EP1253512A1 - 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
EP1253512A1
EP1253512A1 EP02290060A EP02290060A EP1253512A1 EP 1253512 A1 EP1253512 A1 EP 1253512A1 EP 02290060 A EP02290060 A EP 02290060A EP 02290060 A EP02290060 A EP 02290060A EP 1253512 A1 EP1253512 A1 EP 1253512A1
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Prior art keywords
signal
histogram
filtering
generating
random
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EP02290060A
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English (en)
French (fr)
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EP1253512B1 (de
Inventor
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 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • Use signal means the signal which one wishes to convert without distortion by a CNA or CAN.
  • 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.
  • Lifts or overshoots are more or less pronounced in depends in particular on 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 as a function of the histogram resulting from the filtering step F 1 .
  • the pseudo-random signal is for example white noise.
  • the signal generated is for example white noise.
  • 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).
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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 .
  • 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.
  • 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.
  • lifts term known by the English word overshoots
  • 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.
  • 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.
  • 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.
  • 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).
  • 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 .
  • 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 -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 multiplication.
  • 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 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.
  • 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.
  • 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.
  • 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.
  • 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.

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  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Computer Hardware Design (AREA)
  • Mathematical Physics (AREA)
  • Automation & Control Theory (AREA)
  • Evolutionary Computation (AREA)
  • Fuzzy Systems (AREA)
  • General Physics & Mathematics (AREA)
  • Software Systems (AREA)
  • Analogue/Digital Conversion (AREA)
  • Radar Systems Or Details Thereof (AREA)
EP02290060A 2001-01-16 2002-01-10 Verfahren und Vorrichtung zur Erzeugung eines Zufallssignals mit kontrolliertem Histogramm und Spektrum Expired - Lifetime EP1253512B1 (de)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
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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EP1253512A1 true EP1253512A1 (de) 2002-10-30
EP1253512B1 EP1253512B1 (de) 2005-08-03

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US (1) US6559712B2 (de)
EP (1) EP1253512B1 (de)
AT (1) ATE301306T1 (de)
CA (1) CA2367278C (de)
DE (1) DE60205297T2 (de)
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
CN102460172B (zh) 2009-05-07 2015-03-04 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

Citations (1)

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FR2783374A1 (fr) * 1998-09-11 2000-03-17 Thomson Csf Procede et dispositif de generation d'un signal aleatoire et systemes de conversion numerique-analogique utilisant un tel signal aleatoire

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GB2289132B (en) * 1993-11-09 1997-06-18 Motorola Inc Method and apparatus for detecting an input signal level
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
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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Publication number Priority date Publication date Assignee Title
FR2783374A1 (fr) * 1998-09-11 2000-03-17 Thomson Csf Procede et dispositif de generation d'un signal aleatoire et systemes de conversion numerique-analogique utilisant un tel signal aleatoire

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
MOLIASA L T ET AL: "ON THE GENERATION OF NON-GAUSSIAN NOISE USING THE DISCRETE-FOURIER TRANSFORM METHOD", PROCEEDINGS OF THE INSTRUMENTATION AND MEASUREMENT TECHNOLOGY CONFERENCE. IMTC/95. WALTHAM, MA., 23-26 APRIL 1995, 1995, IEEE, NEW YORK, NY, USA, pages 72 - 78, XP000534826, ISBN: 0-7803-2616-4 *

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ATE301306T1 (de) 2005-08-15
DE60205297T2 (de) 2006-03-30
EP1253512B1 (de) 2005-08-03
CA2367278C (fr) 2011-06-28
US20020095449A1 (en) 2002-07-18
FR2819600B1 (fr) 2003-04-11
US6559712B2 (en) 2003-05-06
CA2367278A1 (fr) 2002-07-16
DE60205297D1 (de) 2005-09-08
FR2819600A1 (fr) 2002-07-19

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