FR2814010A1 - Method of analyzing of digital signal representing physical magnitude by forming approximation signal from detail signals and reference signal and de-correlating detail signals - Google Patents

Abstract

A polyphase transform (E1) of a digital signal with conservation of a number of samples. A non-linear filtering (E2) of one of the polyphase signals is performed as a reference signal. Signals of detail (E3) are formed from the filtered signal and the other polyphase signals. An approximation signal (E4) is formed from the detail signals and the reference signal. - The signals of detail are de-correlated (E5). Independent claims are included for: (a) a method of coding of a digital signal (b) a method of synthesizing of a digital signal (c) a method of decoding of a digital signal (d) a device for analyzing a digital signal (e) a device for coding a digital signal (f) a device for synthesizing of a digital signal (g) an apparatus for processing of a digital signal

Description

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The present invention relates to the filtering of digital signals, and more particularly to analysis and synthesis, as well as to coding and decoding integrating respectively analysis and synthesis, of such signals.

In general, the filtering of digital signals can be linear or non-linear.

In the category of linear filtering, we know for example wavelet decompositions, which have the following advantages - conservation of the critical number of samples, that is to say the number of samples of the original signal, - multiresolution representation of the signal, - perfect reconstruction, in the absence of any other processing between analysis and synthesis, - very effective decorrelation of the data allowing great efficiency of subsequent coding.

Furthermore, non-linear filtering also has advantages. For example, morphological filters are not affected by the Gibbs effect, which disturbs the high frequency coefficients of linear filters.

The present invention provides a structure for filtering digital signals, which incorporates non-linear filtering, while presenting the advantages of the linear filtering previously mentioned.

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 To this end, the invention proposes a method for analyzing a digital signal representative of physical quantities, characterized in that it comprises the steps of - polyphase transformation of the digital signal with conservation of the overall number of samples, to generate a number predetermined polyphase signals, - non-linear filtering of one of the polyphase signals, called reference signal, - formation of detail signals, from the filtered signal and the other polyphase signals, - formation of an approximation signal, from the detail signals and the reference signal, - decorrelation of the detail signals, to form decorrelated signals.

Correlatively, the invention provides a digital signal analysis device representative of physical quantities, characterized in that it comprises - means of polyphase transformation of the digital signal with conservation of the overall number of samples, to generate a predetermined number of polyphase signals, - means for non-linear filtering of one of the polyphase signals, called the reference signal, - means for forming retail signals, from the filtered signal and other polyphase signals, - means for forming d an approximation signal, from the detail signals and the reference signal, - means for decorrelating the detail signals, to form decorrelated signals.

Thanks to the invention, it is possible to perform a non-linear filtering of a digital signal, while having the following advantages

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 - conservation of the critical number of samples, that is to say of the number of samples of the original signal, - multiresolution representation of the signal, - perfect reconstruction, in the absence of any other processing between the analysis and the synthesis, - very efficient decorrelation of data allowing high efficiency of subsequent coding.

Indeed, decorrelation makes it possible to obtain a detail signal which contains most of the information and other detail signals containing very little information. These can then be very efficiently compressed.

According to a preferred characteristic, the analysis method further comprises the step of - selecting the approximation signal, and in that the steps of transformation, filtering, formation, and decorrelation are repeated a predetermined number of times, considering at each iteration the approximation signal previously selected as the signal to be analyzed, to form an approximation signal and decorrelated signals at a lower resolution level compared to the previous iteration.

Thus, the analysis of the digital signal is carried out according to several levels of resolution.

After analysis, we thus have a set of sub-images which are more and more simplified as the resolution decreases.

According to another preferred characteristic, the analysis method further comprises the step of - selecting one of the decorrelated signals, the selected decorrelated signal containing high energy coefficients, and in that the steps of transformation, filtering, formation, and decorrelation are reiterated a predetermined number of times, considering at each iteration the decorrelated signal previously selected as the signal to be

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 analyze, to form an approximation signal and decorrelated signals at a lower resolution level compared to the previous iteration.

