WO2006003031A1

WO2006003031A1 - Method and device for mixing digital radio signals

Info

Publication number: WO2006003031A1
Application number: PCT/EP2005/007994
Authority: WO
Inventors: Michel Robbe; Roland Stoffel
Original assignee: Eads Secure Networks
Priority date: 2004-07-02
Filing date: 2005-06-22
Publication date: 2006-01-12
Also published as: FR2872649B1; FR2872649A1

Abstract

A digital output signal of central frequency (f- fo) of maximum amplitude Smax is produced by mixing a digital input signal of central frequency (f), comprising a real input component and an imaginary input component, with a digital mixing signal of central frequency (fo), comprising a real mixing component and an imaginary mixing component each providing eight values of amplitude per period of the mixing signal. The mixing components are decomposable into a plurality of pulses (52, 53, 54) whose amplitude values are determined on the basis of two integers selected from among integer values which satisfy, to within a predefined error, an equation of cancellation of the harmonic component of rank 3 of the mixing signal and which minimize the maximum amplitude Smax of the output signal.

Description

METHOD AtTD DEVICE FOR MIXING DIGITAL RADIO SIGNALS

The present invention relates to the processing of a radio signal and more particularly to a frequency mixer for the processing of a radio signal having two quadrature components.

Frequency mixers are frequently used in radio signal receivers, in particular. Specifically, conventionally, in radio receivers, radio signals centred on a transmission frequency, denoted f_τ, are received and are transposed around an intermediate frequency, denoted f_τ, that is lower than the transmission frequency, before processing these signals. For this purpose, a frequency mixer using a transposition frequency, denoted f₀, provided by a local oscillator is used. These frequencies conventionally satisfy the following equation:

f_τ = fi + fo.

It is noted that a receiver can receive two frequencies that are symmetric with respect to one another relative to the frequency of oscillation of the local oscillator. Thus, the receiver can receive the frequency f_τ = fi + f₀ and the frequency f_τ = £χ - f_o. Now, such a radio signal possesses a priori components at the frequency fi+f_o as well as components at the image frequency fi - f₀. Consequently, the reception of the radio signal at the transmission frequency may be disturbed by the reception of the radio signal at the image frequency fi - f₀. In order to avoid such disturbances during the extraction of the signal at the desired transmission frequency, generally such frequency mixers are mixers having image frequency rejection which make it possible to filter the undesired image frequency.

Such a mixer generally comprises an input for receiving the signal to be mixed as well as a signal generator for generating a mixing signal. It also comprises one or more multipliers so as to carry out frequency transpositions-

The signal obtained at the output of the mixer is a signal of intermediate frequency. It may thereafter be processed.

Such mixers can mix analogue signals or digital signals. A mixer of digital signals generally comprises a digital mixing signal generator. The latter can provide a digital signal obtained by sampling an analogue mixing signal. The maximum amplitude of the signal at the output of such a mixer is dependent on the maximum amplitude of the digital input signal to be mixed and of the maximum amplitude of the digital mixing signal. Consequently, the number of bits used for the binary coding of the output signal, that is to say the binary output format of the mixer, is dependent on the binary format of the digital mixing signal provided by the generator as well as on the , binary format of the digital input signal to be mixed.

A drawback of such systems is the binary output 'format of the mixer. Specifically, the larger the binary format, the more complex and hence costly in terms of computation time is the processing of the signal obtained at the output of the mixer. This results in particular in sizeable energy consumption which may raise problems in particular in embedded systems for which one seeks to reduce this consumption.

Another drawback of these mixers is that the harmonic components of the mixing signals used in such systems may substantially disturb the mixed signal.

The present invention aims to alleviate these drawbacks. For this purpose, the invention proposes a mixer of digital radio signals for producing a digital output signal of central frequency (f- f_o) by mixing a digital input signal of central frequency f, comprising a real input component and an imaginary input component, with a digital mixing signal of central frequency f_o, comprising a real mixing component and an imaginary mixing component each providing eight values of amplitude per period of the mixing signal.

The digital output signal of maximum amplitude S_maχ comprises a real output component and an imaginary output component.

The mixer comprises: means arranged for providing a first intermediate signal by mixing the real input component with the real mixing component; means arranged for providing a second intermediate signal by mixing the imaginary input component with the imaginary mixing component;

- means arranged for providing a third intermediate signal by mixing the imaginary input component with the real mixing component; - means arranged for providing a fourth intermediate signal by mixing the real input component with the imaginary mixing component; means arranged for providing the real component of the output signal by appending the first and second intermediate signals; means arranged for providing the imaginary component of the output signal by appending the third and fourth intermediate signals.

The mixer is characterized in that each of the mixing components is decomposable into a plurality of pulses whose amplitude values are determined on the basis of two integers selected from among integer values which satisfy on the one hand, to within a predefined error, an equation of cancellation of the harmonic component of rank 3 of the mixing signal and which on the other hand minimize the maximum amplitude S_max of the output signal.

