EP1253512A1 - Method and apparatus for generating a random signal with controlled histogram and spectrum - Google Patents

Abstract

Method and device for generating a random signal comprising: a first step (a) of generating a pseudo-random signal, a second step (b) of filtering (F1) the signal from step (a) to obtaining a signal x (t) having a predetermined spectral envelope H (f), a third step (c) where a non-linear function g is applied to the signal x (t) so as to form a signal y (t) and for create lifts or overshoots on the edges of the histogram of signal y (t), a fourth filtering step (d) (F2) making it possible to smooth the lifts or overshoots of the histogram of signal y (t), to compensate the effect of non-linearity and to perform a complementary filtering at (F1). Application in an analog-digital or digital-analog conversion system <IMAGE>

Description

The present invention relates to a method and a device for generation of a random signal. The invention is particularly applicable to digital-analog conversion domain and the domain of analog-to-digital conversion using such a random system.

It applies for example in the field of radar techniques or in that of instrumentation or in the field of communications.

Conversion devices, whether digital-analog or analog-digital are very widely used in many systems and their performance are usually a critical point of these, as illustrated by direct digital synthesis.

Direct digital synthesis is a synthesis technique of frequency which consists in working out in numerical values the samples of a signal that we want to generate and convert these samples into signals analog thanks to a digital-analog converter. The signal synthesizers obtained by this technique are very attractive in regarding their volume, weight and energy consumption, because they can benefit from significant integration. Their other advantages include a very high resolution and switching times very low from one frequency to another. However, passing a useful signal in the digital-to-analog converter is accompanied by the creation of parasitic signals which are due to the non-linearities of these converters. These non-linearities denote the fact that the stairs of the function of transfer from digital to analog converter are not equal heights and that the transition between steps produces phenomena irregular.

The same problem is found in applications based on analog to digital converters where the passage of signals in these converters is also accompanied here by the creation of spurious signals due to non-linearities.

It is known in the prior art to add a random signal to the signal useful, before going through the converter, in order to reduce the level of spurious signals by reducing the effect of converter non-linearities previously mentioned. This random signal is commonly referred to as the English term “dither”. The useful signal is generally band limited and the system clock frequency, for example a synthesizer digital, is generally greater than this band. That leaves a empty spectral space to place the random signal.

To be fully effective, this random signal must have certain characteristics. First, its spectrum must be controlled for that it does not encroach on useful signals in the band. Second, it appears that the quality of the linearization of the converters depends on the histogram of the temporal amplitudes of the random signal. For example, a Gaussian law produces a poorer linearization than that obtained by a rectangular law. There is therefore a real advantage in being able to control for the random signal both the spectrum and the histogram.

Methods are known for obtaining a random signal with a given spectral envelope. Methods are also known for obtaining a random signal with a law of distribution of the amplitudes given. These methods are notably described in the works dealing with the calculation of probabilities such as for example the work entitled:
"Deterministic simulation of chance" by J. Maurin, Masson editions.

Applicant's patent FR 2,783,374 teaches a process and a device for generating a random signal. He describes a method allowing to build a random signal where the spectral envelope and the law distribution of the temporal amplitudes are imposed simultaneously. For this, the method implements a series of four steps or signal processing operations, repeating part of them, especially steps 3 and 4 making the signal parameters converge random to the desired laws. The iteration of the stages makes it possible to approach gradually set the distribution law, then correct the envelope spectral.

Despite all its effectiveness, this iterative method is not suitable for all types of calculation, especially for time calculation real random signal. It involves the use of different non-linear functions to restore the histogram aimed at each iteration.

The idea of the invention is based on a new approach which allows to calculate, in real time, a random signal with a spectral envelope predetermined and a histogram of amplitudes close to a law rectangular, that is to say evenly distributed.

In the following description, we designate under the expression "Useful signal" means the signal which one wishes to convert without distortion by a CNA or CAN. To this end, the random signal or noise which is generated by the device according to the invention is added to this useful signal so as to linearize the transfer characteristic of the CNA or CAN.

