain more than a single frequency.

The operation and features of the present invention will become more apparent upon perusal of the following description taken in conjunction with the accompanying drawing wherein:

BRIEF DESCRIPTION OF THE DRAWING FIG. 1 illustrates a block diagram of a simple sound enhancing system in accordance with the invention;

FIG. 2 illustrates a graph of peak frequencies versus peak number which is used as an aid for designing the resonance network in FIG. 1;

FIG. 3 illustrates the frequency response of a number of basic networks, and the composite frequency response of the resonance network of FIG. 1;

FIG. 4 illustrates an embodiment of the resonance network used in the apparatus of FIG. 1;

FIG. 5 illustrates a basic network which can be used within said resonance network;

FIG. 6 is a block diagram depicting an alternative sound enhancing system;

FIG. 7 illustrates a possible set of spectra appearing at various points within the system shown in FIG. 6; and

FIG. 8 illustrates an alternate embodiment of the resonance network used in the apparatus of FIG. 1.

DETAILED DESCRIPTION FIG. 1 depicts apparatus for enhancing the tone quality of musical instruments that produce sounds rich in harmonics, comprising signal source 10, resonance network 20 responsive to the output of the signal source, and audio convertor 30 responsive to the resonance network output.

Signals emanating from a musical instrument, as for example, from a bowed or plucked string instrument, are converted to electrical signals in signal source 10. Any of a variety of known transducers may be used for this purpose, e.g., magnetic or electrostatic pick-up devices. These signals are then modified in resonance network 20 by altering the amplitude and phase characteristics of the signal as a function of frequency, in a manner to be fully described herein, and in accordance with the desired peak and valley response as described above. Following the signal modification the electrical signal is converted in audio convertor 30, resulting in a pleasant sound.

To achieve the desired peak and valley frequency characteristic of the signal, resonance network 20 transfer function must exhibit a preselected frequency response. That is, the resonance network must exhibit response peaks at nonuniform frequency spacing, the response curve must be steep" almost everywhere, and the peak to valley ratio of the response curve should be between 10 dB and dB as discussed above.

Specification of resonance network parameters can proceed via a number of ways, one of which is described herein by way of a specific example.

First. the nonuniform frequency spacing between response peaks of the resonance network is obtained by defining an equation of peak frequency, f,,, versus peak number, x, which describes the general distribution of peaks that may be required to achieve a particular number and distribution of peaks within the audio range. The peak frequency, f,,, can be a nonstraight line' equation, having, for example, the general form f,,(.r) a r a,.r a x (1) containing any number of terms, wherein a is not the only nonzero coefficient. For example, to enhance the sound of a violin string, it is beneficial to design peaks within the audio range. For that purpose, f., may be the exponential function fp=125 mu: (2)

which may also be described as f,,= l( l 0.174 x (0. l74x) /2! (0.l74x)"/n! (a) This function s nonlinear character is well illustrated by the plot of FIG. 2, wherefrom the frequencies of peak occurrence can be determined by raising a perpendicular, line 40 of FIG. 2, from a chosen peak number, to

intersect with the plotted curve, and by extending a horizontal line, such as line 50, of FIG. 2, toward the vertical axis, to detennine the peaks frequency. Alternatively, equation 2, characterizing f,,(x), can be directly solved for any value of x, as for example, for x 8, f E 500. 1

One configuration of resonance network 20 suitable for this invention is shown, in FIG. 4, where the input to the resonance network drives a plurality of basic networks such as networks 21, 22, 23, and 24, and where the outputs of said basic networks are summed in conventional analog summer 14. A suitable summer is described by G. E. Tobey et al in Operational Amplifiers Design and Description, McGraw-I-Iill Book Company, 197], page 429. Another configuration of resonance network 20 may contain basic networks interconnected in cascade.

Once the peak frequencies of resonance network 20 are known, the network can be constructed to yield the desired peaks and the desired peak to valley ratio by properly proportioning a set of basic networks and combining them in a predetermined manner as shown, for example, in FIG. 4, wherein each basic network is selected to contribute one peak in the resonance networks composite response and a controllably attenuated response at frequencies other than the peak frequency. These peaks are selected to correspond to the frequencies determined from the graph of FIG. 2. FIG. 3 shows response curves 60, 70, and 80, respectively of the basic networks that generate the lOth, 19th and 20th peak, respectively, of the composite response curve 90.

The use of basic networks to configure resonance network 20 imposes the requirement that each basic network must possess one dominant resonance, that the resonance frequency of the basic network be controlled, and that the Q factor of the basic network also be controlled, so that resonance network 20 exhibits a composite frequency response, as shown by curve in FIG. 3, with a 10 to 15 db peak-to-valley ratio.