Thus, as before, the analysis of the digital signal is carried out according to several levels of resolution.

After analysis, we thus have a set of detail signals which are increasingly coarse as the resolution decreases. According to a preferred characteristic, the non-linear filtering is a segmentation.

The approximation signal is close to the segmentation and the detail signals are close to the texture. Segmentation and texture are thus separated after analysis.

According to a preferred characteristic, the decorrelation is a Karhuenen Loewe transformation, or alternatively a discrete wavelet decomposition.

The Karhuenen Loewe transformation is a unitary, reversible transformation and is the best in the sense of decorrelation.

The discrete wavelet decomposition is an independent filtering of the input signal.

The analysis device includes means for implementing the above characteristics.

The invention also relates to a method of coding a digital signal representative of physical quantities, characterized in that it includes the analysis method as previously presented.

The invention also relates to a coding device which includes means for implementing the above characteristics.

The invention also relates to a method for synthesizing a digital signal representative of physical quantities previously analyzed by the method presented above, characterized in that it comprises the steps of - inverse decorrelation of the decorrelated signals to form signals detail,

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 - calculation of a reference signal from the approximation signal and the detail signals, - non-linear filtering of the reference signal, - calculation of polyphase signals from the filtered reference signal and the detail signals, - transformation polyphase inverse of the reference signal and the polyphase signals, to form a reconstructed signal.

According to a preferred characteristic of the synthesis method, the reconstructed signal is considered to be an approximation signal and that the steps of decorrelation, addition, filtering, addition and reverse polyphase transformation are repeated at a higher resolution level.

The invention also relates to a method for decoding a digital signal representative of physical quantities, characterized in that it includes the synthesis method presented above.

The invention also relates to a decoding device which comprises means for implementing the above characteristics.

The analysis device, the method and the device for coding and decoding have advantages similar to those previously presented.

The invention also relates to a digital apparatus including the analysis, synthesis, coding or decoding device, or means for implementing the analysis, synthesis, coding or decoding method. This digital device is for example a digital camera, a digital camcorder, a scanner, a printer, a photocopier, a fax machine. The advantages of the device and of the digital apparatus are identical to those previously exposed.

A means of storing information, readable by a computer or by a microprocessor, integrated or not in the device, possibly removable,

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 stores a program implementing the determination or coding method.

The characteristics and advantages of the present invention will appear more clearly on reading a preferred embodiment illustrated by the attached drawings, in which - FIG. 1 schematically represents a data coding device according to the invention, - Figure 2 shows schematically a data decoding device according to the invention, - 'Figure 3 shows an embodiment of a device according to the invention, - Figure 4 shows an embodiment of a analysis device according to the present invention, - FIG. 5 represents an embodiment of a synthesis device according to the present invention, - FIG. 6 represents an embodiment of an analysis method according to the present invention, - Figure 7 shows an embodiment of a synthesis process according to the present invention, - Figure 8 shows an embodiment of a segmentation process n included in the present invention.

According to an embodiment chosen and represented in FIG. 1, a device 2 for analyzing and coding data according to the invention comprises an input to which is connected a source 1 of non-coded data. The source 1 comprises for example a memory means, such as random access memory, hard disk, floppy disk, compact disc, for memorizing non-coded data, this memory means being associated with a suitable reading means for reading the data there. Means for storing the data in the memory means can also be provided.

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 The source 1 may for example be a video camera in the case of an image signal or a microphone in the case of a sound signal.

The analysis and coding device 2 can be integrated into a data processing apparatus TD1, such as a computer for example.

Means 3 users of coded data are connected at the output of the analysis and coding device 2.

The user means 3 comprise for example means for storing coded data, and / or means for transmitting the coded data.

FIG. 2 represents a device 5 for decoding and synthesizing data coded by the device 2.

Means 4 users of coded data are connected at the input of the decoding and synthesis device 5. The means 4 comprise for example coded data memory means, and / or means for receiving the coded data which are adapted to receive the coded data transmitted by the transmission means 3.