• une première étape (a) de génération d'un signal pseudo-aléatoire,
• une deuxième étape (b) de filtrage (F₁) du signal issu de l'étape (a) pour obtenir un signal x(t) ayant une enveloppe spectrale prédéterminée H(f),
• une troisième étape (c) où une fonction non-linéaire g est appliquée au signal x(t) de façon à former un signal y(t) et pour créer des remontées ou overshoots sur les bords de l'histogramme du signal y(t),
• une quatrième étape (d) de filtrage (F₂) permettant de lisser les remontées ou overshoots de l'histogramme du signal y(t), de compenser l'effet de la non-linéarité et d'effectuer un complément de filtrage à (F₁).

The invention relates to a method for generating a random signal. It is characterized in that it comprises at least the following stages:

• a first step (a) of generating a pseudo-random signal,
• a second step (b) of filtering (F ₁ ) the signal from step (a) to obtain a signal x (t) having a predetermined spectral envelope H (f),
• a third step (c) where a non-linear function g is applied to the signal x (t) so as to form a signal y (t) and to create lifts or overshoots on the edges of the histogram of the signal y (t )
• a fourth filtering step (d) (F ₂ ) making it possible to smooth the ascents or overshoots of the histogram of the signal y (t), to compensate for the effect of the non-linearity and to carry out additional filtering at ( F ₁ ).

Lifts or overshoots are more or less pronounced in depends in particular on the shape of the final histogram.

According to one embodiment, the non-linear function is for example a faceted function D _i and the number of segments and the ratio of the slopes of the different segments are chosen as a function of the histogram resulting from the filtering step F ₁ .

The pseudo-random signal is for example white noise.

a) des moyens pour générer un signal pseudo-aléatoire,

b) des moyens (F₁) pour filtrer le signal pseudo-aléatoire afin d'obtenir un signal x(t) ayant une enveloppe spectrale prédéterminée H(f),

c) un dispositif adapté à générer une fonction non-linéaire pour former à partir du signal x(t) présentant un histogramme de type gaussien, un signal y(t) dont l'histogramme est de type rectangulaire avec des remontées ou overshoots,

d) des moyens (F₂) adaptés à lisser les remontées ou overshoots de l'histogramme du signal y(t), à compenser l'effet de la non-linéarité et à effectuer un complément de filtrage à (F₁).

The subject of the invention is also a device for implementing the above-mentioned method comprising for example at least the following elements:

a) means for generating a pseudo-random signal,

b) means (F ₁ ) for filtering the pseudo-random signal in order to obtain a signal x (t) having a predetermined spectral envelope H (f),

c) a device adapted to generate a non-linear function to form from the signal x (t) having a Gaussian type histogram, a signal y (t) whose histogram is of rectangular type with lifts or overshoots,

d) means (F ₂ ) suitable for smoothing the ascents or overshoots of the histogram of the signal y (t), to compensate for the effect of the non-linearity and to carry out additional filtering at (F ₁ ).

The signal generated is for example white noise.

• améliorer la non linéarité des convertisseurs analogique-numérique ou numérique-analogique,
• pouvoir s'appliquer à de nombreux systèmes,
• être économique et simple dans sa mise en oeuvre.

The invention has in particular the following advantages:

• improve the non-linearity of analog-digital or digital-analog converters,
• be able to apply to many systems,
• be economical and simple in its implementation.

• la figure 1, une illustration des étapes possibles du procédé selon l'invention,
• la figure 2, un exemple détaillé d'un générateur de codes pseudoaléatoires,
• la figure 3, un histogramme en sortie de la première étape du procédé selon l'invention,
• la figure 4 un spectre de bruit en sortie de générateur PRN,
• les figures 5 et 6, respectivement un histogramme et le spectre du signal en sortie du premier filtre,
• les figures 7, 8 et 9 une fonction de non linéarité, l'histogramme et le spectre après application de la fonction de non linéarité,
• les figures 10 et 11 un histogramme et un spectre en sortie du deuxième filtre,
• la figure 12 un mode de réalisation possible d'un système de conversion numérique-analogique utilisant un signal aléatoire généré selon l'invention,
• la figure 13 un exemple de système de conversion analogique-nuémrique utilisant un signal aléatoire généré selon l'invention.

