JP2016075474A - Analyzer - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a system capable of high-speed fitting.SOLUTION: There is provided an analyzer including: a first calculation unit that calculates the inner product of a sampling value of a spectrum distribution obtained along a first coordinate axis and a discrete B-spline that is the accumulation of integer m convolution of integer n sample value arrays arranged at an interval l along the first coordinate axis, and determines the coefficient of coupling in representing the spectrum as linear combination approximation of the discrete B-spline; and a peak separation unit that breaks down the spectrum distribution into a plurality of B-spline distributions on the basis of the coefficient of coupling.SELECTED DRAWING: Figure 1

Description

  The present invention relates to an apparatus for analyzing a spectral distribution.

  The unit for analyzing a sample disclosed in Patent Document 1 supplies measurement data obtained by supplying a sample to an ion mobility sensor that measures the ionic strength of a chemical substance that passes through an electric field controlled by at least two parameters. A functional unit for detecting peaks present in the two-dimensional representation of the included data, the two-dimensional representation showing the ion intensity when the first parameter is changed and the other parameters are fixed, and detected A functional unit that classifies detected peaks based on continuity and extinction of peaks and peaks present in other two-dimensional representations, and estimates chemical substances contained in the sample based on the classified peaks And a functional unit.

International Publication No. WO2012 / 056709

  A curve fitting method using Gaussian characteristics is known as an analysis method of measurement data in which a plurality of peaks may exist. There is a further need for a method that can analyze the presence of multiple peaks at high speed.

  One aspect of the present invention is an integer m-fold convolution accumulation of a sampling value of a spectral distribution obtained along the first coordinate axis and an integer n sample value sequences arranged at an interval l along the first coordinate axis. A first arithmetic unit that calculates an inner product with a certain discrete B-spline and obtains a coupling coefficient when the spectral distribution is expressed by a linear combination approximation of the discrete B-spline, and a plurality of B- And an analysis device including a peak separation unit that decomposes into a spline distribution.

The first arithmetic unit uses the first digital filter unit including the transfer function of the following expression (A) and the second digital filter unit including the transfer function of the following expression (B) to increase the inner product at high speed. Can be calculated.
(1 / (1-z ⁻¹ )) ^m (A)
(1-z ⁻ⁿ ) ^m (B)

  Furthermore, the first arithmetic unit preferably includes a unit that fixes the coupling coefficient to 0 when the obtained coupling coefficient is negative. By eliminating discrete B-splines with negative coupling coefficients, it is possible to converge at higher speed.

  Further, the analysis apparatus obtains a coupling coefficient candidate having at least one of n and m different from each other by the first arithmetic unit, and evaluates an error between the linear combination approximation of the discrete B-spline and the spectrum distribution by the coupling coefficient candidate. It is desirable to further have a second arithmetic unit for obtaining the coupling coefficient. An integer n and / or m suitable for approximating the spectral distribution can be selected, and peak separation performance can be improved.

  An example of the spectral distribution to be analyzed is the output of the ion mobility sensor, and an example of the first coordinate axis is the compensation voltage.

Another aspect of the present invention is an analysis method, which includes the following steps.
1. A sampling value of a spectral distribution obtained along the first coordinate axis, and a discrete B-spline that is an integer m-fold convolution accumulation of an integer n sample value sequences arranged at an interval l along the first coordinate axis. An inner product is calculated to obtain a coupling coefficient for expressing a spectrum by a discrete B-spline linear combination approximation.
2. Decomposing the spectral distribution into a plurality of B-spline distributions based on the coupling coefficient.

The block diagram which shows schematic structure of an analyzer. The figure explaining B-spline. The figure explaining a discrete B-spline. The figure which shows the relationship between the movement of the ion (molecule) in an ion mobility sensor, and a spectrum. The figure which shows each type | formula expressing B-spline. The figure which shows each type | formula which calculates the inner product of B-spline. The figure which shows each type | formula expressing linear combination approximation. The figure which shows the maximum value of linear combination approximation. The figure which shows each type | formula which calculates the inner product of a profile and a B-spline. The figure which shows a mode that an inner product is calculated using a digital filter. The figure which shows each type | formula which calculates | requires a coupling coefficient. The figure which shows a mode that a turning coupling approximation is calculated from a coupling coefficient using a digital filter. The figure which shows square error evaluation. The figure which shows a spar city evaluation. The figure which shows some examples of B-spline approximation. The figure which shows the example from which B-spline approximation differs.