The decoding and synthesis device 5 can be integrated into a data processing apparatus TD2, such as a computer for example.

Means 6 users of decoded data are connected at the output of the decoding and synthesis device 5. The user means 6 are for example means for viewing images, or means for reproducing sounds, depending on the nature of the data processed.

The coding device and the decoding device can be integrated into the same digital device, for example a digital camera provided with a display screen.

With reference to FIG. 3, an example of a device 10 implementing the invention is described. This device is suitable for analyzing a digital signal and / or synthesizing a previously analyzed digital signal, according to the examples developed below.

The device 10 is here a microcomputer comprising a communication bus 101 to which are connected

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 - a central unit 100, - a read-only memory 102, - a random access memory 103, - a screen 104, - a keyboard 114, - a hard disk 108, - a reader 109 adapted to receive and read a disc 110, which can be a floppy disk, a CD ROM, a DVD ROM, a memory card, for example, - an interface 112 for communication with a communication network 113, - a microphone 111.

The hard disk 108 stores the programs implementing the invention, as well as the data processed according to the invention. These programs can also be read from disk 110, or received via the communication network 113, or even stored in read-only memory 102.

More generally, the programs according to the present invention are stored in a storage means. This storage means can be read by a computer or by a microprocessor. This storage means is integrated or not to the device, and can be removable. For example, it may include a magnetic tape, a floppy disk or a CD-ROM (compact disk with frozen memory).

When the device is powered up, the programs according to the present invention are transferred into the random access memory 103 which then contains the executable code of the invention and the variables necessary for the implementation of the invention.

The device 10 can receive data to be processed from a peripheral device 107, such as a digital camcorder, or any other means of acquiring or storing data.

The device 10 can also receive data to be processed from a remote device, via the communication network 113, and transmit processed data to a remote device, still via the communication network 113.

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 The device 10 can also receive data to be processed from the microphone 111. This data is then a sound signal.

The screen 104 allows a user in particular to view the data to be processed, and serves, with the keyboard 114, as a user interface.

The operation of the analysis and synthesis devices according to the invention will now be described.

With reference to FIG. 4, a first embodiment of the device 2 for analyzing a digital signal performs an analysis on a level of resolution.

The device 2 includes a circuit 21 for extracting polyphase signals which receives an input signal at its input S. The extraction circuit 21 includes decimators and delay circuits, for generating a number M of polyphase signals, where M is an integer. In the example shown, the integer M is equal to four. Circuit 21 thus produces four undersampled versions of the input signal, which are four polyphase signals X11, X12, X13 and X14. It should be noted that the decomposition carried out is critical, or in other words, that the overall number of samples is preserved. The polyphase signals X11, X12, X13 and X14 thus together comprise the same number of samples as the original signal.

In the case where the signal S is an image signal, the four polyphase signals correspond for example to the even and odd samples of the signal in the vertical and horizontal directions.

The X11 polyphase signal is selected to be a reference signal. It is applied to the input of a non-linear filtering circuit 22. The circuit 22 performs a non-linear filtering of the reference polyphase signal. For example, non-linear filtering is a segmentation that breaks down the signal into homogeneous and adjacent regions. The regions formed are without overlap and their union is equal to the polyphase signal X11. The segmentation results in a segmented signal XS11 representative of a decomposition of the polyphase signal X11 into homogeneous regions.

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 The segmented signal XS, j is then respectively transmitted to operators 23, 24 and 25. Operators 23, 24 and 25 respectively receive the polyphase signals X12, X13 and X14 and perform the subtraction of the segmented signal XS, j from each of the others polyphase signals X12, X13 and X14.

The result is three detail signals Y12, Y13 and Y14. Each detail signal represents the difference between a polyphase signal and the output of the non-linear filtering circuit 22. The detail signals correspond approximately to the textures of the polyphase signals. By texture of a signal is meant the difference between the signal and its segmentation. The texture is substantially equal to the signals representing the interior of each region.