^■ 5

The present invention is therefore aimed at determining the amplitude of the quadrature analogue mixing signal so that it makes it possible to reduce the maximum amplitude of the digital signal at the output of the

10 generator. Consequently, the format of the binary coding of the amplitude of the digital signal at the output of the mixer may be reduced and thereby the processing of this mixed signal may be simplified. Such an amplitude of the analogue mixing signal is thus

15 determined while substantially reducing the harmonics of the digital mixing signal. Harmonics of higher rank being of lower amplitude than the harmonics of lower rank, an embodiment of the invention aims to substantially cancel the harmonic of rank 3.

20

In an embodiment of the present invention, one of the components of the mixing signal is decomposed into three periodic pulses respectively determined over one and the same period by: S

25 - a first pulse of amplitude of value (X-Y) 'during 2*ττ/4, then of value 0 during 6*τr/4; a second pulse of amplitude of value 0 during 4*π/4 then of value -(X-Y) during 2*π/4 then of value 0 during 2*ττ/4; and

30 a third pulse of amplitude of value Y during 3*τr/4 then of value -Y during 4*π/4, then of value Y during rr/4, where X and Y are nonzero integers.

35 The equation of cancellation of the harmonic component of rank 3 may then be as follows:

in which X is equal to the value of maximum amplitude of the components of the mixing signal. The two integers X and Y may be respectively 169 and 70; and the maximum amplitude of the digital output signal may then be equal to E_max* (169+70) , where E_max is the maximum amplitude of the input signal.

In another embodiment of the present invention, the amplitudes of the real and imaginary components of the digital mixing signal are determined on the basis of a calculation of sampling of an analogue signal at instants t corresponding respectively to 0, ττ/4, ττ/2, 3π/4, TT, 5ττ/4, 3ττ/2, 7ττ/4 to reduce the number of calculations.

In this case, one of the digital mixing components may be decomposed into four periodic pulses respectively determined over one and the same period by: a first pulse of amplitude of value M during

3*ττ/4, and of value 0 during 5*ττ/4; a second pulse of amplitude of value 0 during 4*ττ/4 then of value -M during 3*π/4 then of value 0 during ττ/4;

- a third pulse of amplitude of value 0 during ττ/4, then of value N during ττ/4 then of value 0 during

6*π/4; and - a fourth pulse of amplitude of value 0 during

5*ττ/4, then of value -N during τr/4, then of value 0 over 2*ττ/4, where M and N are nonzero integers, and the equation of cancellation of the harmonic component of rank 3 may be as follows:

the sum of the integers M and N may then correspond to the value of maximum amplitude of the components of the mixing signal.

The two integers M and N may be respectively 169 and

70; and the maximum amplitude of the digital output signal may then be equal to E_max* (169+169) , where E_max is the maximum amplitude of the input signal. Regardless of the embodiment of the present invention, the integer values which satisfy the equation of cancellation of the harmonic of rank 3 of the mixing signal may be determined on the basis of a series of numbers A_n, for n integer greater than or equal to 2, satisfying the following characteristic: An/An-2 converges to (1+V2) .

The series of numbers A_n may then satisfy, for i strictly positive, the following equations:

A₂ = A₁ * ( 1+ V2 /2 ) ;

A₃ = A₂ * V2 ; A_2i = A_2i-₂ + A_2i-i,

A₂i₊i = A₂± + A₂i_2, and also satisfy that the ratio of two consecutive numbers converges alternately to V2 and (1+V2/2) .

Other aspects, aims and advantages of the invention will become apparent on reading the description of one of its embodiments.

The invention will also be better understood wijth the aid of the drawings, in which: '

Figure 1 illustrates the known principle of a mixer having image frequency rejection; Figure 2 is a diagram of the frequency spectrum of an exemplary input signal; - Figure 3 illustrates the quadrature analogue components of the mixing signal that are generated by the mixing signal generator as well as the digital mixing components arising from a sampling of these analogue mixing components in an embodiment of the invention;

Figure 4 illustrates an exemplary waveform of the digital mixing components of Figure 2, as well as an exemplary decomposition of this waveform into a plurality of pulses, in accordance with an embodiment of the present invention;

Figure 5 illustrates the quadrature analogue components of the mixing signal that are generated by the mixing signal generator as well as the digital mixing components arising from a sampling of these analogue mixing components in an embodiment of the present invention;

Figure 6 illustrates an exemplary waveform of the digital mixing components of Figure 4, as well as an exemplary decomposition of this waveform into a plurality of pulses, in accordance with an embodiment of the present invention;

Figure 7 illustrates a multiplier of the mixer in an embodiment of the present invention; - Figure 8 illustrates a multiplier of the mixer in an embodiment of the present invention.

The present invention proposes a method of mixing radio signals for generating a digital signal at the output of the generator making it possible to reduce the binary format, having regard to the number of bits used for the binary coding of the digital input components to be mixed, while minimizing the harmonic components of the digital mixing components.