  FIG. 1 shows an example of an analysis apparatus that analyzes the output (measurement data, IMS data) of the ion mobility sensor 1. The analysis device 10 may analyze the IMS data 19 directly input from the ion mobility sensor 1 or may analyze the IMS data 19 stored in an appropriate storage 2. .

  The analysis apparatus 10 includes an arithmetic unit (first arithmetic unit) 11 that obtains a coupling coefficient for approximating the IMS data 19 by discrete B-splines, and an evaluation unit (first unit) that evaluates an approximation situation based on the obtained coupling coefficient. Selected as a linear combination of discrete B-splines approximating the IMS data 19 by the evaluation unit 12 and the library 13 storing the setting values used by these units 11 and 12. A peak separation unit 14 for separating and recognizing peaks included in the B-spline approximation, an estimation unit 15 for classifying the peaks based on the separated peaks and estimating a measurement target of the IMS data 19, and a separation peak And a database 16 containing data.

  The analysis apparatus 10 is typically configured using computer resources including a CPU and a memory, recorded as software (program or program product) on an appropriate recording medium, or via computer network such as the Internet. Provided. The analysis device 10 may be provided by an ASIC, an LSI, a reconfigurable semiconductor circuit device, an optical circuit device, or the like.

  As a typical ion mobility sensor 1, an asymmetric field ion mobility spectrometer (FAIMS) or a differential electric mobility spectrometer (DMS) is known. An example of the FAIMS sensor 1 is an ion mobility analyzer described in International Publication WO2006 / 013396 or International Publication WO2007 / 014303. These are monolithic or micromachine type compact mass spectrometers, which are sufficiently portable.

  The FAIMS sensor 1 includes a drift chamber that moves the ionized measurement target while affecting the ionized measurement target, and a detector that detects the ionized measurement target (charge of the measurement target) that has passed through the drift chamber. In the drift chamber, the software-controlled electric field generated by the voltage Vd and the voltage Vc fluctuates positively and negatively at a specific period, and the chemical substance to be detected is filtered by the filtering effect of the electric field, For example, it collides with the detector at the msec level and is measured as ion intensity (ion current) Ic.

  The Vd voltage (Dispersion Voltage, dispersion voltage, electric field voltage (Vd)) is an AC component, and the Vc voltage (Compensation Voltage, compensation voltage) is a DC component. In the FAIMS sensor 1, it is possible to detect the ion intensity that changes according to these two variables as an ion current. Since the detected waveform of the ionic current often varies depending on the chemical substance, it is possible to identify the chemical substance. Data (measurement data, IMS data) 19 obtained from the ion mobility sensor is at least three-dimensional data including the value of the ion current. Depending on the chemical substance, for example, when the Vd voltage is fixed due to ion mobility characteristics, the value of the ionic current may form a plurality of peaks when the Vc voltage is changed. Therefore, there is a possibility that the chemical composition (chemical substance contained in the sample) of the sample detected by the ion mobility sensor 1 can be specified based on the peak contained in the IMS data 19.

  FIG. 2 shows an m-th floor B-spline. FIG. 2A is a B-spline obtained by convolving and integrating a rectangular function once, and is a first-order B-spline. FIG. 2B shows a B-spline on the second floor, FIG. 2C shows a B-spline on the third floor, and FIG. 2D shows a B-spline on the fourth floor. It is clear from the central limit theorem that convergence to a normal distribution is achieved in the limit where m is infinite.

  FIG. 3A shows a state in which a discrete B-spline is defined by m-order convolution accumulation of n sample number sequences obtained from a rectangular function. The m-th order discrete B-spline is obtained as the output of the digital filter defined by the transfer function shown in FIG. 3B by z-transforming as shown in FIG.

