EP2243218A1 - Procede et dispositif pour ameliorer la bande passante d'un systeme physique - Google Patents
Procede et dispositif pour ameliorer la bande passante d'un systeme physiqueInfo
- Publication number
- EP2243218A1 EP2243218A1 EP09712207A EP09712207A EP2243218A1 EP 2243218 A1 EP2243218 A1 EP 2243218A1 EP 09712207 A EP09712207 A EP 09712207A EP 09712207 A EP09712207 A EP 09712207A EP 2243218 A1 EP2243218 A1 EP 2243218A1
- Authority
- EP
- European Patent Office
- Prior art keywords
- value
- filter
- impulse response
- sample
- samples
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Withdrawn
Links
Classifications
-
- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
- H03H17/00—Networks using digital techniques
- H03H17/02—Frequency selective networks
- H03H17/0294—Variable filters; Programmable filters
-
- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
- H03H17/00—Networks using digital techniques
- H03H17/02—Frequency selective networks
- H03H17/06—Non-recursive filters
Definitions
- the invention relates to a method and an electronic circuit for improving the bandwidth of a device which, for physical reasons, has a bandwidth less than that which one would like.
- any electronic system made from physical elements has a limited bandwidth due to the non-ideal characteristics of the system. This is the case in particular for all electronic acquisition systems of physical quantities (sensors) but also for all systems for processing electronic signals or for transmitting electronic or optical signals. It follows from this limitation of non-ideal systems that any physical system behaves, with respect to an input quantity, as a filter which is in general a low-pass filter, but which could be more sophisticated than a simple low-pass filter. This is reflected in practice by the fact that the output of the system fails to follow the too fast variations of an input quantity of the system. When we speak here of variation, it can be mainly a temporal variation but also a spatial variation.
- the input variation may be a time variation of light and the output variation is a time variation of voltage that represents this light variation; we then realize that, just because the sensor is a sensor made from physical elements (photodiodes, circuits for collecting electrical charges, amplifiers, transmission circuits, etc.), the electronic signal can not follow instantly. a very sudden variation of light at the entrance; the sensor response includes a low-pass time filter function.
- the sensor can not generate an electron signal spatially varying as abruptly as the pattern.
- the senor produces a certain filtering function, but this time in the spatial domain, therefore, as a function of a spatial variable.
- the bandwidth in the spatial domain can be as important as in the time domain and the correction principles according to the present invention apply in both cases.
- the invention proposes a much simpler solution for increasing the bandwidth of a physical system.
- a finite impulse response filter is used which is calculated in the following manner, from the behavior (observed or known) of the physical system: the impulse response of the physical system is determined according to a temporal or spatial variable; the impulse response is the response to a normalized input pulse of duration tending to zero and vertical rising and falling edges; sample-by-sample is calculated an impulse response of similar shape but compressed according to the scale of the variable in a ratio corresponding to a desired bandwidth increase and expanded in amplitude in the same ratio, and the coefficients of a filter at finite impulse response able to provide at its output a succession of samples of the compressed response when applying a succession of corresponding samples of the response of the physical system to its input.
- This finite impulse response filter is incorporated in the physical system, output (preferably) or input or inside the system, to improve the bandwidth in a ratio n.
- an improved bandwidth signal is collected at the output of the corrected system in a factor n.
- the choice of the interval [0, T] is such that it encompasses the most significant part of the impulse response a (t), for example the part of the response for which the amplitude of the response is greater than at least 5% of the maximum amplitude of the response.
- Samples in the interval [T, nT] may very well be arbitrarily set to zero, even if the values of a (t) are not zero in this interval because these values are small. This may result in a poorer result but a result that is entirely acceptable.
- the coefficients of the filter are preferably coefficients Ci where i is the index varying from 0 to N, the value of the coefficient Ci being defined by the following iteration:
- Ci (bi - ai) C 0 - ai - i Ci .. .. - a ⁇ j.Cj .. .. - a - ⁇ Ci - ⁇ ) / a 0 ,
- the value of the curve a (t) at time 0 is zero or close to zero, it is replaced by an arbitrary value at 0 which is not zero, preferably less than or equal to a ⁇ , for example a- ⁇ / 2.