Figure 1 illustrates a mixer having image frequency rejection according to an embodiment of the present invention. The mixer comprises four multipliers, 104-107, two adders 108 and 109, and a digital generator 101 comprising a real digital mixing component and an imaginary digital mixing component at outputs 112 and 113. In an embodiment of the present invention, the amplitude values of these digital mixing components are calculated on the basis of a sampling of an analogue signal comprising two quadrature components, of amplitude G and of frequency f₀. It is noted that the digital mixing signal generator may not generate such an analogue signal. In an embodiment of the present invention, a digital signal to be processed by the mixer having image frequency rejection is in the form of a real digital input component and an imaginary digital input component to be mixed. Preferably, the amplitude values of each of the digital input components are calculated on the basis of a sampling of an analogue signal having two quadrature components, of amplitude E and of frequency f. These digital inputs components to be processed enter the mixer having image frequency rejection by two inputs 102 and 103 respectively.

In an embodiment of the present invention, the digital generator 101 provides a real digital mixing component and an imaginary digital mixing component, whose amplitude values are calculated by sampling of an analogue mixing signal having two quadrature sinusoidal components of frequency fo. The multiplier 104 receives

^■ as input the real digital input component to be processed as well as the imaginary digital mixing component so as to provide at the output 116 a first intermediate signal. The multiplier 105 receives as input the imaginary digital component to be processed as well as the imaginary digital mixing component! so as to provide at the output 117 a second intermediate signal. The multiplier 106 receives as input the imaginary digital component to be processed as well as the real digital mixing component so as to provide at the output 114 a third intermediate signal. The multiplier 107 receives as input the real digital component to be processed as well as the imaginary digital mixing component so as to provide at the output 115 a fourth intermediate signal. Then, the first and second intermediate signals are processed by the adder 108 so as to provide at the output 110 a real component of the digital output signal of the mixer. The third and fourth intermediate signals are processed by the adder 109 so as to provide at the output 111 an imaginary component of the digital output signal of the mixer.

In an embodiment of the present invention, such a mixer is advantageously implemented at the output of a bandpass sigma-delta modulator. Thus, the digital input signal to be processed by the mixer having band rejection corresponds to the output signal of a sigma-delta modulator.

Conventionally, the absolute values of the amplitudes of the digital components of the output signal of a sigma delta and therefore the digital input components 102 and 103 of the mixer having image rejection, are quantized on a given number of bits, a sign being associated with these bits.

The number of bits used for the coding of the digital signal at the output of the mixer, or else the binary format of the digital signal at the output of the mixer, is dependent on the binary format of the digital input components and on the binary format of the digital mixing components. Hereinafter, the binary format of the digital input components is fixed at 4 bits associated with a sign. This binary input signal format of the mixer is taken merely by way of example, the present invention covering embodiments in which the binary format of the digital input signal is different.

In such frequency mixers having image frequency rejection, the digital mixing components generated at the outputs 112 and 113 of the generator are generally coded on 13 bits associated with a sign.

The purity of the digital output signal is limited by the products of the mixings of the undesirable frequencies of the spectrum of the input signal with the harmonic components of the signal of the generator 101. The even harmonics of such signals are zero on account of the symmetry about the origin. For illustration, by way of explanatory example, when the input signal of the mixer originates from a bandpass sigma-delta modulator, the shaping of the quantization noise in the band of the signal equals substantially -73 dB.

Figure 2 is a spectral representation of a signal/noise ratio of a signal as a function of frequencies. The even harmonic components of the signal are zero. In order that the harmonic component 202 of rank 3 should not disturb the fundamental component 201 of the signal of frequency f, the difference Δ between the signal/noise ratio of the fundamental component of the signal 201 and the signal/noise ratio of the harmonic component 202 of rank 3 is preferably greater than a threshold value of 83 dB, corresponding to the sum of 73 dB and of 10 dB.

In order not to degrade the output signal of the mixer having image rejection, the signal/noise ratio of the harmonic components of the generator 101 is consequently preferably less than a threshold! value defined equal to -83 dB. \

It is conventionally considered that the processing by mixing involves a signal/noise ratio of 6 dB and that each quantization bit of the mixing signal' also involves a signal/noise ratio of 6 dB. Consequently the processing of a mixer according to the invention, comprising the quantization and the mixing of a signal, involves a signal/noise ratio obtained through the following equation:

-6*13-6 = -84 dB.

Therefore, the noise of such mixers is less than the previously defined threshold value of -83 dB. Taking as reference example, an input signal quantized on 4 bits associated with a sign, the intermediate signals in the mixer are quantized on 17 bits associated with a sign. In such a context, so as to avoid overflows at the output of the adders, the outputs 108 and 109 of the mixer having image rejection are therefore conventionally quantized on 18 bits associated with a sign.

In order to increase the purity of the digital output signal, the mixer used is a mixer having image frequency rejection and the amplitude of the mixing signal is determined in such a way as to reduce the harmonic components of the mixing signal.

Moreover, in order to reduce the number of bits necessary for the coding of the components of the digital output signal, in an embodiment of the invention, the binary format, i.e. the number of quantization bits, of the digital mixing components generated by the generator 101 is reduced.