The detail signals are applied to a circuit 26 which combines them and calculates for example the average YM of these signals.

The reference signal X1, and the mean signal YM are applied to an operator 27 which performs the subtraction of the mean signal YM from the reference signal. The result is an approximation signal Y which is a signal very close to the result of the segmentation, that is to say of the signal XS, j supplied by the segmentation circuit 22.

Furthermore, the detail signals are also applied to a decorrelator circuit 28 which provides three decorrelated signals Z12, Z13 and Z14.

The decorrelator circuit performs for example a transformation of Karhuenen Loewe, called KLT, which is described in the work by Rafael Gonzalez and Paul Wintz, entitled Digital image processing, pages 122 to 125, Addison-Wesley, 1987. The KLT transformation is a unitary transformation, reversible, and is the best in the sense of decorrelation. It is also possible to use a wavelet decomposition.

The signals Y12, Y13 and Y14 are on the one hand very similar and on the other hand rich in information. This second point is penalizing for the coding of these signals. We therefore use their resemblance to decorrelate them. The result of the decorrelation is therefore a signal which contains a lot of information and which looks very much like the texture of the image and signals which contain little information. These decorrelated signals are supplied to a coding circuit 29 which performs conventional coding, for example a

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 scalar quantization followed by entropy coding. Circuit 29 provides coded signals ZC12, ZC13 and ZC14.

It is possible to repeat the processing which has just been described, by choosing the approximation signal and by treating it in turn as the input signal S.

As a variant, it is possible to choose the decorrelated signal containing a lot of information in order to treat it like the signal S. The approximation signal is then coded by the coding circuit 29.

Thus, in both cases, another approximation signal and other decorrelated signals are formed, at a lower resolution level compared to the previous iteration.

FIG. 5 represents a first embodiment of the synthesis device 5 corresponding to the analysis device previously described.

The circuit 5 includes a decoding circuit 51 which performs a decoding corresponding to the coding carried out by the circuit 29. The circuit 51 supplies decoded signals Z * 12, Z * 13 and Z * 14 to a reverse decorrelation circuit 52.

Circuit 52 corresponds to circuit 28 and performs reverse operations of the latter. The circuit 52 supplies signals Y * 12, Y * 13 and Y * 14 to a circuit 53 which corresponds to the circuit 26. The circuit 53 combines the signals which it receives and calculates the average YM * of these signals.

The mean YM * is supplied to an operator 54 which also receives the approximation signal Y * ,,. The operator 54 adds these two signals and provides a polyphase signal X * 11.

The polyphase signal X * 11 is supplied to a segmentation circuit 55 and to a reverse polyphase transformation circuit 56.

The segmentation circuit 55 is analogous to the circuit 22 previously described.

The segmentation circuit 55 supplies a segmented signal XS * 11 to each of three operators 57, 58 and 59.

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 The operators 57, 58 and 59 respectively receive the signals Y * 12, Y * 13 and Y * 14 supplied by the circuit 52 and add each of these signals to the segmented signal XS11.

The operators 57, 58 and 59 respectively supply polyphase signals X * 12, X * 13 and X * 14 to the reverse polyphase transformation circuit 56. The reverse polyphase transformation circuit 56 provides a reconstructed signal S *.

Of course, corresponding to the analysis, the reconstructed signal S * can be applied as an approximation signal to the circuit which has just been described, so as to perform the synthesis at a higher resolution level.

As a variant, the reconstructed signal S * can be applied as a decorrelated signal to the circuit which has just been described, so as to perform the synthesis at a higher resolution level. With reference to FIG. 6, an embodiment of the method analysis according to the invention of a digital image, implemented in the analysis device, comprises steps E1 to E7.

The analysis algorithm can be stored in whole or in part in any information storage means capable of cooperating with the microprocessor. This storage means can be read by a computer or by a microprocessor. This storage means is integrated or not to the device, and can be removable. For example, it may include a magnetic tape, a floppy disk or a CD-ROM (compact disk with frozen memory).