With resonance network 20 constructed as shown in FIG. 4, the basic network must exhibit maximum signal transfer at resonance. Accordingly, a conventional second order filter, as illustrated in FIG. 5, can serve as the basic network. From equation 2 the required resonance frequency of each second order filter can be determined. The Q of each second order filter is set to obtain a desired peak height for that filter in order to achieve a peak valley ratio of 10 to 15 db. This determination is shown in an appendix to this specification.

An alternate method may be used to obtain the resonance network specification by the use of basic networks, connected in cascade, as shown in FIG. 8. In such an embodiment each basic network must exhibit a minimum signal transfer at the valleys of the resonance networks composite frequency respone. An equation similar to equation 2 can be used to specify the required valley frequencies. Further, it would be obvious to those skilled in the art that various combinations of parallel and serial interconnections of a num ber of passive or active, basic networks can be specified to realize this invention. Also, it would be equally obvious to those skilled in the art that equation 2 can take on many other forms, such as f, (x) a,,x B where x is the peak number, a, is positive and non zero, and B is a random variable uniformly distributed between 1*:

creasing the spectrum content of the signal, and applies the modified signal to resonance network 17. In this system, resonance network 17 characteristic response is similar to the characteristic response of resonance network 20 except that is is centered about the carrier frequency of the spectrum expander. The output of resonance network 17 is applied to spectrum compressor 18 which performs the inverse function of spectrum expander l6, and the altered signal of spectrum compressor I8 is applied to audio convertor 19, where the signal is transformed to sound.

A more thorough understanding of the system in FIG. 6 and its operation may be obtained by observing the spectra shapes at various points in the system. By way of example, FIG. 7 illustrates a possible set of spectra corresponding to the system of FIG. 6'where the spectrum expander is an FM modulator of carrier frequency f and the spectrum compressor is an FM demodulator of the same carrier frequency.

Assume that signal source produces a single frequency tone having a single line spectrum as shown in FIG. 7A. The spectrum of the signal at the output of modulator 16 is expanded as shown in FIG. 7B in accordance with the standard Bessel function expansion of FM modulated signals. This spectrum is then applied to resonance network 17 which alters the spectrum irregularly, as shown in FIG. 7C, in accordance with the transfer characteristics of resonance network 17, shown by curve 200 of FIG. 7C. Demodulator l8 operates on the spectrum shown in FIG. 7C and produces a baseband signal, shown in FIG. 7D. This baseband signal has the same fundamental frequency as the original tone from signal source 15, but also has additional spectral lines which do not have a strong correlation in amplitude or in phase to the signal of source IS. The signal that corresponds to the spectrum shown in FIG. 7D, when converted to sound by audio convertor 19, produces an interesting and a pleasing tone.

APPENDIX A resonance network comprising second order filters as the basic network exhibits a frequency response that is characterized by (0mm 5 l/ l Substituting for e )mln E i/[( r+1- 1) 3] and the peak to valley ratio. P/V, is

The bandwidth of the filter to achieve a given peak to valley ratio is thus 1 t+l 'r)/ V P/V and the Q of the filter, w,/2B,, is

If peaks of the resonance network follow the equation This result indicates that a resonance network with peaks spaced according to equation Ae and constructed with second order filters requires filters with identical Qs.

Another interesting feature of equation A3 is that w /w, e, which is a constant.

In the example given within the specification, for a peak to valley ratio of 10 dB, and f,,(x) e the requiredQ of each and every filter is What is claimed is:

1. Apparatus for enhancing the sound quality of applied signals comprising:

a plurality of basic networks responsive to said applied signals. each exhibiting a resonance at a preselected frequency and a controllable diminished response at frequencies other than said resonance frequency, and means for combining the output signals of said basic networks to develop a composite frequency response characterized by spectral peaks at a substantially unifonn first level and alternating valleys at a substantially uniform second level, wherein said spectral peaks occur at substan tially nonuniform frequency spacings and said valleys, interposed between said peaks, also occur at substantially nonuniform frequency spacings. I

2. The apparatus defined in claim 1 wherein the ratio of said first level to said second level is between IOdb and l5db.

3. The apparatus defined in claim 1 wherein each of said basic networks exhibits maximum signal transfer at its resonance frequency.

4. The apparatus defined in claim 1 wherein each of said basic networks is a second order filter and in which the ratio of peak frequency of any two adjacent filters is a constant e, and the quality factor of each filter is equal to 2' V P/V/(el where P/V represents the desired peak-to-valley ratio of said resonance network.