As described previously, in an embodiment of the present invention, the amplitudes of the digital mixing components generated by the generator 101 are calculated on the basis of a sampling of an analogue mixing signal having two quadrature components, of amplitude G and of frequency f₀, a real component G cos 2πfot and an imaginary component G sin 2ττfot. Such a sampling is advantageously performed at a frequency 8 times greater than the frequency of the analogue mixing signal. Therefore, a digital mixing component exhibits eight values of amplitude per period of the mixing signal.

In an embodiment of the present invention, a sampling of the two quadrature components of the analogue mixing signal is carried out at the instants corresponding respectively to the values calculated for cosine and sine of 0, ττ/4, ττ/2, 3π/4, π, 5ττ/4, 3π/2, 7ττ/4, as Figure 3 illustrates. In such a sampling method, for each of the digital mixing signals, the amplitude is equal to zero twice per period of the analogue mixing signal. This characteristic of the digital mixing components makes it possible to minimize the number of calculations in the mixer.

Figure 3 illustrates such a sampling of an analogue mixing signal having in quadrature a first sinusoidal component illustrated by the curve 21 and a second sinusoidal component illustrated by the curve 22.

The first digital mixing component resulting from this sampling, the real mixing component, takes the following values over a half period of the analogue mixing signal [0; π] :

G; (V2 /2) * G;0; (Λ/2 / 2) * G .

The second digital component resulting from this sampling, the imaginary mixing component, simultaneously takes the following values over the same half period of the analogue mixing signal: \

0; (V2 /2) * G;G;(V2 /2) * G.

The waveform of the real digital mixing component and the imaginary digital mixing component is identical. The even harmonics of such signals are zero on account of the symmetry about the origin.

In an embodiment of the present invention, in order to substantially reduce the odd harmonics of the digital mixing components, the waveform of a digital mixing component is decomposed into a sum of four pulses as illustrated by Figure 4. The curve 31 illustrates the waveform of a digital mixing component. Then_/ the waveform 31 is decomposed into the sum of a first pulse 32, denoted A, of a second pulse 33, denoted B, of a third pulse 34, denoted C, and of a fourth pulse 35, denoted D. The first pulse A takes over a period equal to 2ττ successively a value M during 3*ττ/4, and the value 0 during 5*π/4. The second pulse takes over the period successively the value 0 during 4*π/4 then a value -M during 3*π/4 then the value 0 during ττ/4. The third pulse takes over the period successively the value 0 during τr/4, then a value N during τr/4 then the value 0 during 6*π/4. Lastly, the fourth pulse takes over the period successively the value 0 during 5*ττ/4, then a value -N during π/4, then the value 0 over 2*ττ/4.

The maximum amplitude of the waveform is denoted M+N, where M and N are positive integers. In this case, the maximum amplitude of the waveform corresponds to the amplitude, denoted G, of the analogue mixing signal of the generator 101. We therefore obtain a first equation: G=M+N. (1)

A harmonic decomposition of a centred periodic pulse P of amplitude E and of width 2kπ may be written in the form of the following equation:

P=E* [k+2/ττ* (sin kπ cos x + ^*sin 2kπ cos 2x + l/3*sin 3kπ cos 3x...+ l/n*sin nkπ cos nx) ] .

By applying this harmonic decomposition to the pulses previously described 32, 33, 34 and 35 we obtain the decompositions in the form of the following results. 8 πl 8 2 8 3 8 /i V o /

C ~ N i + -[sin-cos(x)+-sin^cos2(x) + -sin-^cos3(x)... + -sin ~ cosn(κ)

8 πl 8 V 8 ;

It is noted that by adding together the results of the decompositions A, B, C and D, the continuous component is cancelled out . Moreover, the sampling by a Dirac makes it possible to ignore the harmonics of higher order than the Nyquist half band.

Thus , the fundamental component, denoted F, may be written in the form of the following equation :

F=4/ττ [M sin3π/8 + N sin τr/8 ] . I

The harmonic of rank 3, denoted H3, may be written in the form of the following equation: '

H3 = 4/3π[M sin9ττ/8 + N sin3π/8]=4/3π [N sin3π/8-M sin ττ/8] .

Consequently, an equation which cancels the harmonic component of rank 3 of the digital mixing signals is determined:

M/N = [sin3π/8]/[sin ττ/8] .

Then, the following noteworthy identity is used:

. Therefore, we obtain a second equation making it possible to cancel the harmonic component of rank 3 of the digital mixing signals which may thus be written:

The second equation is therefore dependent on the amplitudes of the pulses denoted M and N.

We then determine integers, M and N, substantially satisfying this second equation. Such integers substantially satisfy equation (2) of cancellation of the harmonic component of rank 3, that is to say with an error. In an embodiment of the invention, an error is defined. Then, among the integers substantially satisfying the equation to within the predefined error, we select those which minimize the amplitude of the output signal of the mixer.

