RU2007877C1 - Method of transmission and reception of reflex-modulated signals - Google Patents

Abstract

FIELD: radio engineering. SUBSTANCE: in compliance with this method reflex-modulated signal is formed on transmitting side by modulation of carrier frequency f by information signal which is less than difference between upper and lower boundary frequencies of one side band of reflex-modulated signal. At receiving side received signals are multiplied by signals which present sum of harmonic components with selected values of frequencies and phases. Obtained signals are summed up. EFFECT: improved reliability of transmission and reception of reflex-modulated signals. 15 dwg

Description

 The invention relates to techniques for communication systems, in particular to telecommunications.

 Modulated radio engineering signals with a “wrapped” or “bent” lower side band (in the English-language technical literature - “fold”, “folded band”, in the Soviet one - “reflected side”) occupy an intermediate position in their properties between the actually modulating (information) signals and high frequency carrier radio signals. In this case, the term "high-frequency" refers to such a carrier of a radio signal when both its side bands are fully deployed, that is, when the ratio of the frequency band of one side to the carrier frequency is equal to or less than one. In theoretical terms, such a definition is not absolutely accurate. Every radio signal, like a time-limited signal, has an infinite spectrum and, therefore, is "reflected lateral". However, for practical purposes, interest is the frequency bands, which are usually defined as finite.

 The necessary frequency band of the radio signal is determined in accordance with the sufficiency criterion for transmitting information with the required speed and quality; the occupied bandwidth of the radio signal frequency is usually determined by the permissible radiation power outside this band (creating interference for other radio equipment).

 The criterion for determining the carrier high frequency should be the permissible power of the frequency components of the "reflected side" falling into the necessary frequency band of the radio signal and creating interference to achieve the necessary speed and quality of information transfer. In the case when this power is so small that no special additional measures are required to suppress the reflected interfering component (aliase component), the carrier of the radio signal can be defined as high-frequency. On the contrary, when the power of the "reflected side" in the signal spectrum is large, which, as a rule, indicates the presence of the necessary lower side frequency band as the "reflected" parts of the components, the carrier of the radio signal can be defined as low-frequency. In this case, the ratio of the unreflected lateral frequency band to the carrier frequency is greater than unity, and it is the magnitude of this ratio that the degree of low-frequency carrier should be estimated. So, for example, with amplitude modulation, if the cutoff frequency of the spectrum of the modulating signal is less than the carrier frequency, then such a carrier can be defined as high-frequency. With frequency modulation, the carrier quiescent frequency, which exceeds the upper boundary frequency of the spectrum of the modulating signal, can be estimated as high and low, depending on the modulation index.

 Since the characteristic distinctive feature of radio signals on a low-frequency carrier is the presence of a partially “reflected” (“reflex”) lower sideband, the terms “reflex radio signal” and “reflex-modulated signal” can be used to designate these signals, and the process of their formation can be proposed the term "reflex modulation". With rare exceptions, they try not to use radio signals on a relatively low-frequency carrier to transmit information, in particular because of the interference caused by the “reflected lower sideband”. In the same cases when it is necessary to use a low-frequency carrier, as, for example, in magnetic video recording, when transmitting television signals via cable lines, special measures are applied to suppress the "reflected side". When recording videos, they try to increase the carrier’s resting frequency (high bend) and decrease the modulation index. In cable communication lines, when a video signal is transferred to a low-frequency carrier, the lower sideband is partially suppressed, forming a signal of the type of a single-band radio transmission - OR (in the literature there are also the terms "single-band modulation" - OM and "transmission of one sideband" - OBP). Meanwhile, signals on a low-frequency carrier with a pronounced "reflected side" (reflex-modulated signals) have a number of interesting properties. In particular, with a sufficiently low-frequency carrier (the ratio of the sideband to the carrier frequency is much greater than unity), the frequency band occupied by the reflex radio signal in the communication channel approaches the bandwidth of one sideband; the spectrum of a reflex radio signal contains the frequency components of both the upper and lower side, this suggests that the information stored on the high-frequency carrier (two-band radio signal) is stored in the reflex-modulated signal; with a broadband modulating signal containing a constant component (“zero frequencies”), the frequency of the carrier of the reflex-modulated signal can be chosen very low (for example, units of kilohertz with a spectrum width of the modulating signal from zero to units and tens of megahertz), and to perform reflex modulation so low-frequency carrier can be simple technical means; It is impossible in practice to carry out a single-band radio transmission at such ratios between the width of the spectrum of the modulating signal and the carrier frequency, since to suppress the second side, the creation of an almost ideal filter (bandwidth — megahertz, cutoff steepness — tens of decibels per tens of kilohertz) would be necessary, therefore, in real systems communications, for example, in cable communication lines when transmitting television signals, only partial suppression of the sideband is carried out and a carrier frequency of the order of 20-40% of the boundary frequency spectrum of the modulating video signal; in reflex form any kind of amplitude modulation can be easily implemented, including quadrature and angular; to denote them, the terms “reflex amplitude modulation” (PAM), “reflex balance modulation” (RBM), “reflex quadrature modulation” (RCM), “reflex angular modulation” (RUM), including “reflex frequency modulation” (RFM), can be suggested ), "reflex phase modulation" (RFM).

In contrast, a single-band radio transmission is practicable only for amplitude modulation by a single signal (in versions with and without suppression of the carrier), for broadband signals with a constant component only approximately, as indicated above, it is possible to show the theoretical representability of the conversion of a two-band radio signal with a quadrature or angular modulation in two packages of single-band radio signals on a very low-frequency carrier and the subsequent restoration of the original two-band radio signal However, in practice it is possible to implement only when the feasibility of an almost ideal filters and nearly ideal wideband phase shifters (to ensure accurate turning maneuver ^90, nappimep for all components of spektpa hertz or kilohertz to several tens of megahertz and).

 However, in the practice of communication, there are a number of tasks for the solution of which the transfer of broadband signals to a low-frequency carrier is necessary. Such tasks include, in particular, the transmission of image signals along the video path, in which it is difficult to transmit “zero” frequencies (for example, when a DC voltage is supplied in the same communication channel to power equipment, with an increased level of low-frequency interference, including background interference currents of industrial frequency and so on); the formation of complex broadband, for example television signals, with the transmission on a low-frequency carrier simultaneously two independent messages in a standard frequency band; providing signal transmission without demodulation and re-modulation in combined paths containing radio and video frequency links, including, for example, fiber-optic communication lines with analog and digital transmission.

