US3697697A
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Communication by smooth high order composites of trigonometric product functions
Assignee: International Business Machines Corp
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Filing: 1970-12-28
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Granted: 1972-10-10
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Expires: 1990-12-28
Abstract
Abstract Member functions of certain disjoint sets of harmonically related trigonometric product functions (the term ''''disjoint'''' is used herein to describe sets which have no common member functions and relatively distinct class properties K) are combined for transmission by simultaneously selecting plural subsets of a first one of the sets, in fundamental half-periods, and superposing the members of each subset by linear addition to form subset composites. These are individually multiplied (''''upconverted'''') by members of other sets and superposed in groups. Such cascaded multiplications and superpositions are continued convergently to provide at one central terminal a comprehensive high order composite transmission waveform which has smooth outline and contains, in a highly distinguishable form, all of the binary intelligence utilized in the initial selections of subsets of the first set. At receiving apparatus the composite transmission waveform is decomposed (down-converted) in divergently cascaded stages of multiplications by locally synthesized functions. Plural sets of higher order product waveforms, issuing from the last stages of such multiplication in parallel, are separately integrated over fundamental half-period intervals. The integrand functions correspond to distinct sums of products of pairs of high order trigonometric product functions having identical class and order. The terms of any sum all have distinct binary coefficients. The product functions form an orthogonal set with associated order and class properties respectively relating to sums and maxima of respective order and class properties of the disjoint sets containing the transmission components. Each integrand sum representation contains a unique term in which the paired product functions are identical and all other terms have unmatched functions. The function in the matching term is different for each integrand. Hence with appropriate timing of integration sampling and resetting functions a unique set of binary state pulse functions, which correspond to the binary coefficients of the matching terms of respective integrands, is sampled at outputs of respective integration stages. Normally these pulse functions correspond identically to the binary selection pulses utilized in the pretransmission subset selections.
Inventors
- 👤 Leo M Audretsch Jr
- 👤 Matthew Elsner
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-10-26 06:11
CPC Classifications
H; H04; H04L; H04L23/00; H04L23/02
Claims Analysis
Total Claims: 12
Claim 1
Independent Claim
231 words
A multiplex signalling system comprising: periodically a first source of multiple smooth signal waveforms representing members of at least two disjoint sets of products of harmonically related trigonometric functions; each product function in each said disjoint set having orthogonal relation to every other product function in the same set; a second source of multiple sets of periodically recurrent parallel binary input pulse signals having periodicity related to the period of the fundamental frequency of said trigonometric functions; means for effecting multiple selections of product function waveform members of one of said sets simultaneously, in multiple parallel subsets, in accordance with respective said sets of binary pulse input signals; means for combining the selected product function waveforms in each selected subset by linear addition into a composite waveform associated with the subset; 1 means for continuously multiplying said composite subsetassociated waveforms by waveform members of another one of said disjoint sets means coupled to said multiplying means for producing a single distinct complex signal of smooth form which is functionally related to all of the component waveforms of all composite waveforms received by said multiplying means; a transmission medium; means for transmitting said complex signal over said medium; means for receiving said complex signal; and means coupled to said receiving means for deriving from said complex signal multiple sets of parallel binary output pulse signals corresponding to said binary input pulse signals.
Claim 2
Dependent Claim
231 words
A multiplex signalling system comprising: periodically a first source of multiple smooth signal waveforms representing members of at least two disjoint sets of products of harmonically related trigonometric functions; each product function in each said disjoint set having orthogonal relation to every other product function in the same set; a second source of multiple sets of periodically recurrent parallel binary input pulse signals having periodicity related to the period of the fundamental frequency of said trigonometric functions; means for effecting multiple selections of product function waveform members of one of said sets simultaneously, in multiple parallel subsets, in accordance with respective said sets of binary pulse input signals; means for combining the selected product function waveforms in each selected subset by linear addition into a composite waveform associated with the subset; 1 means for continuously multiplying said composite subsetassociated waveforms by waveform members of another one of said disjoint sets means coupled to said multiplying means for producing a single distinct complex signal of smooth form which is functionally related to all of the component waveforms of all composite waveforms received by said multiplying means; a transmission medium; means for transmitting said complex signal over said medium; means for receiving said complex signal; and means coupled to said receiving means for deriving from said complex signal multiple sets of parallel binary output pulse signals corresponding to said binary input pulse signals.