The maximum amplitude S_max of the signal at the output of the mixer corresponds to the maximum amplitude of the input signal E_max multiplied by the maximum of the sum of the amplitudes of the simultaneous mixing components.

Thus, the binary format of the digital output signal can be reduced for a binary format of the given digital input signal while reducing the harmonic components of the mixing signal.

In order to determine integers which are solutions to this second equation and therefore determine values of M and N so as to cancel the harmonic of rank 3 of the digital mixing components, we introduce hereinbelow series of numbers exhibiting advantageous characteristics for solving the equation for cancelling, the harmonic component of rank 3 (2) . After having thus determined the values of M and N, it is easy to deduce the value of the amplitude G of the analogue mixing signal through the first equation, as defined previously, and therefore deduce the maximum amplitude of the digital output signal of the mixer.

The objective of the section hereinafter is to provide integers which substantially satisfy equation (2) . The present invention covers any other procedure making it possible to obtain integers substantially satisfying this equation.

By using recursive and additive properties of the numbers v2 and l+v2; we construct series for which the ratio of two consecutive numbers converges alternately

Specifically, a following recursive property is noted:

A following additive property is moreover noted:

It is thus possible to obtain a series of numbers whose construction satisfies the following equations: '

This series of numbers may also be written in the following form:

A_O,A_I,A₂,A₃=A_O(1+Λ/2/2)+A₂,A₄=A₂+A₃,...,

A2n⁼A2n-2+A2n-i ; A2n+l=A2n + A2n-2- •

Specifically, the following equations are obtained, for n greater than or equal to 1:

) ; then A_2n+I=A_2n-I+ V2 *A_2n-i=A2n-l+A2n-2 ; thereafter

A₂n+l=A₂n-2 ( V2 + 1 ) +A_2n-2 ; and therefore

and finally A_2n+I=A_2n-I (1+V2 /2) +A_2n-2 = A_2n + A_2n-₂.

A characteristic of such a series of numbers is that the ratio of two non-consecutive numbers spaced a number apart in the series, or else the ratio A_n/A_n_₂, converges to the value (1+V2) .

By taking as initial numbers ^'of the series:. Ao=2.

Ai=3. ^■

We obtain the following series of integers: 2,3,5,7,12,17,29,41,70,99,169,239....

The table hereinbelow indicates in a first row the integers of this series.

It indicates in a second row, the result of the adjacent ratio, or else the result of the ratio A_n+i/A_n, for n a positive integer.

A third row indicates the result of the bi-adjacent ratio, that is to say the result of the ratio A_n+2/A_n, for n a positive integer.

Then finally, a fourth row indicates the error of this latter ratio relative to the value of (1+-/2), that is to say the error with respect to the equation for cancelling the harmonic component of rank 3(2) .

Table1

Table1

By taking other initial numbers, we easily construct other series. Other examples of such series are described in the tables hereinbelow.

Table 2

Table3

Such series, per pair of numbers, exhibit a rate of convergence equal to (l+v2)², once the error is less than 1/10.

Furthermore, regardless of the numbers taken at the outset of the construction of such a series, the ratio of two non-consecutive numbers spaced an element apart converges to 1+V2.

The series of numbers of presented in table 1 makes it possible to obtain a ratio of two non-consecutive numbers spaced an element apart which converges more quickly to 1+4Ϊ than the other series presented in the other^' tables. Specifically, with such a series, the convergence error corresponding to the value 70 is of the order of 0.00017, while in table 2, the error corresponding to the value 65 is of the order of 0.0028. Now, to reduce the binary format of the first and second digital mixing components and therefore reduce the binary format of the output signal of the mixer, we seek a compromise between on the one hand good convergence of the ratio of the two values of amplitude of the pulses, denoted M and N to be determined, to (l+v2), so as to reduce the harmonic components of rank 3 of the digital mixing signals, and on the other hand values which make it possible to reduce the binary format of the digital signal at the output of the mixer. In addition to the series described previously, series of integers are moreover known which are solutions of the following PELL equation:

X² - 2 Y²=±l.

Thus, two such series are respectively referenced (Sloane's, A000129) and (Sloane's, A001333) . Such series are obtained by the use of continuous fractions. It is also possible to determine integers which substantially satisfy equation (2) on the basis of such series.

It is noted that the series of integers which are solutions of the PELL equation differ from those described previously as to their construction.

Moreover, regardless of the starting numbers for constructing the series previously described, we obtain a series of ratio of integers converging to 1+V2 as detailed in a previous section, this not being the case for series of integers which are solutions of the PELL equation. _{

Thus, in an embodiment of the present invention,! a set of integer values which satisfy, to within a predefined error, the equation for cancelling the harmonic component of rank 3 of the mixing signal is selected.

Then from among this set of integer values are selected the two integers M and N, determining the amplitudes of the pulses, which make it possible to minimize the maximum amplitude S_maχ of the output signal.