5. The apparatus defined in claim 1 wherein the peak frequencies, (f,,(x), of the composite frequency response of said basic networks are determined by the nonlinear equation f,,(x) a x-l-a,x +a x where a is not the only non-zero coefficient, and x is the peak number.

6. The apparatus defined in claim 1 wherein the peak frequencies. f,,(x), of the composite frequency response of said resonance networks are determined by the equation [,(x) a x B, where a is positive nonzero, x is the peak number, and B is a random variable uniformly distributed between i d 7. Apparatus for enhancing the sound quality of applied signals comprising:

a resonance network including a plurality of basic networks responsive to said applied signals and means for combining the output signals of said basic networks, each of said basic networks exhibiting a resonance at a preselected frequency and a controllable diminished response at frequencies other than said resonance frequency, said resonance network exhibiting a frequency response that contains spectral peaks, and valleys situated therebetween, wherein said peaks, at a substantially uniform first level, occur at substantially nonuniform frequency spacing and wherein said valleys are at a substantially uniform second level.

8. The apparatus defined in claim 7, further comprising a spectrum expander electrically interposed between said applied signals and said resonance network and a spectrum compressor responsive to said resonance network.

9. The apparatus defined in claim 8 wherein said spectrum expander and said spectrum compressor comprise a modulator and a demodulator, respectively, with the same carrier signal frequency.

10. Apparatus as defined in claim 9 wherein said modulator is an FM modulator and wherein said demodulator is an FM demodulator.

11. Apparatus for enhancing the sound quality of applied signals comprising:

a resonance network including a plurality of basic networks responsive to said applied signals and means for combining the output signals of said basic networks, each of said basic networks exhibiting a resonance at a preselected frequency and a controllable diminished response at frequencies other than said resonance frequency, said resonance network exhibiting a frequency response that contains spectral peaks at a substantially uniform first level and valleys at a substantially uniform second level situated between said peaks, wherein said peaks occur at substantially nonuniform frequency spacings; and

an audio convertor responsive to the output signals of said resonance network for converting electrical signals to sound.

12. Apparatus for enhancing the sound quality of applied signals comprising:

a resonance network responsive to said applied signals including a plurality of basic networks interconnected in cascade, where each of said basic networks exhibits a minimum signal transfer at its resonance frequency and a controllable diminished response at frequencies other than said resonance frequency, said resonance frequency corresponding to a valley of the resonance networks frequency response, wherein the valleys of said resonance networks frequency response occur at substantially nonuniform frequency spacings and are substantially at a first uniform level and wherein said controllable diminished response is adjusted to provide peaks between said valleys having substantially a second uniform level.

13. The apparatus defined in claim 12, further comprising a spectrum expander electrically interposed between said applied signals and said resonance network and a spectrum compressor responsive to said resonance network.

14. The apparatus defined in claim 13 wherein said spectrum expander and said spectrum compressor comprise a modulator and demodulator, respectively, with the same carrier signal frequency.

15. Apparatus as defined in claim 14 wherein said modulator is an FM modulator and wherein said demodulator is an FM demodulator.

UNITED STATES UFFICE CERTIFICATE OF CORRECTION Patent No. 1 ,851 Dated June 25, 197 4 It is certified that error appears inthe above-identified patent and that said Letters Patent are hereby corrected as shown below:

Column 1, line 23, "qiven" should read --gi en- Column 2, line .26., "in" should read -is-.

Column 5, line 61, "s -w should read "s -w llne 6 6, e W -W /2 should read e (w m )/2,

Column 6, line 1 after equation insert --orline 19, "H(s) 2 AB /e +B should read --H(s)- E AB /(e +B Signed and sealed this 12th day of November 1974.

(SEAL) Attest:

C. MARSHALL DANN McCOY M. GIBSON JR.

Commissioner of Patents Attesting Officer USCOMM-DC 60376-P69 U.S GOVERNMENT PRINTING OFFICE I909 O-3S6-J34.

FORM PO-105O (10-69) UNITED STATES 1 mm UFFICE CERTIFICATE OF CORRECTION Patent No. ,819,861 D ated v June 25 197 1 It is certified that error appears in the abovei.dentl[ied patent and that said Letters Patent are hereby corrected as shown' below:

Column 1, line 23, "qiven" should read "given".

Column 2, line .26, "in" should read --is--. Column 5, line 61, "52 -w should read -S2 -w line 66, "e W -W /2" should read --e (w -w )/2 Column 6, line 1 after equation insert --or--;.