  Ion mobility analysis is a technique for discriminant analysis of chemical molecules. Because it can analyze trace amounts of chemical substances, it can be used to analyze odors and scents and detect poisonous substances, drugs, and explosives. The analysis procedure is roughly divided into physical processing and computational processing.

  4A and 4B schematically show physical processing in the ion mobility sensor 1. FIG. The ionized chemical molecules move inside the ion mobility sensor 1 and are caught by the negative electrode 1a or the positive electrode 1b. A typical ionization method is electron beam irradiation from a radioactive element, and may be a method such as UV irradiation or corona discharge. While the molecules ionized inside the ion mobility sensor 1 are moving, as described above, the molecules move zigzag by the dispersion voltage (Vd voltage) and the compensation voltage (Vc voltage), and the conditions of the Vd voltage and the Vc voltage are satisfied. Thus, only the molecules that have reached the electrode 1a or 1b are measured as measurement data (IMS data) 19 of the ion mobility sensor 1. An example of the IMS data 19 is a spectrum (spectral distribution, spectrum) in which the ion current Ic varies due to a change in the Vc voltage.

  The ionized molecules are affected by the Vd voltage and the Vc voltage in proportion to their charge / mass, and collide with air molecules on the way and proceed while diffusing. For this reason, on average, it proceeds at a speed peculiar to the kind of ions, and it reaches the electrode, for example, the positive electrode 1a, with variations in time. The variation is assumed to follow a normal distribution. This is because if the position change caused by each collision varies according to the same distribution, the distribution obtained through infinite collisions becomes a Gaussian distribution.

  An example of the IMS data 19 is shown in FIG. This waveform is a spectrum (spectral distribution) of the ion current obtained when the Vc voltage is changed with the Vd voltage kept constant. This current waveform is called a profile, and the first coordinate axis is the Cv voltage (compensation voltage). Since one Gaussian distribution corresponds to one kind of ion, the profile is modeled as an unloaded multiple sum of a plurality of Gaussian distributions as shown in FIG.

  Conventional computing processes aim to identify each distribution that constitutes it from a given profile. The type of ion molecule is determined by the average value of each distribution, and the amount is determined by height. Since the number, average, and variance of the Gaussian distribution are unknown, it is a common technique to search for these parameters by the steepest descent method. The search is a sequential process and requires many repeated operations until convergence. For this reason, the current calculation processing takes a lot of time even if a high-performance CPU is used.

  One example of physical processing that is smaller and faster is the FAIMS chip released by Owlstone in 2006. The size of the sensor chip is several tens of millimeters square, and the physical processing speed is several milliseconds. Therefore, by increasing the efficiency of the calculation process, the entire system including the chemical substance analysis sensor 1 such as FAIMS and the analysis device 10 can be incorporated into a portable device.

