EP1253512B1 - Verfahren und Vorrichtung zur Erzeugung eines Zufallssignals mit kontrolliertem Histogramm und Spektrum - Google Patents

Verfahren und Vorrichtung zur Erzeugung eines Zufallssignals mit kontrolliertem Histogramm und Spektrum Download PDF

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Publication number
EP1253512B1
EP1253512B1 EP02290060A EP02290060A EP1253512B1 EP 1253512 B1 EP1253512 B1 EP 1253512B1 EP 02290060 A EP02290060 A EP 02290060A EP 02290060 A EP02290060 A EP 02290060A EP 1253512 B1 EP1253512 B1 EP 1253512B1
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Prior art keywords
signal
histogram
filtering
random
overshoots
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French (fr)
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EP1253512A1 (de
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Pascal Gabet
Jean-Luc De Gouy
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Thales SA
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Thales SA
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06J—HYBRID COMPUTING ARRANGEMENTS
    • G06J1/00—Hybrid computing arrangements

Definitions

  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • the expression 'Wanted signal' means the signal which one wishes to convert without distortion by a CNA or a CAN.
  • 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.
  • the lift or overshoots are more or less pronounced in particular function of the shape of the final histogram.
  • 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.
  • the signal generated is for example a white noise.
  • 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).
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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 .
  • 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.
  • 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.
  • feedbacks term known as overshoots
  • 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.
  • 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.
  • 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.
  • 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).
  • 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 .
  • 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. -linéar Congress. 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.
  • any filter for making the desired filter templates F 1 and F 2 can be used within the scope of the invention.
  • holes for others Spectrum frequencies can be generated using other functions of transfer than those mentioned above.
  • 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.
  • FPGA Field Programmable Gate Array
  • EPLD EPLD type digital circuit
  • 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.
  • a useful signal x (t) digital
  • 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.
  • 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.
  • 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.

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  • Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Computer Hardware Design (AREA)
  • Mathematical Physics (AREA)
  • Automation & Control Theory (AREA)
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Claims (10)

  1. Verfahren zur Erzeugung eines Zufallssignals, dadurch gekennzeichnet, dass es mindestens die folgenden Schritte aufweist:
    einen ersten Schritt (a) der Erzeugung eines Pseudozufallssignals,
    einen zweiten Schritt (b) des Filterns F1 des vom Schritt (a) stammenden Signals, um ein Signal x (t) mit einer vorbestimmten Spektralhülle H(f) zu erhalten,
    wobei das Verfahren gekennzeichnet ist durch
    einen dritten Schritt (c), in dem eine nicht-lineare Funktion g an das ein Gaußsches Histogramm aufweisende Signal x(t) angelegt wird, um ein Signal y(t) zu formen und um Überschwingungen oder Overshoots an den Rändern des Histogramms des Signals y(t) zu erzeugen,
    einen vierten Schritt (d) der Filterung (F2), der es ermöglicht, die Überschwingungen oder Overshoots des Histogramms des Signals y(t) zu glätten, die Wirkung der Nicht-Linearität zu kompensieren und ein Filterungskomplement zu F1 durchzuführen.
  2. Verfahren nach Anspruch 1, dadurch gekennzeichnet, dass die nicht-lineare Funktion eine Funktion mit Facetten Di ist, und dass die Anzahl von Segmenten Di und das Verhältnis der Schrägen der verschiedenen Segmente in Abhängigkeit von dem aus dem Filterungsschritt F1 stammenden Histogramm gewählt werden.
  3. Verfahren nach einem der Ansprüche 1 oder 2, dadurch gekennzeichnet, dass das Filter F1 ein Tal von etwa 10 bis 30 dB, vorzugsweise von 15 bis 25 dB, in einem Band mindestens gleich demjenigen der zu verarbeitenden Nutzsignale erzeugt.
  4. Verfahren nach einem der Ansprüche 1 bis 3, dadurch gekennzeichnet, dass das am Ende des vierten Schritts (d) erhaltene Histogramm im Wesentlichen gleich einem rechteckigen Gesetz ist.
  5. Verfahren nach einem der Ansprüche 1 bis 4, dadurch gekennzeichnet, dass das Pseudozufallssignal ein weißes Rauschen ist.
  6. Vorrichtung zur Erzeugung eines Zufallssignals, dadurch gekennzeichnet, dass sie mindestens die folgenden Vorrichtungen aufweist:
    Mittel zum Erzeugen eines Pseudozufallssignals,
    Mittel F1 zum Filtern des Pseudozufallssignals, um ein Signal x(t) mit einer vorbestimmten Spektralhülle H(f) zu erhalten, gekennzeichnet durch
    ein Mittel, das ausgelegt ist, um eine nicht-lineare Funktion zu erzeugen, um ausgehend von dem ein Gaußsches Histogramm aufweisenden Signal x(t) ein Signal y(t) zu formen, dessen Histogramm vom rechteckigen Typ mit Überschwingungen oder Overshoots ist,
    Mittel F2, die ausgelegt sind, um die Überschwingungen oder Overshoots des Histogramms des Signals y(t) zu glätten, die Wirkung der Nicht-Linearität zu kompensieren und ein Filterungskomplement zu F1 durchzuführen.
  7. Vorrichtung nach Anspruch 6, dadurch gekennzeichnet, dass die Vorrichtung, die ausgelegt ist, um eine nicht-lineare Funktion zu erzeugen, so gestaltet ist, dass eine nicht-lineare Funktion mit Facetten Di erhalten wird.
  8. Vorrichtung nach einem der Ansprüche 6 und 7, dadurch gekennzeichnet, dass mindestens eines der Filter F1 oder F2 ein Filter mit Leistungskoeffizienten 2 ist.
  9. Vorrichtung nach einem der Ansprüche 6 oder 7, dadurch gekennzeichnet, dass das erzeugte Signal ein weißes Rauschen ist.
  10. Anwendung des Verfahrens nach einem der Ansprüche 1 bis 5 oder der Vorrichtung nach einem der Ansprüche 6 bis 8 in einem System der Digital-Analog-Umwandlung oder in einem System der Analog-Digital-Umwandlung.
EP02290060A 2001-01-16 2002-01-10 Verfahren und Vorrichtung zur Erzeugung eines Zufallssignals mit kontrolliertem Histogramm und Spektrum Expired - Lifetime EP1253512B1 (de)