Other characteristics and advantages of the invention will become apparent with the aid of the description which follows, given with reference to the accompanying drawings, by way of illustration and in no way limiting, which represent:

• FIG. 1, an illustration of the possible steps of the method according to the invention,
• FIG. 2, a detailed example of a pseudo-random code generator,
• FIG. 3, a histogram at the output of the first step of the method according to the invention,
• FIG. 4 a noise spectrum at the output of the PRN generator,
• FIGS. 5 and 6, respectively a histogram and the spectrum of the signal at the output of the first filter,
• FIGS. 7, 8 and 9 a function of non-linearity, the histogram and the spectrum after application of the function of non-linearity,
• FIGS. 10 and 11 a histogram and a spectrum at the output of the second filter,
• FIG. 12 a possible embodiment of a digital-analog conversion system using a random signal generated according to the invention,
• FIG. 13 an example of an analog-to-digital conversion system using a random signal generated according to the invention.

Figure 1 describes a possible example of the steps implemented by the method according to the invention. The latter is notably composed of a sequence of steps or signal processing which allows calculation in real time of a random signal with a predetermined spectral envelope and a histogram of amplitudes close to a rectangular law, i.e. equally distributed.

The method according to the invention comprises a first step (a) in which a pseudo-random code is generated, for example by means a generator, 1, PRN (abbreviated as Pseudo-Random Noise). The PRN generator is for example constructed from a register with offset looped back on itself using one or more exclusive OUs. This type of generator is described in many articles or books as for example in the book entitled "Spread Spectrum Communications »Volume 1 by Simon, Omura, Scholtz and Levitt.

The pseudo-random signal generated is for example white noise.

The PRN generator delivers digital words on m bits at its output, for example, whose values are equally distributed in the amplitude interval [-2 ^m-1 , 2 ^m-1 -1] and whose spectral envelope is constant between frequency 0 and frequency F _H / 2 where F _H is the clock frequency which clock the register shifts.

As an example, Figure 2 gives the block diagram of a PRN generator produced from a shift register, 30, of 28 bits.

Bits Nos. 3 and 28 are combined by an Exclusive OR, 31, the output of which is fed back to the input, 32, of the register to give an operating cycle of maximum length equal to ²²⁸ -1 clock strokes. The 28 bits of the register are then combined by Exclusive OUs, 33, to give rise to a random signal on m bits with m = 13 bits in the example of FIG. 2.

FIG. 3 represents the histogram of the amplitudes of the PRN generator of figure 2, the value of the amplitude on the abscissa is between -4096 and +4095, the ordinate corresponds to the rate of appearance of different amplitudes. It should be noted that this rate is significantly equally distributed.

FIG. 4 represents a diagram of the spectral amplitude, expressed in dB, as a function of the frequency of the signal s (t) generated by the PRN. The envelope of this signal is substantially constant between 0 and F _H / 2.

One of the functions of the filters F ₁ and F ₂ used in the present invention is to widen the spectrum of the PRN generator in the frequency band where the useful signal as defined above will be located, namely the useful signal which is wishes to convert without distortion by a DAC or a CAN.

Each filter participates in a different way, the characteristics of the first filter F ₁ are optimized and chosen to dig the signal into a limit where the non-linearity does not destroy the effect of the filtering too much and those of the second filter F ₂ to regroove the spectrum of the number of dB required as a function of the dynamics sought.

For this, the template for each of the filters F ₁ and F ₂ is determined in such a way that the noise residue remaining in the useful band is compatible with the dynamic range sought for the useful signal. The dynamic term represents in this context, the relationship between the level of the useful signal and the maximum level of the spurious signals in a given band where the useful signals are found. Thus, depending on the application of the generator in an analog-digital or digital-analog conversion system, the spectrum of the random signal must not encroach on the band of useful signals. The choice of the filter mask is for example a function of the spectrum width of the random signal, the clock frequency of the DAC or ADC and the dynamics sought for the system.

In addition, in order to obtain a final histogram close to a law rectangular, a non-linearity function is applied between the two filtering steps.

Steps (b), (c) and (d) for obtaining such results are for example described below.

A second step (b) filters the noise band or limit this band by digging a hole in the portion of the spectrum where will placed the useful signal.

The filter F ₁ is for example optimized so that this hole is limited to a depth of the order of 10 to 30 dB relative to the maximum of the noise spectrum in a band at least equal to that of the useful signals and preferably 15 at 25 dB. Indeed, the transition to non-linearity has in particular the consequence of tending to plug this hole at a level generally situated around -25 dBc relative to the maximum of the noise spectrum.