For this purpose, it is desirable to change the calculation processing algorithm from a sequential search based on a traditional Gaussian mixture distribution model to a new calculation processing suitable for chipping. The features of this approach are summarized in the following four points.
(1) Instead of a Gaussian distribution, an integer m-th order B-spline representing a variation in speed obtained through a finite number of (m) collisions according to a uniform distribution is used. If m is increased, the B-spline approaches a Gaussian distribution. According to the principle of ion mobility analysis, the shape of the distribution cannot also be a perfect normal distribution with an infinite base. It is not unnatural to use B-splines instead of the normal distribution.
(2) Use a B-spline high-speed calculation method. It is known that a discrete B-spline obtained by replacing a uniform continuous distribution with a uniform discrete distribution sampled at n points can be generated only by addition and subtraction (T. Saramaki, Y. Neuvo and SK Mitra, Design of computationally efficient interpolated FIR filters, IEEE Trans. Circuits & Syst., 35 (1), 70-88, 1988). The discrete B-spline converges to the original B-spline by increasing the number of sampling points n, and the waveform can be approximated to a discrete B-spline by a high-speed digital filter (K. Ichige and M. Kamada, An approximation for discrete B-splines in time domain, IEEE Signal Process.Lett., 4, 82-84, 1997, and K. Ichige, M. Kamada and R. Ishii, A simple scheme of decomposing and reconstructing continuous-time signals by B-splines, IEICE Trans Fundamentals, E81-A, 2391-2399, 1998).
(3) Discrete B-splines used for approximation are arranged at extremely fine intervals. In the original use of the B-spline as a curved line expression, it has been common knowledge to arrange the B-spline at intervals sufficient for expression. In the ion mobility analysis, the position of the center of the distribution is unknown, but if the position is searched for, it will return to the slow sequential calculation. Therefore, discrete B-splines are arranged in advance at a fine interval, and only the load of the discrete B-splines that are important for the approximation of the profile is increased to be embossed.
(4) Rather than sequentially searching for the distribution of the unknown parameter distribution, the high-speed digital filter is used for n fixed at various values, assuming that the spread of ions reaching the same period is the same. Approximate brute force execution in parallel. The case where a high-precision approximation with a small number of discrete B-splines is obtained is taken as the analysis result. One method that can be used to determine approximate accuracy is sparse approximation (for sparse approximation, M. Vetterli, P. Marziliano and T. Blu, Sampling signals with finite rate of innovation, IEEE Trans. Signal Process., SP-50, 1417-1428, 2002).

  An m-th order B-spline is defined as a m-fold convolution integral of a rectangular function. The central limit theorem shows that this converges to a normal distribution at the limit where m 1 is infinite. Further, it is also known that a discrete B-spline that is an m-fold convolution accumulation of n sample value sequences obtained from a rectangular function converges to a B-spline at the limit that makes n infinite. In the arithmetic unit 11 of the analysis apparatus 10, this discrete B-spline is used as a distribution.

  The discrete B-spline on the first floor is defined by equation (1) in FIG. The z conversion is expressed by the equation (2) in FIG. Therefore, the m-th order discrete B-spline defined recursively and its z-transform are expressed by equations (3) and (4) shown in FIG.

  The inner product of the discrete B-splines (bm [k−l]) and (bm [k−r]) is transformed as shown in FIG. Here, if “˜bm [k]) = bm [−k]” is entered, this is further transformed as shown in FIG. Further, the z transformation is expressed as shown in FIG. Therefore, this inner product can be calculated as equation (5) in FIG.

The linear combination “q [k]” of the m-th order B-spline “bm [kl]” by the coefficient (combination coefficient) “c [l]” whose z-transform is FIG. 7A is shown in FIG. It is expressed by the convolution represented by Equation (6). This calculation corresponds to Expression (7) in FIG. 7C when z conversion is performed. Therefore, the output obtained by inputting the coupling coefficient “c [k]” to the digital filter having the transfer function “((1−z ⁻ⁿ ) / (1−z ⁻¹ )) ^m ” is sampled at time k. Then, a linear combination “q [k]” is obtained. This digital filter can be executed separately for the m-fold accumulation of Expression (A) and the m-th order difference of Expression (B).
(1 / (1-z ⁻¹ )) ^m (A)
(1-z ⁻ⁿ ) ^m (B)

  Therefore, the arithmetic unit 11 includes a first digital filter unit 11a including the transfer function of Expression (A), and a second digital filter unit 11b including the transfer function of Expression (B). Although overflow occurs during the calculation in these digital filter units 11a and 11b, these filter units 11a and 11b have a function of performing a two's complement operation having the number of bits that can accommodate the final result of the calculation. The result is correct.

It should be noted that the absolute maximum value of the linear combination “q [k]” that is the final result is obtained from the inequality (8) in FIG. 8 derived from the fact that the discrete B-spline is non-negative, and the absolute value “| c [ l] | does not exceed the n ^m times the maximum value of ".