Thus, in a preferred embodiment of the invention, the values 70 and 169 are selected, for which good convergence to 1+V2 of the ratio is obtained and whose sum equal to 239, corresponding to the amplitude G via the equation (1) , remains a relatively low value for an amplitude G of the analogue mixing signal. By introducing an error, denoted ε, we obtain the following equation:

We then calculate the fundamental, denoted F, as a function of the value N according to the following equation: F=3.378N.

We also obtain the harmonic of rank 3 as a function of N and of ε according to the following equation: H3=0.3921 ε N.

Consequently the ratio of the harmonic of rank 3 to the fundamental may be written as a function of ε according to the following equation: H3/F=0.1037 ε.

Thus, when the integer values of M and N are solutions of the equations determined previously, the harmonic of rank 3 is very substantially reduced.

When N is equal to 70 and M is equal to 169, we obtain the value of the amplitude of the analogue mixing signal G, whose components 21 and 22 are in quadrature, according to the following equation: G=M+N=239.

According to the preceding equations, the following results are obtained: M/N=2.414286; ε = 0.00003; H3/F=-110 dB.

The latter result is less than the threshold value defined previously.

These values of M and N therefore make it possible to very substantially reduce the harmonics of rank 3. The first digital mixing component therefore takes successively the following values over a quarter of a period of the signal: 239; 169.

Simultaneously, the second digital input component takes successively the following values over the same quarter of a period of the signal: 0; 169.

From this we deduce that the maximum value of the amplitude of the digital signal at the output of the mixer having image rejection is attained when the first and second digital signals simultaneously take the value 169.

Thus, for a digital input signal in the mixer having image rejection having a maximum amplitude value, denoted E_max, we obtain at the output of the mixer, a maximum digital signal amplitude, denoted S_max, according to the following equation:

In an example taken as reference, the value of E_max is

I considered to be equal to 15. We then obtain a value of

S_max equal to 5070. Such a value may be coded on 13 bits. Therefore such a signal may be coded 13 bits associated with. a sign.

In conclusion, by taking an analogue mixing signal having quadrature components of amplitude equal to 239, and sampled as described previously, we are able to reduce the binary format of the digital signal at the output of the mixer while very substantially reducing the harmonic components of the mixing signal. In the example taken as reference, a reduction of this binary format of 5 bits is obtained. In another embodiment of the present invention, a sampling of the two quadrature components of the analogue mixing signal is carried out at the instants corresponding respectively to the values calculated for cosine and sine of ττ/8, 3ττ/8, 5π/8, n, 7ττ/8, 9ττ/8, llτr/8, 13π/8 and 15ττ/8. Such a sampling method makes it possible to reduce the maximum value of the amplitude of the digital mixing signal with respect to the amplitude of the analogue mixing signal. As is detailed hereinbelow, the maximum amplitude of the digital signal at the output of the mixer is reduced with respect to the previous embodiment of the present invention. Consequently, the binary format of the output signal can also be reduced.

Figure 5 illustrates such a sampling of an analogue mixing signal having a first sinusoidal component illustrated by the curve 41 and a second sinusoidal component illustrated by the curve 42.

The first digital component resulting from this sampling takes the following values over a quarter of a period of the analogue mixing signal, corresponding to [0, ττ/2] :

G cos(ττ/8); G cos(3τr/8) .

The second digital component resulting from this sampling simultaneously takes the following values over the same quarter of a period of the analogue mixing signal:

G cos(3π/8); G cos(3π/8) .

The even harmonics of such signals are zero on account of the symmetry about the origin. In order to reduce the odd harmonics of the digital mixing signal, the digital mixing signal is decomposed into a sum of three pulses as illustrated by Figure 6. The curve 51 illustrates the waveform of the digital mixing components. The maximum amplitude of the waveform, denoted X, corresponds to the amplitude of the analogue signal of the generator 101, multiplied by cos(ττ/8) . We therefore obtain a first equation:

G = X/cos(ττ/8) (I¹)

Then, the waveform 51 is decomposed into a first pulse 52, denoted A, a second pulse 53, denoted B, and a third pulse 54, denoted C. The first pulse takes over a period successively a value (X-Y) during 2*ττ/4, and the value 0 during 6*π/4. The second pulse takes over the period successively the value 0 during 4*π/4 then a value - (X-Y) during 2*π/4 then the value 0 during

2*ττ/4. Finally, the third pulse takes over the period successively a value Y during 3*π/4 then a value -Y during 4*ττ/4, then the value Y during ττ/4, where X and

Y are nonzero integers.

The harmonic decomposition of a square centred pulse of amplitude E may be written:

A harmonic decomposition of a centred periodic pulse P of amplitude E and of width 2kπ is:

P=E* [k+2/ττ* (sinkπ cosx + ^*sin2kπ cos2x + l/3*sin3kπ cos3x...+l/n*sinnkπ cosnx) ] .

By applying these harmonic decompositions to the pulses 52, 53 and 54, we obtain the following results.

C = ~ M COS(Λ:)---COS3(Λ:)+ ~COS5(JC) — cos7(*)+... π ^ 3 5 7

We note that by adding together the results of the decompositions A, B and C, the continuous component is cancelled out. Moreover, the sampling by a Dirac makes it possible to ignore the harmonics of higher order than the Νyquist half band.