FIG. 5 shows a histogram of the noise signal after the filter F ₁ , the value of the amplitude being given on the abscissa and the rate of appearance indicated on the ordinates. This histogram tends towards a Gaussian law.

FIG. 6 gives the spectrum of the signal x (t) of the noise at the output of the first filter F ₁ . We note in this example a dug hole of the order of -20 dBc relative to the maximum noise around a frequency close to 0.15 F _H. The value of -20 dBc is only an example given by way of illustration. This value can vary in particular depending on the application. In fact, the characteristics of the filter F ₁ are chosen so that the non-linearity function does not destroy too much the filtering effect as it was exposed previously.

During a third step (c), the method applies a non-linear function to the signal x (t) from the first filter F ₁ so as to create lifts (term known by the English word overshoots) on the edges of the histogram of the signal obtained at the output of F1. We seek to favor the extreme amplitudes of the signal.

The non-linear function is for example made up of facets, that is to say linear segments Di having slopes of different values. The ratio of the slopes of the different segments creates the lifts or overshoots. The number of segments and the values of the slopes of the different segments depend for example on the histogram obtained at the output of the filter F ₁ , therefore on the application.

FIG. 7 illustrates an example of a non-linear function comprising 5 facets, D ₁ , D ₂ , D ₃ , D ₄ and D ₅ , the abscissa corresponding to the instantaneous value of the signal x (t) and the ordinate to the instantaneous value of the signal y (t) obtained by application of the non-linear function.

The histogram of the signal obtained after application of the function non-linear is represented on figure 8. The abscissa corresponds to the value the signal amplitude and the ordinate at its rate of appearance.

Compared to the histogram of figure 5, the histogram presents a rectangular rather than Gaussian shape with lifts or overshoots present on the two extreme edges of the diagram, the part central corresponding more to a rectangular type shape.

The spectrum of the signal y (t) obtained after application of the function non-linear is represented on figure 9. We note that the hole obtained around 0.25 FH has been "plugged in" at a value between -20 and -25 dBc.

Any non-linear function allowing the passage to be effected from a Gaussian probability to a rectangular law with lifts or overshoots can be used to perform the third step of the process.

A fourth step (d) consists in filtering the signal y (t) so as to carry out the filtering part which could not be implemented in F ₁ taking into account for example the constraints imposed by the non-linearity.

Indeed, in order to optimize the roles of each of the filters and taking into account the phenomena resulting from the application of non-linearity, the characteristics of the filter F ₂ are chosen in particular to regroove the spectrum by the number of dB necessary, in as a function of the dynamics sought and as a function of the filling effect resulting from step (c) (application of the non-linear function).

In addition, this step smooths out the lifts or overshoots. of the histogram.

The spectral part removed by the filter F ₂ represents a relatively small part of the overall power of the noise before F ₂ . Thus the passage through the filter F ₂ mainly performs a smoothing of the histogram obtained previously in step (c). The fact that the suppressed part represents a weak part in power is due to the action of F ₁ which eliminated a large part of the noise power in the useful signal band, even if it did not widen the spectrum for example that at -20 dB and that the non-linearity has not degraded this value too much.

FIG. 10 represents the histogram of the noise after the filter F ₂ . We see that this histogram is close to a rectangular law.

FIG. 11 shows in a frequency-amplitude spectral diagram expressed in dB, the noise spectrum obtained after the filter F ₂ and a curve giving the theoretical response of the cascade of the two filters when the function of no is not applied -linéarité. The difference between these two curves is the contribution of the non-linear function.

The filters F ₁ and F ₂ used to implement the invention are preferably filters with power coefficients of 2 which do not require multiplication.

Without departing from the scope of the invention, any filter enabling the desired filtering templates F ₁ and F _{2 to} be produced can be used within the scope of the invention.

The filter F ₁ , corresponding for example to the curve obtained in FIG. 5 has a transfer function H ₁ (z) expressed by the following relation H 1 (z) = 1 - (z + z -1 ) + ½ (z 2 + z -2 )

The F ₂ filter has for response: H 2 (z) = 1.25 - (z + z -1 ) + ½ (z 2 + z -2 ) - 1/8 (z 3 + z -3 )

Note that by changing the negative signs - coefficients of H ₁ and H ₂ into positive signs +, the noise is then spectrally located around zero with a hole around F _H / 2. It is also possible to obtain a hole around F _H / 4 by making the four blocks of the synoptic work at a clock equal to F _H / 2 and by oversampling the signal with a clock at F _H.