When a discrete sampling value of the spectral distribution of the IMS data 19 supplied to the analysis apparatus 10, that is, a profile is represented by “p [k]” and its z-transform is expressed as shown in FIG. The inner product of the profile “p [k]” and the discrete B-spline “bm [kr]” is expressed by equation (9) in FIG. 9B and can be transformed as equation (10). Here, z conversion of “˜bm [k]” is “Bm (z ⁻¹ )”. Therefore, the z-transformed expression corresponds to Expression (11) shown in FIG. This inner product is obtained by inputting an output obtained by inputting a profile “p [r]” to a digital filter having a transfer function “((1-z ⁻ⁿ ) / (1−z ⁻¹ )) ^m ” at time “( n-1) m + r ". Similar to the above, this processing can be executed by the first digital filter unit 11a and the second digital filter unit 11b which are composed of two parts.

  The inner product of the profile “p [k]” and the discrete B-spline “bm [k-r]” is calculated by a product-sum operation as shown in Expression (9) in FIG. However, according to the equations (10) and (11) in FIG. 9, it can be understood that the calculation can be performed by the digital filter units 11a and 11b including only addition and subtraction.

  In FIG. 10, the profile “p [r]” is input to the digital filter units 11a and 11b, and the inner product “<p [•], bm [• −r]>” in “(n−1) m + r” is calculated. It shows a state. The m-th order accumulation calculated by the first digital filter unit 11a that is the first half does not depend on n, and n is included only in the m-th order difference calculated by the second digital filter unit 11b that is the second half. Therefore, the calculation of the m-th order accumulation may be performed only once for each profile, and the discrete B-splines and profiles for different n can be obtained by calculating the m-th order difference while changing n by the second digital filter unit 11b. Can be taken out. The computation required for calculating one inner product is almost m subtractions, and the processing time can be shortened.

  The first arithmetic unit 11 further includes a least square approximation unit 11c that performs non-negative coefficient least square approximation. In the least square approximation unit 11c, a function “q [k]” obtained by linearly combining a profile “p [k]” with K discrete B-splines arranged at an interval l using a coupling coefficient “c [l]”. Calculate the square error when approximated by. The linear combination approximation “q [k]” is expressed by equation (12) in FIG. 11A, the square error is calculated by equation (13) in FIG. 11B, and the square error E is minimized. A small coefficient (coupling coefficient) “c [l]” is determined by solving the linear equation (13) shown in FIG. 11C according to a normal least square approximation method.

  Since the coefficient is proportional to the number of ions, the coefficient “c [l]” is subject to a non-negative constraint. Therefore, the least square approximation unit 11c fixes negative coefficients among the coefficients obtained by the normal least square approximation to determine the coefficients under this condition, and excludes the corresponding discrete B-splines. Then, the function of repeating the least square approximation until all the coefficients become non-negative is included. Solving the linear equation (13) requires four arithmetic operations of floating-point arithmetic, but the linear equation to be solved can be expressed by a band matrix, and the target function gradually decreases, so the processing time increases so much. Does not follow direction. The inner product “<bm [· −k], bm [· −l]>” between the discrete B-splines can be calculated in advance and stored in the library 13.

  However, although discrete B-spline columns arranged at fine intervals are theoretically linearly independent, they are almost linearly dependent, and it is pointed out that the process of determining the load may become numerically unstable. ing. However, in a numerical experiment on test data, although it becomes numerically unstable at an initial stage using a large number of discrete B-splines, discrete discrete B-splines that have obtained negative coefficients are in the process of being excluded. The number of B-splines decreases. For this reason, it has been observed that the calculation eventually becomes stable. In other words, it is determined that limiting the coupling coefficient to non-negative in the least square approximation unit 11c suppresses numerical instability.

  In FIG. 12, the linear combination approximation “q [” obtained for approximating the profile from the coupling coefficient “c [k]” obtained above using the first digital filter unit 11a and the second filter unit 11b. k] "is shown. Since the coupling coefficient is limited to be non-negative, the number of coupling coefficients used in the approximation linear combination is limited, and the peaks included in the profile q can be substantially separated.

  The analysis unit 10 further includes an evaluation unit (second arithmetic unit) 12 that evaluates the linear combination approximation “q [k]” obtained from the coupling coefficient obtained by the first arithmetic unit 10. The evaluation unit 12 determines in advance the coupling coefficients for various n and / or m as coupling coefficient candidates, and obtains the linear coupling approximation “q [k]” obtained by them for the profile “p [k]”. Evaluate and output the optimum coupling coefficient from among the coupling coefficient candidates and thereby the linear coupling approximation.