Step E1 is the polyphase transformation of a digital signal to form polyphase signals X; n, where i is an integer at least equal to one representing the current resolution level and n is an integer at least equal to two representing the current polyphase signal. During the first pass through this step, the digital signal is the original signal S.

The next step E2 is the selection of a reference polyphase signal, for example the polyphase signal X; 1, and the segmentation of the latter to form a segmented signal XS; 1.

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 The next step E3 is the formation of the detail signals Yi ", with n different from one, at the current resolution level, by subtraction of the segmented signal from each of the other polyphase signals.

The next step E4 is the formation of the approximation signal Yi, by subtracting a combination of the detail signals from the reference signal Xi 1 The next step E5 is the decorrelation of the detail signals, to form the detail signals uncorrelated.

The next step E6 is a test to determine whether all the levels of decomposition have been covered. If the answer is negative, this step is followed by step E7 to consider the approximation signal or alternatively one of the decorrelated detail signals as the signal to be processed. Step E7 is followed by step E1 previously described.

When the response is positive in step E6, then the analysis of the signal is finished. Step E6 is followed by a step E8 of coding. It should be noted that the coding is carried out here after the analysis, but that it can also be carried out between steps E5 and E6, that is to say as soon as a level of resolution is processed. The device of FIG. 4 corresponds to the latter case, when the approximation signal or a decorrelated signal is processed at a lower resolution level.

With reference to FIG. 7, an embodiment of the method of synthesis according to the invention of a digital image, implemented in the synthesis device, comprises steps E10 to E17. This synthesis method corresponds to the previously described analysis method.

The synthesis algorithm can be stored in whole or in part in any information storage means capable of cooperating with the microprocessor. This storage means can be read by a computer or by a microprocessor. This storage means is integrated or not to the device, and can be removable. For example, it may include a magnetic tape, a floppy disk or a CD-ROM (compact disk with frozen memory).

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 Step E10 is selection of the detail signals and of the signal for approximation of the current resolution level in the decomposition. During the first pass through this step, the lowest resolution level is considered. It is only in the case where there is no processing or loss between the analysis and the synthesis that the signals which are considered here are identical to the signals supplied at the end of the analysis.

The next step E11 is the inverse decorrelation of the previously selected detail signals.

The next step E12 is the sum of the approximation signal and a combination of the detail signals, so as to form a polyphase signal.

The next step E13 is the segmentation of the previously formed signal, to construct a segmented signal.

The next step E14 is the addition of the segmented signal with each of the detail signals, to form polyphase signals.

The next step E15 is the inverse polyphase transformation of the previously formed polyphase signals, to build a detail signal at the immediately higher resolution level.

The next step E16 is a test to determine whether all the levels of resolution have been covered. If the answer is negative, then this step is followed by step E17 to consider the immediately higher level of resolution. Step E17 is followed by step E10 previously described.

When the response is positive in step E16, this means that the detail signal which has just been constructed in step E15 is the signal S which it was wished to synthesize. The synthesis is therefore complete.

We will now describe, with reference to FIG. 8, an embodiment of segmentation of a polyphase signal, using a flowchart comprising the steps E90 to E92.

Step E90 is a simplification of the polyphase signal. A simplified version of the polyphase signal, more generally of an image, will for example be obtained by applying a morphological operator to the latter.

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 opening / closing, followed by a morphological reconstruction. A full description of this process can be found in the article by Philippe Salembier entitled Morphological multiscale segmentation for image coding published in Signal Processing magazine number 38 of 1994. This type of processing eliminates objects smaller than a certain size, and restores the contours of objects that have not been deleted. At the end of this step, there is therefore a simplified version of the polyphase signal, which will be easier to process by the following steps.