 It was possible to use single-band or type of single-band modulation to solve such problems only in some cases (television in cable lines). The obstacle was either the need for a significant expansion of the frequency band, or the technical complexity, or even the impossibility of practical implementation. Reflex-modulated signals were not used, although they were known. The fact is that, as a rule, such signals were obtained randomly, for example, when a modulated two-band radio signal on a high-frequency carrier was transferred to another carrier frequency by heterodyning, when for some reason the local oscillator frequency was close to the original frequency of the radio signal carrier and it was transferred to low frequency carrier with spectrum folding. Thus, the reflex radio signal itself (although it was not called that way) was known, as well as the methods of its reception (what is called reflex modulation), but since such a signal could be used to transmit useful information (still not were known methods of extracting a modulating signal from a reflex radio signal), then no one purposefully transferred the signal to a low-frequency carrier with spectrum folding.

 The basis of the invention is the creation of a method for transmitting reflex-modulated signal useful information and receiving reflex-modulated signals with the allocation of transmitted information by bringing the spectrum of the reflex-modulated signal to a form that allows you to select a modulating signal from it.

The problem is solved in that in the method for transmitting and receiving reflex-modulated signals according to the invention on the transmitting side, a reflex-modulated signal containing all the frequency components of the upper and lower side bands is formed by modulating the carrier with information signals, the frequency f _of which is less than the difference between the upper and lower boundary frequencies of the unfolded one side band of the reflex-modulated signal, and on the receiving side, the processing of the received reflex-modulated their multiplications by signals with signals representing the sum of the harmonic components of the selected frequency values and phases, and the summation voltages resulting from these multiplications lead reflex-spectrum modulated signal to a form allowing isolated from treated reflex-modulated signal the modulation signal.

It is advisable that in the proposed method, when receiving signals with reflex amplitude modulation, signals with reflex balance modulation, the processing of the received reflex-modulated signals is performed by converting the carrier frequency of the reflex-modulated signal by successively multiplying the reflex-modulated voltages by N harmonic signals, and the frequency i th harmonic signal would be equal
f _o ˙2 ^i-1 , where 1≅i≅N, and a modulated signal with unfolded side bands on the carrier would be detected, the converted frequency f _о ˙2 ^{N of} which would be higher than the upper cutoff frequency of the spectrum of the modulating signal.

(-1)ⁱ sin (2i-1) ω_ot, где ω_o= 2πf_o, 1≅i≅N и осуществляли детектирование модулированного сигнала с развернутыми боковыми полосами на несущей, частота f_o˙2^Nкоторой была бы выше верхней граничной частоты спектра модулирующего сигнала.It is advisable that in the proposed method, when receiving signals with reflex amplitude modulation of signals with reflex balanced modulation, the processing of reflex-modulated signals is performed by converting the frequency f _{o of the} carrier of the reflex-modulated signal by multiplying this reflex-modulated signal with a signal of the form
U (t) =

(-1) ⁱ sin (2i-1) ω _o t, where ω _o = 2πf _o , 1≅i≅N, and a modulated signal with unfolded side bands on the carrier was detected, the frequency f _o ˙ 2 ^{N of} which would be higher than the upper cutoff frequency of the spectrum of the modulating signal.

It is advisable that in this method, when receiving signals with reflex amplitude modulation, signals with reflex balance modulation, the processing of reflex-modulated signals is carried out by converting the frequency f _{about the} carrier of the reflex-modulated signal by N independent multiplications, in each of which this reflex-modulated signal multiplied by a harmonic signal of the form
U (t) = (-1) ⁱ sin [ω _x + ω _o (2i-2)] t, where ω _x = 2πf _x ≥ω _o = 2πf _o , the stresses obtained as a result of all multiplications were summed up, and the modulated a signal with the side sweeps on the carrier, the frequency f _x + f _o x x (2N-1) of which would be higher than the frequency f _x - f _o by an amount greater than the upper cutoff frequency of the spectrum of the modulating signal.

It is also advisable that in this method, when receiving signals with reflex quadrature modulation, signals with reflex angular modulation, joint processing of two sendings of reflex-modulated signals, the carriers of which would have a phase difference Δφ _o ≠ ± Kπ, where K is an integer, by multiplying each of the parcels to the corresponding harmonic signal, and the frequency f _{x of} both harmonic signals would be chosen the same and exceeding the upper boundary frequency of the spectrum of the processed reflex-modulated signal a, and the phase difference of the harmonic signals was chosen equal to π-Δφ _o , the voltages obtained as a result of both multiplications would be algebraically summed, forming a modulated signal with unfolded side signals on the high-frequency carrier f _x ± f _o , and this signal would be detected.

It is advisable that in the proposed method, when receiving signals with reflex quadrature modulation, joint processing of two packages of reflex-modulated signals, the carriers of which would have a phase difference Δφ _o ≠ ± Kπ, where K is an integer, by multiplying one package by a harmonic signal of the form U ₁ (t) = 2 sin 2 π f _o t, another premise - on a harmonic signal of the form U ₂ (t) = 2 sin (2πf _o + π-Δφ _o ) and by algebraic summation of the voltages obtained as a result of both multiplications, were isolated directly one of the modulating signals, and put m multiplication of a parcel to form a harmonic signal U ₃ (t) = 2 cos 2 π f _to t, the other parcel on the harmonic signal of the form U ₄ (t) = 2 cos (2 π f _o t- - Δφ _o) and summing algebraically the voltages obtained as a result of these multiplications, the second modulating signal was isolated directly.

It is advisable that in the proposed method on the transmitting side, when generating signals with reflex amplitude modulation, signals with reflex balance modulation, signals with reflex quadrature modulation, signals with reflex angular modulation, modulation with information carrier signals with a frequency f _{o is} carried out by preliminary modulation with carrier information signals whose frequency f _x would be greater than the difference between the upper and lower boundary frequencies of the unfolded one side strip s of the reflex-modulated signal, generating an intermediate signal with unfolded sidebands, and heterodyning converted this intermediate signal into a reflex-modulated signal at the carrier frequency f _o .

It is advisable that in this method on the transmitting side the formation of signals with reflex amplitude modulation, signals with reflex balance modulation, signals with reflex quadrature modulation is carried out by modulating information signals with a carrier frequency f _about which would be chosen lower than the upper cutoff frequency of the spectrum of the modulating signal . It is also advisable that on the transmitting side the signals with reflex angular modulation are generated by modulating the carrier with information signals, the frequency f _about which would be higher than the upper cutoff frequency of the spectrum of the modulating signal, but less than the difference between the upper and lower cutoff frequencies of the unfolded one side band, required for the selected angle modulation index.

It is advisable that on the transmitting side the formation of signals with reflex angular modulation is carried out by modulating the carrier with information signals, the frequency f _about which was lower than the upper one and did not exceed the carrier frequency deviation at the selected angular modulation index.