The evaluation unit 12 includes a first evaluation unit 12a that evaluates a square error and a second evaluation unit 12b that performs a sparsity evaluation. The first evaluation unit 12a calculates the linear combination approximation “q [k]” from the coupling coefficient “c [k]” according to the equation (6) as shown in FIG. This can be simplified by the digital filter units 11a and 11b. The square error of the linear combination approximation “q [k]” obtained and the given profile “p [k]” is calculated by accumulating “(p [k] −q [k]) ² ”. Is required. The first evaluation unit 12a calculates the mean square error E1 using the formula shown in FIG.

  The second evaluation unit 12b sets a case where the square error E1 is sufficiently small by the first evaluation unit 12a from among the coupling coefficient candidates obtained for various n, and is further sparse. Search for combinations of coupling coefficients that give approximate results. This is based on the assumption that the profile p can be approximated by a small number of discrete B-splines among the obtained candidates, which is an essential condition for a correct analysis.

Since both the profile “p [k]” and the linear combination approximation “q [k]” are non-negative, if the square error is extremely small, their areas Σk (p [k]) and Σk (q [k]) It should be almost the same. Therefore, an approximate expression obtained by normalizing the discrete B-spline “bm [kl]” with its area Σk (bm [kl]) = n ^m ”is considered as shown in Expression (15) of FIG. The sum of the corrected coefficients “n ^m c [l]” becomes substantially constant as shown in the equation (16) in FIG. In this situation, sparsity means that the linear combination approximation “q [k]” consists of a small number of large chunks. One of the evaluation amounts is E2 shown in FIG. The second evaluation unit 12b selects and outputs a case where the evaluation amount E2 is maximum as an analysis result.

  In FIGS. 15A to 15J, m is fixed to 4, and an example of the profile “p [k]” is approximated for various n within a local window range of sample values of 128 points in length. Results are shown. The profile is the output (ion current, IMS data, spectral distribution) 19 of the ion mobility sensor 1, and the coordinate axis (first coordinate axis) is the compensation voltage Vc. In the figure, a solid line indicates a profile, a broken line indicates an approximate curve (linear combination approximation) “q [k]”, and an alternate long and short dash line indicates a discrete B-spline constituting the approximate curve “q [k]”.

  15A to 15J, the approximate error E1 obtained by the first evaluation unit 12a is 10% or less when n is 6 to 12, and is larger than 15% in other cases. Therefore, the second evaluation unit 12b calculates the evaluation amount E2 for the approximate curve (linear combination approximation) “q [k]” in the former case where n is 6 to 12. When n is 6 to 12, the evaluation amount E2 of the sparsity is maximized when n is 12. This case is adopted as a sparse good approximation, and the second evaluation unit 12b outputs. In this example, a result that two peaks are included in the profile p is output.

  FIG. 16 shows an example of an approximation result obtained by sampling an entire profile and calculating those values. The optimum n may change according to the progress of the first coordinate axis. For example, the optimum n can be estimated for each window of the local compensation voltage Cv value. In the example shown in FIG. 16, the optimum values of n for the left peak and the right peak are 12 and 14, respectively.

  The peak separation unit 14 of the analysis device 10 updates the peak database 16 with the peaks separated (detected peaks) based on the above results. The peak classification and estimation unit 15 determines the peak type using the evaluation rules provided by the peak classification rule table and the peak type (type) rule table of the peak database 16. The evaluation rules include the theoretical relationship between the peak characteristics of reactance RIP and the peak characteristics of monomers, dimers and trimers derived from chemicals. Further, the classification and estimation unit 15 includes a function of estimating a chemical substance contained in the sample gas measured by the ion mobility sensor 1. The separation and estimation unit 15 includes a selection function for selecting a chemical candidate included in the sample gas based on the identified peak indicating at least one of a monomer, a dimer, and a trimer, and the identified peak and the third It includes a selection function that obtains a correlation with the parameter concentration and selects a chemical substance candidate contained in the sample gas.