- the invention relates to an electronic system comprising a set of physical elements whose nature induces a bandwidth limitation of the system, and an electronic filter.
- compensation system for giving the system a bandwidth n times greater than the system without this filter, n being a number greater than 1, in which the system without the filter has a pulse response a (t) in function a variable t, characterized in that the compensation filter is a finite impulse response filter with N + 1 coefficients Ci where i is an index varying from 0 to N, the value of the coefficient Ci being defined by the following iteration :
- Ci (bi - ai.C 0 - a ⁇ i Ci .. .. - a ⁇ j.Cj .. .. - ai Ci-i) / a 0 , where ai is a sample value of index i varying from 1 at
- a 0 is zero, we choose for a 0 other non-zero value, preferably between 0 and ai.
- FIG. 1 symbolically represents a physical system receiving an input quantity e and providing an output quantity F (e);
- FIG. 2 represents the impulse response F [x (t)] of the physical system
- FIG. 3 represents the principle of frequency response compensation by an inverse transfer function in the frequency domain
- FIG. 4 represents the principle of establishing a desired impulse response from the actual impulse response of the system
- FIG. 5 represents the principle according to the invention of correction of the bandwidth by a finite impulse response filter associated with the physical system to be corrected
- FIG. 6 represents the general structure of a finite impulse response filter
- FIG. 7 represents the detail of the elaboration of the desired impulse response b (t) from the natural response a (t) of the system
- FIG. 8 represents the frequency behavior of an uncorrected physical system in the presence of an input variable e (t) in slots of increasing frequency
- FIG. 9 represents the behavior of the corrected physical system, under the same conditions as in FIG. 8.
- FIG. 1 represents in a symbolic form (a simple rectangle) any physical system SP which, when an input input quantity e is applied to it, provides an output quantity F (e) at the output.
- the input quantity e is an electronic signal and the output quantity F (e) is another electronic signal.
- the input quantity e is a luminance and the output quantity F (e) is an electronic signal, a luminance sensor being present in the system.
- the system In many applications, it would be desirable for the system to behave in an ideal manner, that is, the magnitude F (e) varies according to a determined function of e both when e varies slowly and when e varies rapidly.
- the light sensor produce an electronic signal of amplitude proportional to the luminance with the same coefficient of proportionality when the luminance varies slowly and when it varies rapidly.
- the system is a physical system and has limitations specific to any physical system, in particular limitations of ability to respond instantaneously to an instantaneous variation of the input quantity e. It introduces function deformations F (e) when e varies too rapidly.
- rapid variation we must understand that we can speak of speed in time or in space. Indeed, we must consider the problems of limitation of physical systems both in terms of variation over time and variations in space as will be detailed below.
- the variable considered for the impulse response is time t but the reasoning would be the same if the variable was spatial; this is all the more true that the spatial variable can be reduced to a temporal variable, for example when the spatially varying signals are read sequentially.
- temporal variable t is generic and can be directly or indirectly transposed to a spatial variable.
- a compensation filter having the transfer function H (f) in the frequency space, thus a filtering curve like that of FIG.
- FIG. 4 shows at 4a the input pulse x (t) (as in FIG. 2a), at 4b the impulse response a (t) of the initial physical system (as in FIG. 2b), and at 4c an answer impulse b (t) desired, similar in shape to that of Figure 4b but compressed according to the time scale and expanded according to the scale of the amplitudes.
- the width at half height of the response b (t) is that of the curve a (t) but divided by a factor n.
- the maximum height of the response b (t) is that of the curve a (t) but multiplied by n.
- the impulse response of the physical system is determined, an improved impulse response is deduced which is a response similar to the initial response, amplified in amplitude and compressed according to the time scale, and the characteristics of the impulse response are calculated.
- a compensation filter which, when it receives at its input the initial impulse response produces at its output the improved impulse response.
- the filter is a finite impulse response filter whose coefficients are easy to calculate once the desired output response for a given input signal form is known.