Thus, the fundamental, denoted F, can be defined by the following equation:

[1-4Ϊ/2] ]

COSX.

The harmonic of rank 3, denoted H3, is defined by the following equation: H3 = 4/3π [(X-Y) sin3π/4 cos3x - Y cos3x]= 4/3π [X Λ/2/2 - Y (1+V2 /2) ] cos3x.

The harmonic 3 is cancelled through the following equation:

X/Y = 1 + VI. (2')

The values X and Y therefore satisfy the same equation as the values M and Ν of equation (2) obtained previously.

Consequently, the same series of integers as those presented previously make it possible to determine values which substantially satisfy equation (2'). In a preferred embodiment of the present invention, the values 70 and 169 are selected for the same reasons as those stated previously.

By introducing an error, denoted ε, we^' obtain the following equation:

We then calculate the fundamental as a function of the value Y according to the following equation: F=2.546Y.

We also obtain the harmonic of rank 3 as a function of Y and of ε according to the following equation:

H3=0.723 ε Y.

Consequently the ratio of the harmonic of rank 3 to the fundamental may be written as a function of ε according to the following equation: H3/F=0.284 ε.

Thus, when the values of X and of Y substantially satisfy the equations previously determined;, the harmonic of rank 3 and therefore the odd harmonjics of higher rank are very substantially reduced. '

When Y is equal to 70 and X is equal to 169, and according to the previous equations, the following results are obtained: X/Y=2.414286; ε=0.00003; H3/F=-101.4 dB.

This latter result is less than the threshold value equal to -83 dB defined previously.

These values of X and Y therefore make it possible to very substantially reduce the harmonics of rank 3 and of higher rank. The first digital mixing component successively takes the following values over a quarter of a period of the signal corresponding to [0;τr/2] :

169;169.

Simultaneously, the second digital mixing component takes successively the following values over the same quarter of a period of the signal:

-70;70.

From this we deduce that the maximum value of the amplitude of the digital signal at the output of the mixer having image rejection is attained when the first and second digital components simultaneously take the respective values 169 and 70.

S_max=(169+70) *E_max

In an example taken as reference, the value of E_max is regarded as equal to 15. We then obtain a value of S_max equal to 3585. Such a value can be coded on 12 bits. Therefore such a signal can be coded on 12 bits associated with a sign.

In conclusion, by taking a sinusoidal analogue mixing signal of amplitude equal to 169/cos(π/8) and by performing a sampling as described previously to obtain a maximum amplitude of the digital mixing component equal to 169, we are able to reduce the binary format of the digital output signal. In the example taken as reference, we obtain a reduction of this binary format of 6 bits.

The present invention covers embodiments in which other values satisfying equations (2) and (2') are chosen.

It is noted that the values 169 and 70 are advantageously selected in such a mixer for the reasons stated previously and also for reasons of ease of calculations in the mixer in the course of the multiplications of signals, as is detailed hereinbelow.

Specifically, using such numbers, partial multipliers are advantageously implemented. The binary expression for the number 70, 001000110 has the advantage of comprising a large number of 0 relative to the total number of bits. Figure 7 illustrates a partial multiplier advantageously implementing the binary expression for the number 70. Specifically, it is possible to embody, as illustrated in Figure 7, a partial multiplier by 70 with two adders each having an output on four bits.

Consider the binary input format denoted: \ E₃E₂EiE₀

We can multiply this binary format by 70, by processing each bit equal to 1 of the binary format of 70. Such a multiplication is thus decomposed as described hereinbelow.

We firstly shift the binary input format by 1: E₃E₂EiE₀O.

Then we shift the binary input format by 2: E₃E₂EiE₀OO.

And finally, we shift the binary input format by 6:

E₃E₂EIE₀OOOOOO.

The adder 61 taking as input:

E₃E₂EiE₀OE₃E₂Ei provides as output: E₃(E₃ + E₂) (E₂ + Ei) (Ei + E₀) . Then the adder 62 taking as input: E₃E₂E_IE₀OOO provides as output E₃E₂EiE₀•

The inputs 63 and 64 make it possible to manage overflows.

One thus obtains an output on 11 bits which may be written in the following form: E₃E₂EiE₀E₃(E₃ + E₂) (E₂ + E_x) (Ei + E₀) .E₀O.

This result corresponds to a multiplication of E₃E₂EiE₀ by 70.

Then, the binary expression for the number 169, 010101001, also exhibits a sizeable number of 0 relative to the total number of bits. Figure 8 illustrates a partial multiplier advantageously implementing the binary expression for the number 169. Such a multiplier may advantageously be embodied with three adders, 71, 72, 73 having an output on 4 bits.

An embodiment of the present invention may be implemented in an embedded receiver of radio signals. Specifically, the binary format at the output of such a mixer being substantially reduced, the processing of the signal thus obtained is easier and less expensive to achieve. Thus, such a receiver can exhibit greater autonomy in terms of energy.