Claim 3
Dependent Claim
119 words
A system according to claim 1 wherein said means coupled to said receiving means includes: a third source of multiple smooth signal waveforms corresponding to said product functions supplied by said first source; meAns for maintaining synchronism between respective member waveforms of said first and third sources; means for multiplying waveforms supplied by said third source by said complex signal and by products of said complex signal and other said waveforms in a diverging network of multiplying circuits; means for recurrently integrating and sampling signals issuing in parallel from said multiplication network, over half-periods of the fundamental frequency common to all member waveforms supplied by said first and third sources, to obtain thereby said corresponding binary output pulse signals.
Claim 4
Dependent Claim
199 words
For a communication system including a multiplex signal transmitter, a multiplex signal communication channel and a multiplex signal receiver, an improved transmitter comprising: a first source of plural disjoint sets of harmonically related smooth trigonometric product function signals; a second source of multiple sets of periodically recurrent binary input pulse signals having parallel form and having recurrence periodicity related to half-cycle periods of the fundamental frequency associated with said disjoint sets of product functions; means for effecting recurrent selections of multiple subsets of member product function signals of one of said disjoint sets simultaneously in parallel in accordance with instantaneous states of respective signals in said sets of binary input signals; and means coupled to receive signal outputs of said selection effecting means together with signals from said first source representing members of a said disjoint set other than said one set, said coupled means being operative to produce a composite waveform of smooth outline, which is functionally related to each of said received signals, by a convergent series of linear addition and multiplication operations performed upon said received signals; and means for coupling a signal associated with said composite waveform to said communication channel as a transmission signal.
Claim 5
Dependent Claim
199 words
For a communication system including a multiplex signal transmitter, a multiplex signal communication channel and a multiplex signal receiver, an improved transmitter comprising: a first source of plural disjoint sets of harmonically related smooth trigonometric product function signals; a second source of multiple sets of periodically recurrent binary input pulse signals having parallel form and having recurrence periodicity related to half-cycle periods of the fundamental frequency associated with said disjoint sets of product functions; means for effecting recurrent selections of multiple subsets of member product function signals of one of said disjoint sets simultaneously in parallel in accordance with instantaneous states of respective signals in said sets of binary input signals; and means coupled to receive signal outputs of said selection effecting means together with signals from said first source representing members of a said disjoint set other than said one set, said coupled means being operative to produce a composite waveform of smooth outline, which is functionally related to each of said received signals, by a convergent series of linear addition and multiplication operations performed upon said received signals; and means for coupling a signal associated with said composite waveform to said communication channel as a transmission signal.
Claim 6
Dependent Claim
154 words
For a communication system in accordance with claim 3 an improved receiver comprising: a third source of plural disjoint sets of trigonometric product function signals corresponding to and synchronous with the signals of said first source; means coupled to receive said transmission signal and said product function signals of said third source and to produce therefrom, in parallel, multiple sets of smooth ultra-complex signals associated with respective said sets of binary input signals; multiple sets of integrating means coupled to receive respective said ultra-complex signals in parallel and to effect simultaneous integrations thereof periodically in periods corresponding to successive half cycle intervals of the fundamental frequency associated with said product function signals of said first and third sources; and means coupled to said integrating means and operative to sample and store outputs thereof at terminal instants of said integration periods; said sampled outputs having binary significance corresponding to states of said binary input signals.
Claim 7
Dependent Claim
290 words
For a communication system including a complex signal transmitter, a complex signal communication channel and a complex signal receiver, an improved transmitter comprising: a first source of plural signals representing member functions of plural disjoint sets of harmonically related smooth trigonometric product functions having form: fp,k,q(t) Asin(S1w0t+ r1 pi /2)sin(2s2w0t+r2 pi AB 2)sinKs33 Kw0t+ rK pi /2) wherein: each s(i 1, . . . ,K) 0 or 1 each ri(i 1, . . . ,K) 0 or 1 p designates the ''''order'''' of the function and represents the number of non-trivial sine and cosine factors in f. K designates the ''''class'''' of the fUnction and represents the highest harmonic in any factor of f. q designates the rank of the function relative to all functions of the same order p and class K; a second source of multiple sets of periodically recurrent binary input pulse signals having parallel form and having recurrence periodicity related to half-cycle periods of the fundamental frequency associated with said disjoint sets of product functions; means for effecting recurrent selections of multiple subsets of member function signals of one of said disjoint sets simultaneously in parallel in accordance with instantaneous states of respective signals in said sets of binary input signals; and means coupled to receive outputs of said selection effecting means together with outputs of said first source representing members of a said disjoint set other than said one set, said coupled means being operative to produce a composite transmission signal of smooth outline by a convergent series of linear addition and multiplication operations performed upon said outputs of said selection effecting means, wherein each of said received outputs is represented as a distinguishable component; means for coupling said transmission signal to said communication channel.