The next step E91 is the marking, or extraction of the markers, of the simplified polyphase signal. This step identifies the presence of the homogeneous regions of the simplified polyphase signal, using a criterion which can for example be a criterion of homogeneity of the intensity of the region (flat regions). Concretely, a region growth algorithm is used here for example: the polyphase signal is scanned in its entirety (for example from top to bottom and from right to left). We are looking for a seed, that is to say a point, here a coefficient, representative of a new region (the first coefficient of the polyphase signal will automatically be one). The characteristic of this region (average value) is calculated on the basis of this point. Then all the neighbors of this point are then examined, and for each of the neighbors there are two possibilities - if the point encountered has an intensity close to the average value of the region considered, it is assigned to the current region, and the statistics of this region are updated according to this new element, - if the point encountered has a different intensity (within the meaning of a proximity criterion) from the average value of the region, it is not assigned to the region (it can later be considered as a new germ representative of a new region).

All the neighbors assigned to the current region are then themselves examined, that is to say that all their neighbors are examined (growth phase).

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 The processing of the region thus continues until all the points neighboring the points belonging to the region have been examined. After this treatment, the region is considered good or bad. If it is bad (typically too small), it is the decision stage which will deal with the points in the region in question. If it is good, the treatment is finished for it. A unique label or identifier is then assigned to all points in the region. The overall treatment then continues with the search for a new germ.

For a region to be considered good or bad, a minimum region size parameter is used.

The next step E92 is the decision. It consists in attaching to a region all the points which have no label at the end of the marking step E91 (typically, the points which have been attached to regions which are too small). This step can be carried out simply by considering each of the points which does not have a label, and by assigning it to the neighboring region to which it is closest (in the sense of a proximity criterion).

Of course, the present invention is not limited to the embodiments described and shown, but encompasses, quite the contrary, any variant within the reach of ordinary skill in the art.

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Claims (24)