- FIG. 5 represents the corrected SPC physical system whose impulse response is the impulse response of FIG. 4c.
- This system comprises the initial physical system SP and a finite impulse response filter FIR whose function is to convert the waveform a (t) of FIG. 4b into the waveform b (t) of FIG. 4c, and at the same time to improve the bandwidth of any waveform F (e) out of the physical system SP.
- a finite impulse response filter it is a circuit that processes an analog signal sampled at a sampling frequency F, and cyclically adds a series of weighted successive samples. by individual coefficients chosen according to the filtering function to be obtained.
- the number of samples in the series can be of ten or several tens, or even several hundreds depending on the complexity of the filtering function to be performed.
- the sampling of the signal to be processed by the filter can be done in the filter or upstream of the filter depending on whether the physical system delivers unsampled or sampled signals.
- Figure 6 shows a finite impulse response filter.
- the signal to be filtered is a signal u (t), applied in the form of successive samples at the frequency F and the output signal of the filter is a signal u '(t) output in the form of samples.
- the filter is represented as a set of delay circuits represented by the boxes z "1 and a set of multiplier circuits making it possible to apply to multiply the signal by a weighting coefficient d specific to this circuit
- the letter z is the variable conventionally used for the representation mathematical sampling of sampled systems and the function z "1 represents a unit delay applied to a sample, therefore a delay 1 / F if the sampling frequency is F.
- the filter further comprises an adder ADD.
- the output signal u '(t) of the filter is a sampled signal which is the weighted sum of the series of N + 1 last successive samples received.
- u '(t) U 0 -C 0 + ui. Ci + U 2 -C 2 + .... U N -C N if there are N + 1 samples by counting the sample U 0 .
- the successive samples U 0 , u- ⁇ , U 2 , etc. until u N respectively represent the current sample u (t 0 ) at a time t 0 and the previous samples u (t o -dt), u (t o -2dt), etc.
- the coefficients of the FIR filter are calculated according to the invention from the knowledge of the impulse response a (t) of the physical system SP. This impulse response is measurable or computable from the known constitution of the physical system.
- the calculation of the filter coefficients is done by determining which coefficients are to be used in the filter for a sampled input signal having the shape of the impulse response a (t) of Figure 4b so that the filter with the sampled form of the answer b (t) of Figure 4c.
- n integer and greater than 1, the bandwidth of the physical system SP.
- n can be 2 or 3.
- the duration T may be the duration during which the impulse response is at least equal to 5% of its maximum value.
- N is an arbitrarily chosen integer, which is all the higher since we want to represent more finely the impulse response b (t).
- the improved response b (t) is in dashed lines: it is a curve established by smoothing from the N + 1 samples bj calculated according to the formula above. From the samples ai and bj the coefficients of the finite impulse response filter are calculated which makes it possible to obtain at its output the response b (t) when a signal whose time variation is that of the response a is applied to its input. (t).
- b n a n .C 0 + a n -i .Ci + a o .C n
- Ci (bi - a -
- C 0 ) / a 0 (2.a 2 - a -
- Ci (na n i - ai, C 0 - ai.-i .Ci - ai .Ci-i) / a 0
- CN (na n N - aN-Co - aN-i .Ci - ai.C ⁇ ⁇ ⁇ -i) / ao
- this filter receives the output F [e (t)] of the physical system whose bandwidth is to be increased, and it provides an output F '[e (t)] with increased bandwidth.
- the FIR compensation filter is placed in the physical system rather than at the output thereof, that is to say that the filter can be placed upstream of the physical elements that tend to reduce bandwidth.
- n is a non-integer value, for example 2.5 or 3.5 (or even any number that this has in practice little interest).
- Samples values a n i are no longer available when neither is nor an integer. In this case, it will be possible to use as sample value a n i an interpolated value between the two real samples closest to the non-existent sample of rank
- FIG. 8 represents a simulation performed for a physical system SP whose transfer function is assimilated to a first-order low-pass filter.
- An input rectangular slot waveform (solid line) at a frequency that is greater than a filter cut-off frequency and which is variable in time (the duration of the slots decreases) is applied as a magnitude.