In FIG. 1 is an exemplary spectrum view of a reflex modulated signal; in FIG. 2 - the upper side band of the reflex-modulated signal; in FIG. 3 - unreflected part of the lower sideband of the reflex-modulated signal; in FIG. 4- reflected part of the lower sideband of the reflex-modulated signal; in FIG. 5 is a functional diagram of the formation of a reflex-modulated signal with preliminary modulation of the high-frequency carrier f _x and transfer of the intermediate signal to the frequency f _o heterodyning; in FIG. 6 is an exemplary view of the spectrum of an intermediate signal on a high-frequency carrier; in FIG. 7 is a functional diagram of the formation of reflex modulated signals at a carrier frequency f _o by direct modulation; in FIG. 8 is an exemplary spectrum view of a modulating signal; in FIG. 9 is a functional diagram of processing a reflex-modulated signal by sequential multiplication; in FIG. 10 is a functional diagram of processing a reflex-modulated signal by multiplying it with a signal representing the algebraic sum of N harmonic signals; in FIG. 11 is a functional diagram of processing a reflex-modulated signal by N independent multiplications; in FIG. 12 is a functional diagram of the processing of two signal packets with reflex modulation with the formation of a modulated signal at a high frequency; in FIG. 13 is a functional diagram of the processing of two signal bursts with reflex quadrature modulation on a low frequency carrier; in FIG. 14 - the same, when the phase difference of the carrier packages of the signal with reflex quadrature modulation is not equal to ± π / 2; in FIG. 15 is an exemplary view of a complex signal spectrum with angular modulation by one harmonic signal.

 The method of transmitting and receiving reflex-modulated signals is as follows.

On the transmitting side, a reflex-modulated signal is formed, the spectrum of which contains all the frequency components of the upper and lower side bands. The formation of a reflex-modulated signal is carried out by modulating an information signal, for example, a television video signal, with a carrier whose frequency f _o is less than the difference between the upper f _o + f _lim and the lower f _lim -f _{about the} boundary frequencies of the unfolded one side band of the reflex-modulated signal la, where f _lim is the width of the expanded sideband of the reflex-modulated signal, since for the television video signal the lower cut-off frequency is "0". Modulation can be carried out either directly at _the carrier frequency f or by pre-modulation with information signals of the high-frequency carrier f _x .

As a result of pre-modulation, an intermediate signal with unfolded sidebands is generated, which is transferred to the carrier with a frequency f _about heterodyning. The latter process can be carried out, for example, by the functional diagram shown in FIG. 5. Here the information modulating signal E ₁ (t) is supplied to one input of modulator 1, to the other input of which voltage E ₂ (t) is supplied. With amplitude and balanced modulation, E ₂ (t) is a harmonic signal with a frequency f _x , which is the carrier. With angular modulation, E ₂ (t) can also be, for example, the voltage of a harmonic signal to stabilize the quiescent frequency. In quadrature modulation, modulator 1, which, as you know, includes two balanced multipliers and an adder (not shown), respectively, is supplied with two independent information signals and two carrier frequency voltages, the phase difference between which is ± π / 2. At the output of modulator 1, an intermediate signal E ₃ (t) with unfolded sidebands is generated, the spectrum of which is shown in FIG. 6. The intermediate signal E ₃ (t) is fed to the first input of the mixer 2, the second input of which receives a harmonic signal E ₄ (t) with a frequency of f _x + f _о or f _x - f _o . At the output of the mixer 2, as a result of heterodyning, a reflex modulated signal E ₅ (t) appears on the carrier with a frequency f _o , the spectrum of which is shown in FIG. 1.

In the case when the direct reflex modulation is performed without the formation of an intermediate signal E ₃ (t), the voltage of the harmonic signal E ₂ (t), the frequency of which is equal to f _{o, is} supplied to the second input of the modulator 1. At the output of the modulator 1 immediately receive a reflex-modulated signal E ₅ (t). When generating signals with reflex amplitude modulation or signals with reflex balance modulation, or signals with reflex quadrature modulation, the frequency f _o is lower than the upper cutoff frequency f _{max of the} spectrum of the modulating signal, and consequently, less than the difference between the upper and lower cutoff frequencies unfolded one sideband of a reflex modulated signal.

When generating signals with reflex angular, that is, frequency or phase modulation, the frequency f _{o is} chosen below the upper cutoff frequency f _{max of the} spectrum of the modulating signal, and it should also be less than the frequency deviation pi of the selected angular modulation index and, therefore, less than the difference between the upper f _lim + f _o and lower f _{o the} boundary frequencies of the unfolded one side band of the reflex-modulated signal. The generation of signals with reflex angular modulation can also be carried out by modulating the carrier with information signals, the frequency f _about which is chosen above the upper cutoff frequency f _{max of the} spectrum of the modulating signal, but less than the frequency deviation. On the receiving side, reception of the generated reflex-modulated signals is carried out and their processing is performed.

Common to the processing of received reflex-modulated signals generated by any of the types of reflex modulation is that the received reflex-modulated signal E ₅ (t) is multiplied with signals representing the sum of harmonic components. The frequencies and phases of the harmonic components are selected in such a way that when summing the voltages obtained as a result of partial multiplications, the spectrum of the processed reflex-modulated signal is brought to a form that allows the modulating signal E ₁ (t) to be extracted from the processed reflex-modulated signal by known methods. The specific type of processing of reflex-modulated signals depends on the type of reflex modulation of a given reflex-modulated signal. Moreover, for some groups of types of reflex modulation, more than one type of processing is possible, as will be shown below. At the same time, the same type of processing can be applied for several types of reflex modulation, which will also be shown below. The following operations are applicable to convert the spectrum of signals with reflex amplitude modulation or signals with reflex balanced modulation to the spectrum of an amplitude-modulated or, accordingly, balanced-modulated signal with unfolded sidebands.

 1. Reflex-modulated signal processing by sequential multiplication.

t·2cos2

t= 0+E₁(t)sin2ⁱω₀t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E₁(t)sin2

t= 0+E₁(t)sin2^Nω₀t .A functional diagram for implementing such processing of a reflex modulated signal is shown in FIG. 9, it includes N multipliers 3 ₁ , 3 ₂ ,. . . , 3 _i,. . . , 3 _N , where N is an integer, 1≅i≅ N. In each of the multipliers 3 _{i, the} reflex-modulated voltage from the output of the previous multiplier 3 _i-1 is multiplied by a harmonic signal of the form U _i (t) = 2 cos 2 ^{i -1} ω _o t, where ω _o = 2 π f _o . Having written the expression for E ₅ (t) in the form E ₅ (t) = E ₁ (t) sin ω _o t and multiplying it with a harmonic signal 2 cos ω _o t, we obtain E ₅ (t) · 2cosω ₀ t = E ₁ (t) sinω ₀ t · 2cos · ω ₀ t = 0 + E ₁ (t) sin2ω ₀ t E ₁ (t) · sin2ω _with t · 2cos2ω ₀ t = 0 + E ₁ (t) sin4ω ₀ t. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E ₁ (t) sin2

t2cos2

t = 0 + E ₁ (t) sin2 ⁱ ω ₀ t. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E ₁ (t) sin2

t = 0 + E ₁ (t) sin2 ^N ω ₀ t.