CLAIMS 1. Method for analyzing a digital signal representative of physical quantities, characterized in that it comprises the steps of - polyphase transformation (E1) of the digital signal with conservation of the overall number of samples, to generate a predetermined number of signals polyphases, - non-linear filtering (E2) of one of the polyphase signals, called reference signal, - formation (E3) of detail signals, from the filtered signal and the other polyphase signals, - formation (E4) of an approximation signal, from the detail signals and the reference signal, - decorrelation (E5) of the detail signals, to form decorrelated signals. 2. Analysis method according to claim 1, characterized in that it further comprises the step of - selection (E7) of the approximation signal, and in that the steps of transformation, filtering, formation, and decorrelation are repeated a predetermined number of times, considering at each iteration the approximation signal previously selected as the signal to be analyzed, to form an approximation signal and decorrelated signals at a lower resolution level compared to the previous iteration. 3. Analysis method according to claim 1, characterized in that it further comprises the step of - selection (E7) of one of the decorrelated signals, the selected decorrelated signal containing high energy coefficients, <Desc / Clms Page number 18>  and in that the steps of transformation, filtering, formation, and decorrelation are repeated a predetermined number of times, considering at each iteration the decorrelated signal previously selected as the signal to be analyzed, to form an approximation signal and decorrelated signals to a lower resolution level compared to the previous iteration. 4. Analysis method according to any one of claims 1 to 3, characterized in that the non-linear filtering (E2) is a segmentation. 5. Analysis method according to any one of claims 1 to 4, characterized in that the decorrelation (E5) is a transformation of Karhuenen Loewe. 6. Analysis method according to any one of claims 1 to 4, characterized in that the decorrelation is a discrete wavelet decomposition. 7. Method for coding a digital signal representative of physical quantities, characterized in that it includes the analysis method according to any one of claims 1 to 6. 8. Method for synthesizing a digital signal representative of physical quantities previously analyzed by the method according to claim 1, characterized in that it comprises the steps of - inverse decorrelation (E11) of the decorrelated signals to form detail signals, - calculation (E12) of a reference signal from the approximation signal and the detail signals, - non-linear filtering (E13) of the reference signal, - calculation (E14) of polyphase signals from the reference signal filtered and detail signals, <Desc / Clms Page number 19>  - inverse polyphase transformation (E15) of the reference signal and of the polyphase signals, to form a reconstructed signal. 9. Synthesis method according to claim 8, characterized in that the reconstructed signal is considered as an approximation signal and that the steps of decorrelation, addition, filtering, addition and inverse polyphase transformation are repeated at a higher resolution level. 10. Method for decoding a digital signal representative of physical quantities, characterized in that it includes the synthesis method according to any one of claims 8 and 9. 11. Digital signal analysis device (S) representative of physical quantities, characterized in that it comprises - means (21) for polyphase transformation of the digital signal with conservation of the overall number of samples, to generate a predetermined number polyphase signals, - means (22) for non-linear filtering of one of the polyphase signals, called the reference signal, - means (23, 24, 25) for forming detailed signals, from the filtered signal and other polyphase signals, - means (26) for forming an approximation signal, from the detail signals and the reference signal, - means (28) for decorrelating the detail signals, for forming signals uncorrelated. 12. Analysis device according to claim 11, characterized in that it further comprises - means for selecting the approximation signal, and in that the means for transformation, filtering, formation, and decorrelation are adapted to repeat their operation a predetermined number of times, considering at each iteration the signal <Desc / Clms Page number 20>  approximation signal previously selected as the signal to be analyzed, to form an approximation signal and decorrelated signals at a lower resolution level compared to the previous iteration. 13. Analysis device according to claim 11, characterized in that it further comprises - means for selecting one of the decorrelated signals, the selected decorrelated signal containing high energy coefficients, and in that the means transformation, filtering, training, and decorrelation are adapted to reiterate their operation a predetermined number of times, considering at each iteration the decorrelated signal previously selected as the signal to be analyzed, to form an approximation signal and decorrelated signals at a level lower resolution than the previous iteration. 14. Analysis device according to any one of claims 11 to 13, characterized in that the means (22) of non-linear filtering are adapted to implement a segmentation. 15. Analysis device according to any one of claims 11 to 14, characterized in that the means (28) for decorrelation are adapted to implement a Karhuenen Loewe transformation. 16. Analysis device according to any one of claims 11 to 14, characterized in that the decorrelation means (28) are adapted to implement a discrete wavelet decomposition. 17. Device for coding a digital signal representative of physical quantities, characterized in that it includes the analysis device according to any one of claims 11 to 16. <Desc / Clms Page number 21>  18. Device for synthesizing a digital signal representative of physical quantities previously analyzed by the device according to claim 11, characterized in that it comprises - means (52) for inverse decorrelation of the decorrelated signals to form detail signals, - means (53, 54) for calculating a reference signal from the approximation signal and the detail signals, - means (55) for non-linear filtering of the reference signal, - means (57, 58, 59) for calculating polyphase signals from the filtered reference signal and the detail signals, - means (56) for reverse polyphase transformation of the reference signal and of the polyphase signals, to form a reconstructed signal. 19. Synthesis device according to claim 18, characterized in that it is suitable for considering the reconstructed signal as an approximation signal and for reiterating the operation of the means of decorrelation, addition, filtering, addition and inverse polyphase transformation to a higher resolution level. 20. Device for decoding a digital signal representative of physical quantities, characterized in that it includes the synthesis device according to any one of claims 18 and 19. 21. Analysis device (10) according to any one of claims 11 to 16, characterized in that the polyphase transformation, filtering, formation and decorrelation means are incorporated in - a microprocessor (100), - a read only memory ( 102) comprising a program for processing the data, and - a random access memory (103) comprising registers adapted to record variables modified during the execution of said program. <Desc / Clms Page number 22>  22. Synthesis device (10) according to claim 18 or 19, characterized in that the reverse decorrelation, calculation, filtering and reverse polyphase transformation means are incorporated in - a microprocessor (100), - a read only memory (102) comprising a program for processing the data, and - a random access memory (103) comprising registers adapted to record variables modified during the execution of said program. 23. Digital signal processing apparatus, characterized in that it comprises means suitable for implementing the method according to any one of claims 1 to 10. 24. Digital signal processing apparatus, characterized in that it comprises the device according to any one of claims 11 to 22.