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FR0100541A FR2819600B1 (fr) 2001-01-16 2001-01-16 Procede et dispositif de generation d'un signal aleatoire a histogramme et spectre controles
FR0100541 2001-01-16

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EP1253512B1 true EP1253512B1 (de) 2005-08-03

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AT (1) ATE301306T1 (de)
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FR (1) FR2819600B1 (de)

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FR2860662B1 (fr) * 2003-10-03 2006-02-03 Thales Sa Procede et dispositif de generation de bruit d'agitation conforme a histogramme predetermine, et le bruit d'agitation obtenu
FR2880219B1 (fr) * 2004-12-23 2007-02-23 Thales Sa Procede et systeme de radiocommunication numerique, notamment pour les stations sol mobiles
CN104655840B (zh) 2009-05-07 2018-03-23 生物梅里埃有限公司 用于抗微生物剂抗性测定的方法
US20110191129A1 (en) * 2010-02-04 2011-08-04 Netzer Moriya Random Number Generator Generating Random Numbers According to an Arbitrary Probability Density Function
US9634863B2 (en) * 2011-11-11 2017-04-25 Kollmorgen Corporation Systems and methods for supporting two different protocols on a same physical connection
US9311681B2 (en) 2012-01-24 2016-04-12 Facebook, Inc. Claiming conversations between users and non-users of a social networking system
US9331681B2 (en) * 2013-11-05 2016-05-03 STMicroelectronics International N.V System and method for gaussian random noise generation
US10142743B2 (en) * 2016-01-01 2018-11-27 Dean Robert Gary Anderson Parametrically formulated noise and audio systems, devices, and methods thereof

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BR9405747A (pt) * 1993-11-09 1995-12-05 Motorola Inc Detector de nível e processo de operar um nível de um sinal de entrada
FR2765419B1 (fr) 1997-06-27 1999-09-17 Thomson Csf Dispositif de generation de signaux analogiques a partir de convertisseurs analogique-numerique, notamment pour la synthese numerique directe
DE59710269D1 (de) * 1997-07-02 2003-07-17 Micronas Semiconductor Holding Filterkombination zur Abtastratenumsetzung
FR2780831B1 (fr) 1998-07-03 2000-09-29 Thomson Csf Synthetiseur numerique de signaux
FR2783374B1 (fr) 1998-09-11 2000-12-08 Thomson Csf Procede et dispositif de generation d'un signal aleatoire et systemes de conversion numerique-analogique utilisant un tel signal aleatoire
FR2794309B1 (fr) 1999-05-28 2001-08-31 Thomson Csf Dispositif compensateur de la non-linearite d'un convertisseur analogique-numerique

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DE60205297D1 (de) 2005-09-08
CA2367278C (fr) 2011-06-28
DE60205297T2 (de) 2006-03-30
FR2819600A1 (fr) 2002-07-19
EP1253512A1 (de) 2002-10-30
US6559712B2 (en) 2003-05-06
US20020095449A1 (en) 2002-07-18
CA2367278A1 (fr) 2002-07-16
FR2819600B1 (fr) 2003-04-11

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