--H(s)- e AB /(e +B i) Signed and sealed this 12th day of November 1974.

(SEAL) Attest:

C. MARSHALL DANN McCOY M. GIBSON. JR.

Commissioner of Patents Attesting Officer USCOMM-DC 60376-P69 FORM PO-1050 (10-69) h u.s. covzmmzm rmm'ms ornc: nu 0-366-334.

Claims (15)

1. Apparatus for enhancing the sound quality of applied signals comprising: a plurality of basic networks responsive to said applied signals, each exhibiting a resonance at a preselected frequency and a controllable diminished response at frequencies other than said resonance frequency, and means for combining the output signals of said basic networks to develop a composite frequency response characterized by spectral peaks at a substantially uniform first level and alternating valleys at a substantially uniform second level, wherein said spectral peaks occur at substantially nonuniform frequency spacings and said valleys, interposed between said peaks, also occur at substantially nonuniform frequency spacings.

2. The apparatus defined in claim 1 wherein the ratio of said first level to said second level is between 10db and 15db.

3. The apparatus defined in claim 1 wherein each of said basic networks exhibits maximum signal transfer at its resonance frequency.

4. The apparatus defined in claim 1 wherein each of said basic networks is a second order filter and in which the ratio of peak frequency of any two adjacent filters is a constant ec, and the quality factor of each filter is equal to 2. Square Root P/V/(ec-1), where P/V represents the desired peak-to-valley ratio of said resonance network.

5. The apparatus defined in claim 1 wherein the peak frequencies, (fp(x), of the composite frequency response of said basic networks are determined by the nonlinear equation fp(x) a0x+a1x2+a2x3+. . . , where a0 is not the only non-zero coefficient, and x is the peak number.

6. The apparatus defined in claim 1 wherein the peak frequencies, fp(x), of the composite frequency response of said resonance networks are determined by the equation fp(x) a0x +B, where a0 is positive non-zero, x is the peak number, and B is a random variable uniformly distributed between + or - a0.

7. Apparatus for enhancing the sound quality of applied signals comprising: a resonance network including a plurality of basic networks responsive to said applied signals and means for combining the output signals of said basic networks, each of said basic networks exhibiting a resonance at a preselected frequency and a controllable diminished response at frequencies other than said resonance frequency, said resonance network exhibiting a frequency response that contains spectral peaks, and valleys situated therebetween, wherein said peaks, at a substantially uniform first level, occur at substantially nonuniform frequency spacing and wherein said valleys are at a substantially uniform second level.

8. The apparatus defined in claim 7, further comprising a spectrum expander electrically interposed between said applied signals and said resonance network and a spectrum compressor responsive to said resonance network.

9. The apparatus defined in claim 8 wherein said spectrum expander and said spectrum compressor comprise a modulator and a demodulator, respectively, with the same carrier signal frequency.

10. Apparatus as defined in claim 9 wherein said modulator is an FM modulator and wherein said demodulator is an FM demodulator.

11. Apparatus for enhancing the sound quality of applied signals comprising: a resonance network including a plurality of basic networks responsive to said applied signals and means for combining the output signals of said basic networks, each of said basic networks exhibiting a resonance at a preselected frequency and a controllable diminished response at frequencies other than said resonance frequency, said resonance network exhibiting a frequency responsE that contains spectral peaks at a substantially uniform first level and valleys at a substantially uniform second level situated between said peaks, wherein said peaks occur at substantially nonuniform frequency spacings; and an audio convertor responsive to the output signals of said resonance network for converting electrical signals to sound.

12. Apparatus for enhancing the sound quality of applied signals comprising: a resonance network responsive to said applied signals including a plurality of basic networks interconnected in cascade, where each of said basic networks exhibits a minimum signal transfer at its resonance frequency and a controllable diminished response at frequencies other than said resonance frequency, said resonance frequency corresponding to a valley of the resonance network''s frequency response, wherein the valleys of said resonance network''s frequency response occur at substantially nonuniform frequency spacings and are substantially at a first uniform level and wherein said controllable diminished response is adjusted to provide peaks between said valleys having substantially a second uniform level.

13. The apparatus defined in claim 12, further comprising a spectrum expander electrically interposed between said applied signals and said resonance network and a spectrum compressor responsive to said resonance network.

14. The apparatus defined in claim 13 wherein said spectrum expander and said spectrum compressor comprise a modulator and demodulator, respectively, with the same carrier signal frequency.

15. Apparatus as defined in claim 14 wherein said modulator is an FM modulator and wherein said demodulator is an FM demodulator.

Images