Without departing from the scope of the invention, holes for others spectrum frequencies can be generated using other functions of transfer than those mentioned above.

The filters will preferably be produced in a FPGA (Field Programmable Gate Array) or EPLD type digital circuit or ASIC. Any digital circuit comprising the known elements of Those skilled in the art for making filters can also be used. The filters are therefore filters of the digital type.

Without departing from the scope of the invention, any filter suitable for obtaining the desired filtering template and any pseudo code generation device Random or noises can be used in the present invention.

FIG. 12 illustrates the application of the method according to the invention to a digital-analog conversion system, contained for example in a digital synthesizer. In this application, a useful signal x (t), digital, must be converted to analog quantity with the best possible linearity, i.e. in fact with the least amount of spurious signals possible. This useful signal x (t) is therefore added to a random signal s (t) obtained according to the method according to the invention by generation means 20 adapted. The two signals x (t) and s (t) are combined by an adder 21. These two signals are digital. In a preferred embodiment of the conversion system, the random signal s (t) has an amplitude close to or greater than that of signal x (t) and a histogram and a spectral envelope obtained according to the steps implemented in the process. Truncation means 22 can optionally be used before passing through the converter 23.

FIG. 13 shows an example of application of the method according to the invention for an analog-digital conversion system. In this case, the useful signal x (t) and the random signal s (t) are analog signals. These two signals are added by an analog adder 30. The sum signal x (t) + s (t) is present at the input of an analog-digital converter 31 whose output is for example coded on N bits. The signal has characteristics substantially identical to those of the signal described in figure 12. It can also be generated by means substantially identical to those described in Figure 12, then be converted by a DAC so as to obtain an analog signal before adding it.

Claims (10)

Method for generating a random signal, characterized in that it comprises at least the following steps: a first step (a) of generating a pseudo-random signal, a second step (b) of filtering (F ₁ ) the signal from step (a) to obtain a signal x (t) having a predetermined spectral envelope H (f), a third step (c) where a non-linear function g is applied to the signal x (t) so as to form a signal y (t) and to create lifts or overshoots on the edges of the histogram of the signal y (t ) a fourth filtering step (d) (F ₂ ) making it possible to smooth the ascents or overshoots of the histogram of the signal y (t), to compensate for the effect of the non-linearity and to carry out additional filtering at ( F ₁ ). Method according to Claim 1, characterized in that the non-linear function is a faceted function D _i and in that the number of the segments D _i and the ratio of the slopes of the different segments are chosen as a function of the histogram from l filtering step F ₁ . Method according to either of Claims 1 and 2, characterized in that the filter F ₁ generates a dip of approximately 10 to 30 dB, preferably from 15 to 25 dB, in a band at least equal to that of the useful signals. Method according to one of claims 1 to 3 characterized in that the histogram obtained at the end of step (d) is substantially identical to a rectangular law. Method according to one of claims 1 to 4 characterized in that the pseudo-random signal is white noise. Device for generating a random signal characterized in that it comprises at least the following devices: means for generating a pseudo-random signal, means (F ₁ ) for filtering the pseudo-random signal in order to obtain a signal x (t) having a predetermined spectral envelope H (f), a device adapted to generate a non-linear function to form from the signal x (t) having a Gaussian type histogram, a signal y (t) whose histogram is of rectangular type with lifts or overshoots, means (F ₂ ) suitable for smoothing the ascents or overshoots of the histogram of the signal y (t), to compensate for the effect of the non-linearity and to carry out additional filtering at (F ₁ ). Device according to Claim 6, characterized in that the device suitable for generating a non-linear function is designed to obtain a non-linear function with facets Di. Device according to either of Claims 6 and 7, characterized in that at least one of the filters F ₁ or F ₂ is a filter with power coefficients of 2. Device according to either of Claims 6 and 7, characterized in that the signal generated is white noise. Application of the method according to one of claims 1 to 5 or of device according to one of claims 6 to 8 in a system of digital-to-analog conversion or in a conversion system analog to digital.

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