Claim 8
Dependent Claim
290 words
For a communication system including a complex signal transmitter, a complex signal communication channel and a complex signal receiver, an improved transmitter comprising: a first source of plural signals representing member functions of plural disjoint sets of harmonically related smooth trigonometric product functions having form: fp,k,q(t) Asin(S1w0t+ r1 pi /2)sin(2s2w0t+r2 pi AB 2)sinKs33 Kw0t+ rK pi /2) wherein: each s(i 1, . . . ,K) 0 or 1 each ri(i 1, . . . ,K) 0 or 1 p designates the ''''order'''' of the function and represents the number of non-trivial sine and cosine factors in f. K designates the ''''class'''' of the fUnction and represents the highest harmonic in any factor of f. q designates the rank of the function relative to all functions of the same order p and class K; a second source of multiple sets of periodically recurrent binary input pulse signals having parallel form and having recurrence periodicity related to half-cycle periods of the fundamental frequency associated with said disjoint sets of product functions; means for effecting recurrent selections of multiple subsets of member function signals of one of said disjoint sets simultaneously in parallel in accordance with instantaneous states of respective signals in said sets of binary input signals; and means coupled to receive outputs of said selection effecting means together with outputs of said first source representing members of a said disjoint set other than said one set, said coupled means being operative to produce a composite transmission signal of smooth outline by a convergent series of linear addition and multiplication operations performed upon said outputs of said selection effecting means, wherein each of said received outputs is represented as a distinguishable component; means for coupling said transmission signal to said communication channel.
Claim 9
Dependent Claim
178 words
In a communication system including a transmitter according to claim 5 an improved receiver comprising: a third source of plural disjoint sets of signals corresponding to the signals produced by said first source; multiple sets of integrator elements; means coupled to receive said transmission signal and the signals produced by said third source and responsive thereto to supply to said integrator elements as inputs uniquely distinguishable integrand function signals having the form: (fp,K,q (t))(U(t)), where: i is an integer varying over a range consisting of one unique value for each respective integrator input; p,K and qi are integers denoting order, class and rank properties of respective functions f ; functions fp,K,q i(t) for all values of i comprise an orthogonal set; and U(t) has the form: where j is an integer variable having the same range of variation as i; and means coupled to said integrator elements to operate said elements in parallel to produce as outputs discrete parallel binary signals bi each corresponding to a different one of said binary input signals produced by said second source.
Claim 10
Dependent Claim
30 words
A communication system according to claim 6 wherein said integrator element operating means controls integration of said integrand signals over intervals corresponding to said half-cycle periods of said fundamental frequency.
Claim 11
Dependent Claim
76 words
A communication system according to claim 5 wherein all but one of the signals fp,K,q(t) in said one of said disjoint sets have smooth zero points at ends of said half-cycle periods and a binary input signal associated with selection of said one signal is conditioned to have a constant value inhibiting selection of said one signal for producing said transmission signal with an envelope which is invariably smooth at said ends of said half-cycle periods.
Claim 12
Dependent Claim
37 words
A system according to claim 8 in which elements of the system participating in the encoding and decoding of said binary input signal associated with selection of said one signal are utilized as a permanent test channel.
References Cited (Backward Citations)
No citation records indexed.
USPTO Annuity & Maintenance Windows
| Annuity Stage | Window Opens | Payment Deadline | Surcharge Period Until | Estimated Fee | Status |
|---|---|---|---|---|---|
| 3.5 Years (Year 4) | 1975-10-10 | 1976-04-10 | 1976-10-10 | $2000.00 | Window Closed / Lapsed |
| 7.5 Years (Year 8) | 1979-10-10 | 1980-04-10 | 1980-10-10 | $3760.00 | Window Closed / Lapsed |
| 11.5 Years (Year 12) | 1983-10-10 | 1984-04-10 | 1984-10-10 | $7700.00 | Window Closed / Lapsed |