EP1253512B1 - Method and apparatus for generating a random signal with controlled histogram and spectrum - Google Patents

Abstract

A method and device for the generation of a random signal, comprising: A first step (a) for the generation of a pseudo-random signal, a second step (b) for the filtering (F1) of the signal coming from the step (a) to obtain a signal x(t) having a predetermined spectral envelope H(f), a third step (c) in which a non-linear finction g is applied to the signal x(t) so as to form a signal y(t) and create overshoots on the edges of the histogram of the signal y(t), a fourth filtering (F2) step (d) used to smoothen the overshoots of the histogram of the signal y(t), compensate for the effect of the non-linearity and carry out an additional filtering at (F1). Application to a system of analog-digital conversion or digital-analog conversion.

Description

The present invention relates to a method and a device for generating a random signal. The invention applies in particular to field of digital-to-analog conversion and to the field of analog-to-digital conversion using such a random system.

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

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

Direct digital synthesis is a technique of synthesis of Frequency which involves developing in numerical values the samples of a signal that we want to generate and to convert these samples into signals analog thanks to a digital-to-analog converter. The signal synthesizers obtained by this technique are very attractive in in terms of 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, the passage of a useful signal in the digital-to-analog converter is accompanied by the creation of spurious signals that are due to the non-linearities of these converters. These non-linearities refer to the fact that the stair steps of the function of transfer of the digital to analog converter are not equal heights and that the transition between markets produces 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 by the creation of spurious signals due to non-linearities.

It is known from the prior art to add a random signal to the signal useful, before passing through the converter, in order to decrease the level of spurious signals by reducing the effect of converter non-linearities previously mentioned. This random signal is commonly referred to as the Anglo-Saxon term "dither". The useful signal is usually band limited and the clock frequency of the system, for example a synthesizer digital, is usually greater than this band. This leaves a Empty spectral space to place the random signal.

To be fully effective, this random signal must have certain characteristics. First of all, its spectrum must be controlled for that it does not encroach on the band of useful signals. Second, he 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 linearization worse than that obtained by a rectangular law. So there is a real advantage to being able to control for the random signal both the spectrum and the histogram.

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

FR 2 783 374 of the applicant teaches a method 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 temporal amplitude distributions are imposed simultaneously. For this, the method uses a sequence of four steps or signal processing operations, the repetition of some of them, especially steps 3 and 4 converging the signal parameters random to the desired laws. The iteration of the steps makes it possible to approach gradually the distribution law fixed, then correct the envelope spectral.

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

The idea of the invention is based on a new approach that 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 equidistributed.

In the remainder of the description, the expression 'Wanted signal' means the signal which one wishes to convert without distortion by a CNA or a CAN. For this purpose, the random signal or noise that is generated by the device according to the invention is added to this useful signal so as to linearize the transfer characteristic of the NAC 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 subject of the invention is a method for generating a random signal. It is 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 upstrokes or overshoots on the edges of the signal histogram y (t) )
• a fourth step (d) filtering (F ₂ ) for smoothing the rise or overshoots of the histogram of the signal y (t), to compensate for the effect of non-linearity and to perform a filtering complement to ( F ₁ ).

The lift or overshoots are more or less pronounced in particular function of 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 according to the histogram resulting from the filtering step F ₁ .

The pseudo-random signal is for example a 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 invention also relates to a device for implementing the aforementioned 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 to obtain a signal x (t) having a predetermined spectral envelope H (f),

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

d) means (F ₂ ) adapted to smooth the rise 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 a 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 notably has the following advantages:

• improve the non-linearity of analog-to-digital or digital-to-analog converters,
• can be applied to many systems,
• to 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 pseudo-aléatoires,
• 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 features and advantages of the invention will become apparent with the aid of the description which follows, given with reference to the attached 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 nonlinearity function, the histogram and the spectrum after application of the nonlinearity function,
• FIGS. 10 and 11 a histogram and a spectrum at the output of the second filter,
• FIG. 12 a possible embodiment of a digital-to-analog conversion system using a random signal generated according to the invention,
• FIG. 13 is 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 process according to the invention. The latter is composed in particular of a sequence of steps or signal processing that allows the calculation in real time of a random signal with a predetermined spectral envelope and a histogram of the amplitudes close to a rectangular law, that is to say 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 of of a generator, 1, PRN (Abbreviated Anglo-Saxon Pseudo-Random Noise). The PRN generator is for example built from a register to offset looped back to itself using one or more exclusive ORs. This type of generator is described in many articles or books as for example in the book entitled "Spread Spectrum Communications »Volume 1 of Simon, Omura, Scholtz and Levitt.

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

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

By way of example, FIG. 2 gives the block diagram of a PRN generator made from a 30-bit, 30-bit shift register.

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 2 ²⁸ -1 clock ticks. The 28 bits of the register are then combined by exclusive ORs, 33, to give rise to a random signal on m bits with m = 13 bits in the example of Figure 2.

FIG. 3 represents the histogram of the amplitudes of the PRN generator of FIG. 2, the value of the amplitude in abscissa is between -4096 and +4095, the ordinate corresponds to the rate of appearance 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 dig the spectrum of the PRN generator in the frequency band where will be located the useful signal as defined above, namely the useful signal that one wants to convert without distortion by a CNA 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 to a limit where the non-linearity does not destroy too much the effect of filtering and those of the second filter F ₂ to regress the spectrum of the number of dB required according to the desired dynamics.