Thus, at the output of the multiplier 3 _N , a signal E ₁ (t) sin 2 ^N ω _o t appears, which is a modulated signal with unfolded side bands, since the converted frequency of its carrier is 2 ^N ω _o / 2π = 2 ^N f _o ≥ f _max spectrum of the modulating signal; the spectrum view of this signal at a frequency f _x = 2 ^N f _{o is} shown in FIG. 6. Then carry out the detection of this signal by conventional methods.

A(ω)cos[ωt+φ(ω)] dω где A(ω) и φ(ω) - амплитудный и фазовый спектры сигнала, ω_max= 2πf_max.An example of spectrum conversion of a reflex-modulated signal at the output of a multiplier 3 ₁ . The modulating signal E ₁ (t) has the form
E ₁ (t) =

A (ω) cos [ωt + φ (ω)] dω where A (ω) and φ (ω) are the amplitude and phase spectra of the signal, ω _max = 2πf _max .

A(ω)cos[(ω+ω₀)t+φ(ω)] dω+ +

A(ω)cos[(ω₀-ω)t-φ(ω)] dω+

A(ω)cos[(ω-ω₀)t+φ(ω)] dω
На выходе первого перемножителя 3₁ напряжение будет равно 2E₁(t)cosω₀t·sinω₀t= E₁(t)sin2ω₀t=

A(ω)·sin[(ω+ω₀)t+ +φ(ω)] dω-

A(ω)sin[ωt+φ(ω)] dω+

A(ω)sin[(2ω₀-ω)t-φ(ω)] dω+ +

A(ω)sin

[ωt+φ(ω)] dω+

A(ω)sin[ωt+φ(ω)] dω+

+

A(ω)sin[(2ω₀-ω)t-φ(ω)] dω-

Как следует из приведенного выше выражения, в процессе перемножения происходит суммирование напряжений отдельных компонент частотного спектра. Причем суммирование в одной группе слагаемых дает в сумме нуль, а суммирование в другой группе слагаемых - действующее значение. Аналогично осуществляются преобразования спектра рефлексно-модулированного сигнала в последующих умножителях 3₂ - 3_N. Таким образом, в каждом умножителе 3_i частота f_о несущей удваивается и спектр полностью "разворачивается", когда 2^N ω_o≥ω_max.When ω _o <ω _max (case for reflex balanced modulation) E ₅ (t) = 2E ₁ (t) cosω ₀ t =

A (ω) cos [(ω + ω ₀ ) t + φ (ω)] dω + +

A (ω) cos [(ω ₀ -ω) t-φ (ω)] dω +

A (ω) cos [(ω-ω ₀ ) t + φ (ω)] dω
At the output of the first multiplier March ₁ voltage will be equal to 2E ₁ (t) cosω ₀ t · sinω ₀ t = E ₁ (t) sin2ω t = ₀

A (ω) · sin [(ω + ω ₀ ) t + + φ (ω)] dω-

A (ω) sin [ωt + φ (ω)] dω +

A (ω) sin [(2ω ₀ -ω) t-φ (ω)] dω + +

A (ω) sin

[ωt + φ (ω)] dω +

A (ω) sin [ωt + φ (ω)] dω +

+

A (ω) sin [(2ω ₀ -ω) t-φ (ω)] dω-

As follows from the above expression, in the process of multiplication, the stresses of the individual components of the frequency spectrum are summed. Moreover, the summation in one group of terms gives a total of zero, and the summation in another group of terms gives the effective value. Similarly, transformations of the spectrum of the reflex-modulated signal are carried out in subsequent multipliers 3 ₂ - 3 _N. Thus, in each multiplier 3 _{i, the} carrier frequency f doubles and the spectrum completely “unfolds” when 2 ^N ω _o ≥ω _max .

 2. Processing a reflex-modulated signal by multiplying by the sum of the harmonic signals.

(-1)ⁱ sin(2i-1) ω_o t, представляющим собой сумму гармонических составляющих.The processing of the received reflex-modulated signals is performed by converting, as in the case described above, the frequency f _{o of the} carrier of the reflex-modulated signal E ₅ (t). This is achieved by multiplying this reflex-modulated signal E ₅ (t) with a signal of the form
U (t) =

(-1) ⁱ sin (2i-1) ω _o t, which is the sum of the harmonic components.

(-1)ⁱ sin(2i-1) ω_o t, поступающий на один вход перемножителя 3, на другой вход которого поступает рефлексно-модулированный сигнал Е₅(t). В перемножителе 3 осуществляется их перемножение 2E₅(t)·U(t)= E₁(t)cosω₀t

(-1)ⁱsin(2i-1)ω₀t= E₁(t)·sin2Nω₀t
В перемножителе 3 одновременно осуществляется и суммирование частотных составляющих, как следует из приведенного выше выражения.A functional diagram for implementing this type of reflex modulated signal processing is shown in FIG. 10, where each i-th input of adder 4 receives a harmonic signal of the form (-1) ⁱ x хsin U (t) =

(-1) ⁱ sin (2i-1) ω _o t supplied to one input of the multiplier 3, the other input of which receives a reflex-modulated signal E ₅ (t). In the multiplier 3, they are multiplied 2E ₅ (t) · U (t) = E ₁ (t) cosω ₀ t

(-1) ⁱ sin (2i-1) ω ₀ t = E ₁ (t) sin2Nω ₀ t
In the multiplier 3, the summation of the frequency components is simultaneously carried out, as follows from the above expression.

выше верхней граничной частоты f_max спектра модулирующего сигнала Е₁(t), то обе боковые полосы модулированного сигнала на частоте f_o 2^N несущей развернуты (подобно приведенному процессу для последовательного умножения), и детектирование его может быть произведено известными методами.Since the converted carrier frequency f _o 2 ^N = 2 ^N

above the upper cutoff frequency f _{max of the} spectrum of the modulating signal E ₁ (t), then both side bands of the modulated signal at the carrier frequency f _o 2 ^{N are} deployed (similar to the above process for sequential multiplication), and its detection can be performed by known methods.