  As explained above, a known calculation mechanism relating to the calculation method of discrete B-splines was first applied to ion mobility analysis. In the conventional application scene, the arrangement interval of the discrete B-splines is fixed to n, but in the present application scene, the finest interval l is appropriate. Performing a least-squares approximation with an almost linear cascade of functional systems can lead to numerical instabilities. In the numerical examples tried so far, the final processing result is not greatly affected.

  That is, by using a discrete B-spline which is a good alternative to the Gaussian distribution, a method suitable for hardware implementation that is useful for analyzing a profile waveform obtained by ion mobility analysis can be configured. It can be provided as a system that is easy to realize. One factor that is suitable for hardware implementation is that the inner product of a given waveform and a discrete B-spline and the load sum of the discrete B-spline can be calculated with a very simple digital filter.

  In this system, the profile waveform is approximated by the least squares under the constraint that the load is non-negative, with the load sum of the discrete B-splines arranged at fine intervals, so that the main components buried in the profile are Detected when load increases. Since discrete B-splines arranged at fine intervals are almost linearly dependent, their least-square approximation becomes numerically unstable, but the discrete load given a negative load in the process of numerical calculation Since the B-spline is removed, the approximate result can be finally obtained stably. Since one-time approximation can be performed at high speed, a case where a good sparse approximation using a large and small load is obtained by testing discrete B-splines of various widths can be adopted as an analysis result.

  In the above, the evaluation unit 12 may set a single evaluation amount for evaluating the goodness of analysis by combining the mean square error E1 and the evaluation amount E2 of the sparsity, and may be applied to various current waveforms. Numerical stability, analytical performance, and processing speed may be evaluated. The spectrum distribution (profile) to be analyzed is not limited to the output of the ion mobility sensor 1. The analysis target of the analysis apparatus 10 may be a measurement result of a phenomenon involving a finite number of collisions according to a uniform distribution, a measurement result of a phenomenon estimated to follow a normal distribution, or the like. Further, the first coordinate axis of the spectrum is not limited to the compensation voltage, and may be another physical quantity, time, or the like.

1 ion mobility sensor, 10 analyzer

Claims (6)

A sampling value of a spectral distribution obtained along a first coordinate axis, and a discrete B-spline that is an integer m-fold convolution accumulation of an integer n sample value sequences arranged at an interval l along the first coordinate axis; A first arithmetic unit for obtaining a coupling coefficient when expressing the spectral distribution by linear combination approximation of the discrete B-spline;
And a peak separation unit that decomposes the spectral distribution into a plurality of B-spline distributions based on the coupling coefficient. The first arithmetic unit according to claim 1, wherein the first arithmetic unit includes a first digital filter unit including a transfer function of the following expression (A):
And a second digital filter unit including a transfer function of the following equation (B).
(1 / (1-z ⁻¹ )) ^m (A)
(1-z ⁻ⁿ ) ^m (B)   3. The analysis apparatus according to claim 1, wherein the first arithmetic unit includes a unit that fixes the coupling coefficient to 0 when the obtained coupling coefficient is negative.   4. The combination coefficient candidate according to claim 1, wherein at least one of n and m is different from each other by the first arithmetic unit, and linear combination approximation of discrete B-splines by the combination coefficient candidate and An analysis apparatus further comprising a second arithmetic unit that evaluates an error from a spectrum distribution and obtains the coupling coefficient.   5. The analysis device according to claim 1, wherein the spectral distribution includes an output of an ion mobility sensor. A sampling value of a spectral distribution obtained along a first coordinate axis, and a discrete B-spline that is an integer m-fold convolution accumulation of an integer n sample value sequences arranged at an interval l along the first coordinate axis; Calculating the inner product, and obtaining a coupling coefficient for expressing the spectral distribution by a linear combination approximation of the discrete B-spline;
An analysis method comprising: decomposing the spectral distribution into a plurality of B-spline distributions based on the coupling coefficient.

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