Moreover, the harmonics of the mixing signal are very appreciably reduced, thereby helping to reduce the disturbances introduced by a mixing method.

Claims

1. Mixer of digital radio signals for producing a digital output signal of central frequency (f- f_o) by mixing a digital input signal of central frequency (f), comprising a real input component (102) and an imaginary input component (103) , with a digital mixing signal of central frequency (f_o)^ comprising a real mixing component (112) and an imaginary mixing component (113) each providing eight values of amplitude per period of said mixing signal; said digital output signal of maximum amplitude S_max comprising a real output component (110) and an imaginary output component (111) ; said mixer comprising: means arranged for providing a first intermediate signal (116) by mixing said real input component (102) with said real mixing component (112) ; means arranged for providing a second intermediate signal (117) by mixing said imaginary input component (103) with said imaginary mixing component (113); - means arranged for providing a third intermediate signal (114) by mixing said imaginary input component (103) with said real mixing component (112) ; J - means arranged for providing a fourth intermediate signal (115) by mixing said real input component (102) with said imaginary mixing component (113) ; means arranged for providing said real component (110) of the output signal by appending said first and second intermediate signals; means arranged for providing said imaginary component (111) of the output signal by appending said third and fourth intermediate signals; characterized in that each of said mixing components is decomposable into a plurality of pulses (52, 53, 54) whose amplitude values are determined on the basis of two integers selected from among integer values which satisfy, to within a predefined error, an equation of cancellation of the harmonic component of rank 3 of said mixing signal and which minimize said maximum amplitude S_maχ of the output signal.

2. Mixer according to Claim 1, in which the amplitudes of the real (112) and imaginary (113) components of the digital mixing signal are determined on the basis of a calculation of sampling of an analogue signal, having a real component and an imaginary component, at instants t corresponding respectively to ττ/8, 3π/8, 5ττ/8, 7π/8, 9ττ/8, llττ/8, 13π/8, 15ττ/8.

3. Mixer according to Claim 2, in which one of the components of the mixing signal is decomposed into three periodic pulses (52, 53, 54) respectively determined over one and the same period by: a first pulse (52) of amplitude of value (X-Y) during 2*ττ/4, then of value 0 during 6*ττ/4; a second pulse (53) of amplitude of value 0 during 4*ττ/4 then of value -(X-Y) during 2*ττ/4 then of value 0 during 2*ττ/4; and a third pulse (54) of amplitude of value Y during 3*ττ/4 then of value -Y during 4*ττ/4, then of value Y during ττ/4, where X and Y are nonzero integers; in which the equation of cancellation of the harmonic component of rank 3 is as follows: X/Y = 1+V2; and in which X is equal to the value of maximum amplitude of the components of the mixing signal.

4. Mixer according to Claim 3, in which the two integers X and Y are respectively 169 and 70; and in which the maximum amplitude of the digital output signal is equal to E_max* (169+70) , where E_max is the maximum amplitude of the input signal.

5. Mixer according to Claim 1, in which the amplitudes of the real (112) and imaginary (113) components of the digital mixing signal are determined on the basis of a calculation of sampling of an analogue signal at instants t corresponding respectively to 0, ττ/4, ττ/2, 3π/4, rr, 5π/4, 3π/2, 7ττ/4 to reduce the number of calculations.

6. Mixer according to Claim 5, in which one of the digital mixing components is decomposed into four periodic pulses (32, 33, 34, 35) respectively determined over one and the same period by: a first pulse (32) of amplitude of value M during

3*ττ/4, and of value 0 during 5*rr/4; a second pulse (33) of amplitude of value 0 during

4*ττ/4 then of value -M during 3*ττ/4 then of value 0 during ττ/4; a third pulse (34) of amplitude of value 0 during ττ/4, then of value N during π/4 then of value 0 during

6*τr/4; and a fourth pulse (35) of amplitude of value 0 during 5*π/4, then of value -N during π/4, then of value 0 over 2*π/4, where M and N are nonzero integers, in which the equation of cancellation of the harmonic component of rank 3 is as follows:

and in which the sum of the integers M and N corresponds to the value of maximum amplitude of the components of the mixing signal.

7. Mixer according to Claim 6, in which the two integers M and N are respectively 169 and 70; and in which the maximum amplitude of the digital output signal is equal to E_max* (169+169) , where E_max is the maximum amplitude of the input signal.

8. Mixer according to any one of the preceding claims, in which the integer values which satisfy the equation of cancellation of the harmonic of rank 3 of the mixing signal are determined on the basis of a series of numbers A_n, for n integer greater than or equal to 2, satisfying the following characteristic: An/An-2 converges to (1+V2).

9. Mixer according to Claim 8, in which the series of numbers A_n satisfies, for i strictly positive, the following equations:

A₃ = A₂ * V2;

A2i = A21-2 + A₂I-I,

and in which the ratio of two consecutive numbers converges alternately to V2 and (1+V2/2) .