 3. Processing a reflex-modulated signal by N independent multiplications.

On the receiving side, the processing of signals with reflex amplitude modulation and signals with reflex balance modulation is performed by converting the frequency f _{o of the} carrier of the reflex-modulated signal. This is done by N independent multiplications of the reflex-modulated signal E ₅ (t) with a harmonic signal of the form
U _i (t) = (-1) ⁱ sin [ω _x + ω _o (2i-2)] t, where ω _x = 2πf _x ≥ω _o = 2πf _o .

This operation is carried out by means of a functional circuit in which a reflex modulated signal E ₅ (t) is supplied to the first inputs of N multipliers 3 ₁ -3 _N , and corresponding harmonic signals U ₁ (t) are supplied to the second inputs of these multipliers 3 ₁ -3 _N = -sin (ω _x t), U ₂ (t). . . U _N (t) of the form U _i (t) above.

The output of each multiplier 3 _i removes voltage
2E ₅ (t) · U _i (t) = 2E ₁ (t) cosω ₀ t (-1) ⁱ sin [ω _x + ω ₀ (2i-2)] t = = 2E ₁ (t) · (-1 ) ⁱ sin [ω _x + ω ₀ (2i-3)] t + 2E ₁ (t) (- 1) ⁱ sin [ω _x + ω ₀ (2i-1)] t.

-(2N-5)ω₀] t} +

+(2N-3)ω₀] t} + = E₁(t)(-1)^Nsin[ω_x+(2N-1)ω₀] t
В процессе перемножения и суммирования осуществляют разворачивание спектра рефлексно-модулированного сигнала, получая модулированный сигнал с развернутыми боковыми полосами на частоте несущей f_x + f_o (2N-1), превышающей частоту f_x - f_o на величину, большую, чем верхняя граничная частота f_max спектра модулирующего сигнала, и детектируют его известными способами. Все три изложенных выше процесса обработки рефлексно-модулированных сигналов позволяют привести спектр преобразованного рефлексно-модулированного сигнала к описанному выше виду с развернутыми боковыми полосами, позволяющему выделить из обработанного рефлексно-модулированного сигнала модулирующий сигнал, то есть полезную информацию, известными методами. При приеме сигналов с рефлексной квадратурной модуляцией производят совместную обработку двух принятых посылок сигналов с рефлексной квадратурной модуляцией, причем их несущие имеют разность фаз Δφ≠±Kπ , где К - целое число. Функциональная схема, в которой осуществляют обработку сигналов с рефлексной квадратурной модуляцией, представлена на фиг. 12. На вход перемножителей 3₁ и 3₂ поступают посылки сигналов с рефлексной квадратурной модуляцией, например,
E_5-1(t) = E_1-1(t) cos ω_o t + E_1-2(t) sin ω_o t;
E_5-2(t) = E_1-1(t) cos(ω_ot+Δφ_o ) +
+ E_1-2(t) sin(ω_ot+Δφ_o ), где Е_1-1(t) - первый информационный сигнал и Е_1-2(t) - второй информационный сигнал, поступающие на передающей стороне на вход модулятора 1, ω_o= 2πf_o.In the adder 4 summarizes the output voltage N of the multipliers 3 ₁ -3 _N
E ₅ (t) · U ₁ (t) = E ₁ (t) · [-sin (ω _x -ω ₀ ) t-sin (ω _x + ω ₀ ) t] + E ₅ (t) · U ₂ ( t) = E ₁ (t) · [sin (ω _x + ω ₀ ) t + sin (ω _x + 3ω ₀ ) t] + E ₅ (t) · U ₃ (t) = E ₁ (t) · [ -sin (ω _x + 3ω ₀ ) t-sin (ω _x + 5ω ₀ ) t]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- (2N-5) ω ₀ ] t} +

+ (2N-3) ω ₀ ] t} + = E ₁ (t) (- 1) ^N sin [ω _x + (2N-1) ω ₀ ] t
In the process of multiplication and summing, the spectrum of the reflex-modulated signal is expanded, obtaining a modulated signal with unfolded sidebands at the carrier frequency f _x + f _o (2N-1), exceeding the frequency f _x - f _o by an amount greater than the upper cutoff frequency f _{max the} spectrum of the modulating signal, and detect it by known methods. All three of the above processes for processing reflex-modulated signals make it possible to bring the spectrum of the converted reflex-modulated signal to the form described above with unfolded sidebands, which makes it possible to extract a modulating signal from the processed reflex-modulated signal, i.e., useful information, by known methods. When receiving signals with reflex quadrature modulation, the two received packets of signals with reflex quadrature modulation are jointly processed, and their carriers have a phase difference Δφ ≠ ± Kπ, where K is an integer. A functional diagram in which signal processing with reflex quadrature modulation is performed is shown in FIG. 12. At the input of the multipliers 3 ₁ and 3 ₂ received sending signals with reflex quadrature modulation, for example,
E _5-1 (t) = E _1-1 (t) cos ω _o t + E _1-2 (t) sin ω _o t;
E _5-2 (t) = E _1-1 (t) cos (ω _o t + Δφ _o ) +
+ E _1-2 (t) sin (ω _o t + Δφ _o ), where E _1-1 (t) is the first information signal and E _1-2 (t) is the second information signal received on the transmitting side at the input of the modulator 1, ω _o = 2πf _o .

The second input of the multiplier 3 ₁ receives a harmonic signal U ₁ (t) = 2 cos ω _x t, and the input of the multiplier 3 ₂ receives a harmonic signal U ₂ (t) = 2 cos (ω _x t + + π-Δφ _o ) . The frequencies ω _{x of} both harmonic signals are the same and exceed the upper cutoff frequency f _o + f _{lim of the} spectrum of the reflex-modulated signal. The phase difference of the harmonic signals is equal to π-Δφ _o .

The output of the multiplier 3 ₁ is removed voltage
E _5-1 (t) U ₁ (t) = E _1-1 (t) x
x [cos (ω _x -ω _o ) t + cos (ω _x + ω _o ) t] +
+ E _1-2 [-sin (ω _x -ω _o ) t + sin (ω _x -ω _o ) t].

The output of the multiplier 3 ₂ is removed voltage
E _5-2 (t) · U ₂ (t) = E _1-1 (t) [cos (ω _x t-ω ₀ t + Π + 2Δφ ₀ ) + cos (ω _x t + ω ₀ t + Π) ] +
+ E _1-2 [sin (ω _x t-ω ₀ t + Π-Δφ ₀ ) + sin (ω _x t + ω ₀ t + Π)]
From the outputs of the multipliers 3 ₁ and 3 _{2, the} voltages E _5-1 (t) ˙U ₁ (t) and E _5-2 (t) ˙U ₂ (t) go to the inputs of the adder 4, where they are algebraically summed, as a result of which the output of the adder 4 appears voltage
E ₆ (t) = E _5-1 (t) ˙ U ₁ (t) + E _5-2 (t) ˙ U ₂ (t) =
= 2E _1-1 (t) ˙ cos [(ω _x -ω _o ) t + π / 2 - Δφ _o ] x
x cos (π / 2 - Δφ _o ) -2E _1-2 sin [(ω _x -ω _o ) t +
+ π / 2 - Δφ _o ] cos (π / 2 - Δφ _o ).