- e (t) at the input of the physical system SP.
- the output of the system is a magnitude F [e (t)] which is represented by a dashed curve.
- FIG. 9 represents the output F '[e (t)] of the system corrected by the FIR filter calculated in the manner explained above, the same slots e (t) being applied to the input. We see that this exit follows much better slots and only deteriorates for the shortest slots.
- the coefficients calculated are as follows:
- This filter is only given as an illustrative example showing the considerable improvement that can be achieved in the bandwidth.
- the physical system will not be as simple as a first-order filter, the number of coefficients N of the filter will be rather 32 or 64 and the n-factor of bandwidth increase will be rather between 2 and 4.
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- Physics & Mathematics (AREA)
- Engineering & Computer Science (AREA)
- Computer Hardware Design (AREA)
- Mathematical Physics (AREA)
- Filters That Use Time-Delay Elements (AREA)
- Complex Calculations (AREA)
Abstract
Description
Claims
Applications Claiming Priority (2)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
FR0800885A FR2927741B1 (fr) | 2008-02-19 | 2008-02-19 | Procede et dispositif pour ameliorer la bande passante d'un systeme physique |
PCT/EP2009/051424 WO2009103624A1 (fr) | 2008-02-19 | 2009-02-09 | Procede et dispositif pour ameliorer la bande passante d'un systeme physique |
Publications (1)
Publication Number | Publication Date |
---|---|
EP2243218A1 true EP2243218A1 (fr) | 2010-10-27 |
Family
ID=39791282
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
EP09712207A Withdrawn EP2243218A1 (fr) | 2008-02-19 | 2009-02-09 | Procede et dispositif pour ameliorer la bande passante d'un systeme physique |
Country Status (4)
Country | Link |
---|---|
US (1) | US20100332577A1 (fr) |
EP (1) | EP2243218A1 (fr) |
FR (1) | FR2927741B1 (fr) |
WO (1) | WO2009103624A1 (fr) |
Family Cites Families (8)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US4703447A (en) * | 1985-04-05 | 1987-10-27 | The Grass Valley Group, Inc. | Mixer controlled variable passband finite impulse response filter |
US5168459A (en) * | 1991-01-03 | 1992-12-01 | Hewlett-Packard Company | Adaptive filter using continuous cross-correlation |
US5208596A (en) * | 1992-04-10 | 1993-05-04 | Rca Thomson Licensing Corporation | DAC distortion compensation |
US5982305A (en) * | 1997-09-17 | 1999-11-09 | Microsoft Corporation | Sample rate converter |
US7031379B2 (en) * | 2001-08-24 | 2006-04-18 | Texas Instruments Incorporated | Time domain equalizer for DMT modulation |
JP4113758B2 (ja) * | 2002-10-29 | 2008-07-09 | 株式会社イシダ | 重量測定装置、ノイズ除去方法およびディジタルフィルタの設計方法 |
US7584235B2 (en) * | 2004-03-18 | 2009-09-01 | Tektronix, Inc. | Variable passband autoregressive moving average filter |
US7206722B2 (en) * | 2005-04-01 | 2007-04-17 | Tektronix, Inc. | Oscilloscope having an enhancement filter |
-
2008
- 2008-02-19 FR FR0800885A patent/FR2927741B1/fr not_active Expired - Fee Related
-
2009
- 2009-02-09 WO PCT/EP2009/051424 patent/WO2009103624A1/fr active Application Filing
- 2009-02-09 US US12/918,337 patent/US20100332577A1/en not_active Abandoned
- 2009-02-09 EP EP09712207A patent/EP2243218A1/fr not_active Withdrawn
Non-Patent Citations (2)
Title |
---|
None * |
See also references of WO2009103624A1 * |
Also Published As
Publication number | Publication date |
---|---|
FR2927741A1 (fr) | 2009-08-21 |
US20100332577A1 (en) | 2010-12-30 |
WO2009103624A1 (fr) | 2009-08-27 |
FR2927741B1 (fr) | 2011-08-05 |
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