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 desired dynamics for the useful signal. In this context, the dynamic term represents the ratio between the level of the wanted signal and the maximum level of the spurious signals in a given band where the useful signals are located. Thus, depending on the application of the generator in an analog-to-digital or digital-to-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 CNA or CAN and the desired dynamics for the system.

Moreover, 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) to obtain such results are for example described below.

A second step (b) makes it possible to filter the band of the noise 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 spectrum of the noise in a band at least equal to that of the useful signals and preferably 15 at 25 dB. Indeed, the passage in the non-linearity has the particular consequence of tending to fill this hole to a level generally 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 appearance rate indicated on the ordinate. This histogram tends to 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 hollow hole of the order of -20 dBc relative to the maximum noise around a frequency of 0.15 F _H. The value of -20 dBc is just an example for illustrative purposes. This value may vary, depending on the application. In fact, the characteristics of the filter F ₁ are chosen so that the non-linearity function does not destroy the filtering effect as it has been explained above.

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 feedbacks (term known as 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 nonlinear function is for example constituted by 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 of the application.

FIG. 7 illustrates an example of a nonlinear 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 applying the nonlinear function.

The histogram of the signal obtained after applying the function nonlinear is shown in Figure 8. The abscissa corresponds to the value instantaneous amplitude of the signal and the ordinate at its rate of appearance.

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

The spectrum of the signal y (t) obtained after application of the function nonlinear is shown in Figure 9. It is noted that the hole obtained around 0.25 FH was "plugged back" to a value between -20 and -25 dBc.

Any non-linear function that makes it possible to perform the passage 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 that could not be implemented in F _1, for example taking into account 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 the non-linearity, the characteristics of the filter F ₂ are chosen in particular to regress the spectrum of the number of dB required, in particular. depending on the desired dynamics and depending on the filling effect resulting from step (c) (application of the non-linear function).

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

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

FIG. 10 represents the histogram of the noise after the filter F ₂ . It can be seen that this histogram is close to a rectangular law.

FIG. 11 shows in a spectral frequency-amplitude 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 multiplications.

Without departing from the scope of the invention, any filter for making the desired filter templates F ₁ and F ₂ can be used within the scope of the invention.

The filter F ₁ , for example corresponding 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 )

Filter F ₂ to for answer: 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 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 realization of the filters will preferably be carried out in a Field Programmable Gate Array (FPGA) or EPLD type digital circuit or ASIC. Any digital circuit containing the known elements of the skilled person for making filters can also be used. Filters are therefore digital type filters.

Without departing from the scope of the invention, any filter adapted to obtain the desired filter mask and any device for generating pseudo codes random or noise can be used in the present invention.

FIG. 12 illustrates the application of the method according to the invention to a digital-to-analogue conversion system, for example contained in a digital synthesizer. In this application, a useful signal x (t), digital, should be converted to analog size with the best linearity possible, that is to say in fact with the least parasitic signals possible. This useful signal x (t) is therefore added to a random signal s (t) obtained according to the process according to the invention by means of generation 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 near or above that of the signal x (t) and a histogram and a spectral envelope obtained according to the steps implemented in the process. Truncation means 22 may optionally be used before passing through the converter 23.

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

Claims (10)

1. Method for the generation of a random signal, characterized in that it comprises at least the following steps:

   a first step (a) for the generation of a pseudo-random signal,

   a second step (b) for the filtering F₁ of the signal coming from the step (a) to obtain a signal x(t) having a predetermined spectral envelope H(f),

   the said method being characterized by

   a third step (c) in which a non-linear function g is applied to the signal x(t) having a Gaussian-type histogram so as to form a signal y(t) and create overshoots on the edges of the histogram of the signal y(t),

   a fourth filtering (F₂) step (d) used to smooth the overshoots of the histogram of the signal y(t), compensate for the effect of the non-linearity and carry out an additional filtering at F₁.
2. Method according to Claim 1, characterized in that the non-linear function is a function with facets D_i and in that the number of the segments Di and the ratio of the slopes of the different segments are chosen as a function of the histogram obtained from the filtering step F₁.
3. Method according to either of Claims 1 and 2, characterized in that the filter F₁ generates a notch of about 10 to 30 dB, preferably 15 to 25 dB, in a band at least equal to that of the useful signals to be processed.
4. Method according to one of Claims 1 to 3,
   characterized in that the histogram obtained at the end of the fourth step (d) is substantially identical to a rectangular law.
5. Method according to one of Claims 1 to 4,
   characterized in that the pseudo-random signal is white noise.
6. Device for generating a random signal, characterized in that it comprises at least the following devices:

   means for generating a pseudo-random signal,

   means F₁ for filtering the pseudo-random signal in order to obtain a signal x(t) having a predetermined spectral envelope H(f),

   characterized by

   a means configured to generate a non-linear function to form a signal y(t) from the signal x(t) having a Gaussian-type histogram, the histogram of this signal y(t) being of a rectangular type with overshoots,

   means F₂ configured to smooth the overshoots of the histogram of the signal y(t), compensate for the effect of the non-linearity and carry out an additional filtering at F₁.
7. Device according to Claim 6, characterized in that the device configured to generate a non-linear function is designed to obtain a non-linear function with facets Di.
8. Device according to either of Claims 6 and 7, characterized in that at least one of the filters F₁ and F₂ is a filter with coefficients to the power 2.
9. Device according to either of Claims 6 and 7 characterized in that the signal generated is white noise.
10. Application of the method according to one of Claims 1 to 5 or of the device according to one of Claims 6 to 8 in a digital-analogue conversion system or in an analogue-digital conversion system.

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