Thus, the formation of a modulated signal with unfolded side bands on a high-frequency carrier f _x - f _o = (ω _x -ω _o ) / 2. This modulated signal is then detected by conventional methods. The joint processing of two signal packets with reflex quadrature modulation, the carriers of which have a phase difference Δφ _o ≠ Kπ, can also be carried out directly at f _x = f _o . In FIG. 13 is a functional diagram of the processing of packets of a reflex-modulated signal. The first package E _5-1 (t) of the reflex-modulated signal is supplied to the first inputs of the multipliers 3 ₁ and 3 ₃ . The second package E _5-2 (t) is supplied to the first inputs of the multipliers 3 ₂ and 3 ₄ . The second inputs of the multipliers 3 ₁ , 3 ₂ , 3 ₃ and 3 ₄ respectively receive harmonic signals
U ₁ (t) = 2 sin 2 π f _o t,
U ₂ (t) = 2 sin (2 πf _o t + π-Δφ _o ),
U ₃ (t) = 2 cos 2 π f _o t and
U ₄ (t) = 2 cos (2 πf _o t + π-Δφ _o ).

Assuming that 2 πf _o = ω _o , imagine the voltage at the outputs of the multipliers 3 ₁ , 3 ₂ , 3 ₃ , 3 ₄ . At the output of the multiplier 3 ₁
E _5-1 (t) ˙U ₁ (t) = E _5-1 (t) ˙2 sin ω _o t =
= E _1-1 (t) sin 2 ω _o t + E _1-2 (t) - E _1-2 (t) cos 2ω _o t.

At the output of the multiplier 3 ₂ E _5-2 (t) ˙U ₂ (t) = E _5-2 (t) 2 sin (2 πf _o + π-Δφ _o ) = E _5-2 (t) sin (ω _o t + π-Δφ _o ) = = E _1-1 (t) sin (π-2Δφ _o ) + E _1-1 (t) sin (2 ω _o t + π) + + E _1-2 (t) cos (π-2Δφ _o ) - E _1-2 (t) cos (2 ω _o t + π).

) = 1, sin ( π - 2

) = 0.The stresses obtained as a result of multiplications in the multipliers 3 ₁ and 3 ₂ are algebraically summed in the adder 4 ₁ , obtaining E _1-2 (t) cos (π-2Δφ _o ) + E _1-1 sin (π-2Δφ _o ), then there is at the output of the adder 4 _{1 the} modulating signal E _1-2 (t) immediately appears at Δφ _o = π / 2, since
cos (π - 2

) = 1, sin (π - 2

) = 0.

At the output of the multiplier 3 ₃ we have a signal whose voltage is
E _5-1 (t) U ₃ (t) = E _1-1 (t) +
+ E _1-1 (t) cos 2 ω _o t + E _1-2 sin 2 ω _o t.

At the output of the multiplier 3 ₄ similarly we obtain a signal whose voltage is
E _5-2 (t) ˙ U ₄ (t) = E _1-1 (t) cos (π-2Δφ _o ) +
+ E _1-1 (t) cos (2 ω _o t + π) -
-E _1-2 (t) sin (π-2Δφ _o ) +
+ E ₁ (t) sin (2 ω _o t + π).

The voltages obtained at the outputs of the multipliers 3 ₃ and 3 ₄ are algebraically summed in the adder 4 ₂ , obtaining E _1-1 (t) cos (π-2Δφ _o ) - E _1-2 (t) sin (π-2Δφ _o ), that is, at the output of the adder 4 _{2 the} second modulating signal E _1-1 (t) is directly extracted at Δφ _o = π / 2.

In the event that Δφ _o differs from π / 2, then the signals received from the outputs of the adders 4 ₁ and 4 ₂ in the additional adders 4 ₃ and 4 _{4 are} additionally algebraically summed. Thus, in this case, the processing operations of the reflex-modulated signals and detection are combined. When receiving signals with reflex angular modulation, it is possible to process them as described above with reference to FIG. 12 for the case of signals with reflex quadrature modulation. In this case, joint processing of two received signal packets with reflex angular modulation, the carriers of which have a phase difference Δφ _o ≠ Kπ, is performed. Since the mathematical expressions for the frequency and phase spectra with angular modulation are rather cumbersome, we give a simplified description of the processes. In FIG. Figure 15 shows the complex spectrum for angular modulation of a high-frequency carrier by one harmonic signal with a frequency of Ω. In this spectrum, the amplitude of the nth side component is equal to a _n = U _o I _n (m), that is, for a given modulation index m is proportional to | I _n (m) | , where I _n (m) is the first-order Bessel function of the nth order of the argument m, U _o is the amplitude of the modulating signal. The odd upper and lower side components are in antiphase, and even in-phase. The first input of the multiplier 3 ₁ receives a reflex-modulated signal E _5-1 (t), the second input is a harmonic signal U ₁ (t) = 2 sin ω _x t. At the output of the multiplier 3 ₁ a signal appears - the result of the multiplication - E _5-1 (t) ˙U ₁ (t). Similarly, the reflex modulated signal E _5-2 (t) and the harmonic signal U ₂ (t) = 2 sin (ω _x t + π-Δφ _o ) are respectively supplied to the first and second inputs of the multiplier 3 ₂ .

The output of the multiplier 3 ₂ removes the voltage E _5-2 (t) ˙U ₂ (t).

The voltage from the outputs of the multipliers 3 ₁ and 3 _{2 is} supplied to the inputs of the adder 4. We describe this process in more detail.

