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.