= (-1)ⁿa_ncos[(ω_x-ω₀)t+

-Δφ₀-nΩt]
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The signal at the output of the adder 4

= (-1) ⁿ a _n cos [(ω _x -ω ₀ ) t +

-Δφ ₀ -nΩt]
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

-Δφ₀-4Ωt]
-a₃cos[(ω_x-ω₀)t+

-Δφ₀-3Ωt]
+a₂cos[(ω_x-ω₀)t+

-Δφ₀-2Ωt]
-a₁cos[(ω_x-ω₀)t+

-Δφ₀-Ωt]
+a₀cos[(ω_x-ω₀)t+

-Δφ₀]
+a₁cos[(ω_x-ω₀)t+

-Δφ₀+Ωt]
+a₂cos[(ω_x-ω₀)t+

-Δφ₀+2Ωt]
+a₃cos[(ω_x-ω₀)t+

-Δφ₀+3Ωt]
+a₄cos[(ω_x-ω₀)t+

-Δφ₀+4Ωt]
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .+ a ₄ cos [(ω _x -ω ₀ ) t +

-Δφ ₀ -4Ωt]
-a ₃ cos [(ω _x -ω ₀ ) t +

-Δφ ₀ -3Ωt]
+ a ₂ cos [(ω _x -ω ₀ ) t +

-Δφ ₀ -2Ωt]
-a ₁ cos [(ω _x -ω ₀ ) t +

-Δφ ₀ -Ωt]
+ a ₀ cos [(ω _x -ω ₀ ) t +

-Δφ ₀ ]
+ a ₁ cos [(ω _x -ω ₀ ) t +

-Δφ ₀ + Ωt]
+ a ₂ cos [(ω _x -ω ₀ ) t +

-Δφ ₀ + 2Ωt]
+ a ₃ cos [(ω _x -ω ₀ ) t +

-Δφ ₀ + 3Ωt]
+ a ₄ cos [(ω _x -ω ₀ ) t +

-Δφ ₀ + 4Ωt]
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

-Δφ₀+nΩt]
Полученный сигнал имеет спектр, аналогичный спектру сигнала с угловой модуляцией на высокочастотной несущей, и отличается лишь сдвигом по частоте на величину ω_o и по фазе на величину π/2-Δφ_o , то есть осуществлено преобразование сигнала с рефлексной угловой модуляцией в сигнал с угловой модуляцией на высокочастотной несущей, который детектирует известными приемами, получая модулирующий сигнал.+ a _n cos [(ω _x -ω ₀ ) t +

-Δφ ₀ + nΩt]
The received signal has a spectrum similar to the spectrum of a signal with angular modulation on a high-frequency carrier, and differs only in frequency shift by ω _o and in phase by π / 2-Δφ _o , that is, a signal with reflex angular modulation is converted into a signal with angular modulation on a high-frequency carrier, which is detected by known techniques, receiving a modulating signal.

 The proposed method for transmitting and receiving a reflex-modulated signal has several advantages compared to the known methods for transmitting and receiving information of technology and communication. Thus, in comparison with the known methods for transmitting and receiving broadband signals on a relatively low-frequency carrier with a partially suppressed lower sideband, reflex modulation allows the use of a carrier whose frequency can be several orders of magnitude lower than the difference between the upper and lower boundary frequencies of one sideband.

 The technical implementation, formation and reception of reflex-modulated signals with broadband modulating signals, the spectrum of which contains "zero" frequencies, do not cause such technical difficulties as when generating and receiving signals of a single-band radio transmission. Due to the preservation of the frequency components of the upper and lower side components in the spectrum of the reflex-modulated signal, it does not have the quadrature component present in the signals of single-band transmission and reception, therefore, the error in the phase of the reconstructed carrier of the reflex-modulated signal does not lead to distortions in the selection of the modulating signal, in contrast what happens in this case when receiving signals of a single-band radio transmission. In addition, no methods were known for transmitting simultaneously two signals (quadrature modulation), signals with angular modulation on a relatively low-frequency carrier, since with these types of modulation even partial suppression of one sideband is unacceptable.

 Compared with the transmission of quadrature modulated signals and angular modulated signals at high frequencies, the reflex-modulated signal occupies a frequency band in the communication channel that is almost equal to the width of one side band. This is due to the equivalent exchange of bandwidth during transmission. The operation of completely exchanging the frequency band for the transmission time for wideband signals with quadrature and angular modes of modulation on a high-frequency carrier, although theoretically possible, is not feasible in practical terms due to the impossibility of implementing filters with an infinitely steep or almost infinitely steep slice of the frequency response. As a rule, when transmitting signals with quadrature modulation at a carrier frequency equal to or slightly greater than the difference between the upper and lower side frequencies, a significant obstacle to its reception and demodulation is the presence of phase distortion in the modulated signal band, so they try not to use this type of transmission. On the contrary, with reflex quadrature modulation and reflex angular modulation, unevenness of the phase-frequency characteristic almost equally affects the upper and lower sidebands, especially at a low carrier frequency, that is, there is practically no crosstalk between modulating signals when demodulating reflex quadrature modulated signals, and there are also no distortion during demodulation of signals with reflex angular modulation.

 It is known that cross-sectional distortions between modulating signals during quadrature modulation, as well as distortions of the emitted signals during angular modulation of a high-frequency carrier, occur when the amplitude-frequency characteristics (AFC) of the communication channel are irregular, leading to spurious attenuation of one side band. When transmitting signals with reflex quadrature modulation and signals with reflex angular modulation on a low-frequency carrier, the frequency response of the communication channel can lead to almost the same limitation of both the upper and lower side bands, which is equivalent to a symmetric limitation of the side bands of signals with quadrature modulation and signals with angular high frequency carrier modulation. Such restrictions do not impede the complete separation of signals during quadrature modulation; they create less distortion during angular modulation.

cos(ω_xt+ϑ_N) где a(t) и b(t) - модулирующие сигналы с полосой частот Δf каждый, Р_N - мощность "белого" шума в полосе частот Δf, ω_x= 2πf_x, f_x - высокочастотная несущая, Ψ_N - шумовая фаза.The noise immunity of reflex-modulated signals is not inferior to noise immunity when transmitting video signals or balanced-modulated signals with two side signals on a high-frequency carrier. So, for example, with quadrature modulation on a high-frequency carrier
a (t) cosω _x t + b (t) sinω _x t +

cos (ω _x t + ϑ _N ) where a (t) and b (t) are modulating signals with a frequency band Δf each, Р _N is the power of white noise in the frequency band Δf, ω _x = 2πf _x , f _x - high-frequency carrier, Ψ _N - noise phase.

The frequency band of the communication channel when transmitting such a quadrature modulated signal is f _x ± Δf, the power of the "white" noise in this frequency band is 2P _N.

cosϑ_N, поскольку в общем случае принято считать среднее значение Ψ_N равным π/4, cos Ψ_N = = 0,707 и отношение сигнала к шуму на выходе фильтра низких частот в канале выделения модулирующего сигнала a(t) составит

.When the modulating signal a (t) is extracted by the method of synchronous detection, the total signal and noise voltage equal to the signal and noise equal to
a +

cos ϑ _N , since in the general case it is customary to consider the average value Ψ _N equal to π / 4, cos Ψ _N = = 0.707, and the signal-to-noise ratio at the output of the low-pass filter in the channel of selection of the modulating signal a (t) will be

.

With reflex quadrature modulation of a low-frequency carrier, the frequency of which is f _o << Δf, the frequency band of the communication channel when transmitting such a reflex-modulated signal is ≈Δf.

, где ω_o= 2πf_o.The first package of the reflex-modulated signal and noise voltage in the communication channel
a (t) cosω ₀ t + b (t) sinω ₀ t +

where ω _o = 2πf _o .

причем напряжения шумов в первой и второй посылках статистически независимы.
Напряжения сигнала и шумов в канале выделения сигнала а(t)
a(t)+

cosω₀t-

sinω₀t= a(t)+

sin(ω₀t+ϑ_N)
Мощность шума в канале выделения сигнала a(t) составляет
2P

cos²(ω₀t+ϑ_N)dϑ= P_N отношение сигнал-шум -

.The second premise of a reflex-modulated signal and noise voltage in a communication channel
a (t) sinω ₀ t + b (t) cosω ₀ t +

moreover, the noise voltage in the first and second premises is statistically independent.
Signal voltage and noise in the channel selection signal a (t)
a (t) +

cosω ₀ t-

sinω ₀ t = a (t) +

sin (ω ₀ t + ϑ _N )
The noise power in the signal isolation channel a (t) is
2P

cos ² (ω ₀ t + ϑ _N ) dϑ = P _N signal-to-noise ratio -

.

 Thus, the advantages of the proposed method for transmitting and receiving reflex-modulated signals are not accompanied by a weakening of noise immunity.

 The following are the applications of the method of receiving and transmitting reflex-modulated signals in various communication systems.

 The most obvious are the transmission of broadband signals along the video path, in which there is a high level of low-frequency noise, including interference from industrial frequency currents, as well as the simultaneous transmission of low-frequency voltages with the signal to power the equipment (long-distance cable communication lines). The application of the method allows in this case to exclude from the signal zero frequencies on the transmitting side and to effectively suppress low-frequency interference at the receiving side by the filtering method.

 Another area of application is in combined paths consisting of series-connected radio-frequency, video-frequency and fiber-optic communication lines. In such paths, the application of the proposed method allows avoiding repeated intermediate detection, repeated modulation and, accordingly, distortions of the information signal during these operations.

 Another area of application of the method of transmitting and receiving reflex-modulated signals is the creation of complex multifunctional signals in various radio engineering and television systems, for example in color television systems, stereo color television and high-definition television systems.

Claims (10)

1. A METHOD FOR TRANSMITTING AND RECEIVING REFLEX-MODULATED SIGNALS, which consists in the fact that on the transmitting side a reflex-modulated signal is formed by modulating the carrier with information signals, the frequency f _{0 of} which is less than the difference between the upper and lower boundary frequencies, and on the receiving side the received signal is multiplied with the sum of harmonic signals and demodulate the received signal. 2. The method according to p. 1, characterized in that when receiving signals with reflex amplitude modulation, the multiplication of the received signal is carried out by sequentially multiplying the reflex-modulated signal by N harmonic signals, the frequency of the i-th harmonic signal being equal to f ₀ ^2i-1 , where 1 <i <N, and demodulation is carried out on a carrier whose converted frequency is f ₀ · 2N above the upper cutoff frequency f _{max of the} spectrum of the modulating signal. 3. The method according to p. 1, characterized in that when receiving signals with reflex amplitude and reflex-balance modulations, the multiplication of the received reflex-modulated signals is carried out by multiplying the reflex-modulated signal with a signal of the form
U _i (t) =

(-1) ⁱ sin (2i-1) ω ₀ t,
where ω ₀ = 2πf ₀ ;
1 <i <N,
and demodulation is carried out on a carrier 2Nf ₀ , the frequency of which is higher than the upper cutoff frequency f _{max of the} spectrum of the modulating signal E ₁ (t). 4. The method according to p. 1, characterized in that when receiving signals with reflex-amplitude and reflex-balance modulation, the multiplication of the received reflex-modulated signals is carried out with a harmonic signal of the form
U _i (t) = (-1) ⁱ sin [ω _x + ω ₀ (2i-2)] t,
where ω _x = 2πf _x ≥ω ₀ = 2πf ₀ ,
multiplied signals are summed, and demodulation is performed on a carrier whose frequency f _x + f ₀ (2N - 1) is higher than the frequency f _x - f ₀ by an amount greater than the upper cutoff frequency f _{max of the} spectrum of the modulating signal E ₁ (t). 5. The method according to p. 1, characterized in that when receiving signals with reflex-quadrature modulation, signals with reflex-angular modulation, multiplying each of the received reflex-modulated signals, the carriers of which have a phase difference Δφ + Kπ, where K is an integer are carried out with harmonic signals of the same frequency of the form ω _x = 2πf _k > ω ₀ and the multiplied signals are algebraically summed. 6. The method according to p. 1, characterized in that when receiving signals with reflex quadrature modulation, the multiplication of the received reflex-modulated quadrature signals is performed with harmonic signals of the form U ₁ (t) = 2sin2πf ₀ t and U ₂ (t) = 2sin (2πf ₀ t + π-Δφ ₀ ), respectively, and the received signals are summed and multiplied by reflex modulated quadrature with harmonic signals of the form U ₃ (t) = 2cos2πf ₀ (t) and U ₄ (t) = 2cos2πf ₀ t + π-Δφ _0, respectively and the received signals are summed. 7. The method according to PP. 1 - 6, characterized in that on the transmitting side when generating signals with reflex-amplitude modulation with reflex-balance modulation, reflex-quadrature modulation, reflex-angular modulation with information carrier signals with a frequency f _{0 is} produced by modulation with carrier information signals, frequency f _to which is greater than the difference between the upper and lower cutoff frequencies, and heterodyning are converted into a reflex-modulated signal at a carrier frequency f ₀ . 8. The method according to PP. 1-4 and 6, characterized in that on the transmitting side the formation of signals with reflex-amplitude modulation, reflex-balanced modulation, reflex-quadrature modulation is carried out by modulating the carrier with information signals, the frequency f _{0 of} which is selected less than the upper cutoff frequency f _{to the} spectrum of the baseband signal. 9. The method according to PP. 1 and 5, characterized in that on the transmitting side the formation of signals with reflex-angular modulation is carried out by modulating information signals with a carrier frequency f ₀ , the frequency of which is higher than the upper cutoff frequency f _{x of the} spectrum of the modulating signal, but less than the difference between the upper and lower boundary frequencies of one side cavity of a reflex-modulated signal necessary for the selected angular modulation index. 10. The method according to PP. 1 and 5, characterized in that on the transmitting side, the formation of signals with reflex-angular modulation is carried out by modulating with information signals a carrier whose frequency f ₀ is lower than the upper cutoff frequency f _{x of the} spectrum of the modulating signal and does not exceed the carrier frequency deviation at the selected index and angular modulation.

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