Data processing device for chromatograph, data processing method, and chromatograph

Abstract

Provided is a data processing device for a chromatograph, a data processing method, and a chromatograph, which can perform aggregation processing that can cope with cases where data points are not arranged at equal intervals and various peak shapes. A data processing device for a chromatograph that performs data processing based on plot data measured by a chromatograph includes an imaginary curve calculation data generation section that obtains imaginary curve calculation data that is less in number than the plot data measured, and an imaginary curve calculation section that obtains an imaginary curve based on the imaginary curve calculation data, the imaginary curve calculation data generation section obtaining a representative value for each prescribed number of plot data and setting the representative value as the imaginary curve calculation data, the prescribed number being obtained based on a set peak width.

Description

[0001] This application is a divisional application of the patent application with application number 202010026841.5, titled "Data processing device of chromatograph, data processing method, and chromatograph", and filed on January 10, 2020. TECHNICAL FIELD

[0002] The present application relates to a chromatographic analysis technology of a liquid chromatograph or the like, and particularly relates to a data processing device of a chromatograph, a data processing method, and a chromatograph. BACKGROUND

[0003] In a chromatograph, the kind and amount of a component contained in an analysis sample are found from waveform data in which the horizontal axis is time and the vertical axis is signal intensity. At this time, waveform processing is performed based on data detected by the device, and a characteristic point such as a start point of an increase in signal intensity or an end point of a decrease is detected. Specifically, for example, a Gaussian function or the like is calculated using a nonlinear least square method (curve fitting), and a characteristic point such as a start point is found (for example, refer to Patent Literature 1).

[0004] Patent Literature 1: Japanese Patent Application Publication No. 2006-177980

[0005] In the case where curve fitting using a Gaussian function or the like of the above-described nonlinear least square method is performed, if the number of plots is small, the calculated curve is likely to deviate from the actual waveform, and on the other hand, if the number of plots is large, the computational load of the curve fitting processing becomes large. In addition, due to the influence of noise, the calculated curve is likely to deviate from the actual waveform. SUMMARY

[0006] The present application is a data processing device of a chromatograph that performs data processing based on plot data measured by a chromatograph, and is characterized by including a hypothetical curve calculation data generation section that calculates hypothetical curve calculation data in a smaller number than the measured plot data, and a hypothetical curve calculation section that calculates a hypothetical curve based on the hypothetical curve calculation data, wherein the hypothetical curve calculation data generation section calculates a representative value for each of a predetermined number of plot data and sets the representative value as the hypothetical curve calculation data, and the predetermined number is calculated based on a set peak width.

[0007] To achieve the above object, the present application is a data processing device of a chromatograph that performs data processing based on plot data measured by a chromatograph, and is characterized by including a hypothetical curve calculation data generation section that calculates hypothetical curve calculation data in a smaller number than the measured plot data, and a hypothetical curve calculation section that calculates a hypothetical curve based on the hypothetical curve calculation data, wherein the hypothetical curve calculation data generation section calculates a representative value for each of a predetermined number of plot data and sets the representative value as the hypothetical curve calculation data, and the predetermined number is calculated based on a set peak width.

[0008] A chromatograph is provided, characterized by a chromatograph unit that separates components contained in a sample and performs measurement, and the data processing device.

[0009] A data processing method for a chromatograph is provided, which performs data processing based on plot data measured by a chromatograph, characterized by comprising: a hypothetical curve calculation data generation step of obtaining hypothetical curve calculation data that is less in number than the measured plot data; and a hypothetical curve calculation step of obtaining a hypothetical curve based on the hypothetical curve calculation data, wherein in the hypothetical curve calculation data generation step, a representative value is obtained for each of a prescribed number of plot data and set as the hypothetical curve calculation data, the prescribed number being obtained based on a set peak width.

[0010] Thus, the number of data at the time of obtaining the hypothetical curve can be suppressed to be small, and therefore, it is possible to easily reduce the influence of the operation processing load, noise, and the like.

[0011] According to the present application, it is possible to perform the aggregation processing that can cope with the case where the data points are not arranged at equal intervals in time and various peak shapes, and it is possible to easily reduce the operation processing load at the time of the hypothetical curve calculation processing, reduce the influence of noise, and the like. BRIEF DESCRIPTION OF DRAWINGS

[0012] Figure 1 is a block diagram showing the outline structure of a chromatograph.

[0013] Figure 2 is a block diagram showing the outline structure of a data processing device of a chromatograph.

[0014] Figure 3 is a graph showing an example of a chromatogram.

[0015] Figure 4 is an explanatory diagram showing an example of extraction of a characteristic point.

[0016] Figure 5 is an explanatory diagram showing an example of extraction of another characteristic point.

[0017] Figure 6 is an explanatory diagram showing an example of obtaining a non-inductive displacement.

[0018] Figure 7 is an explanatory diagram showing an example of extraction of another characteristic point.

[0019] REFERENCE NUMERALS

[0020] 100: liquid chromatograph; 110: mobile phase container; 120: pump; 130: autosampler; 140: column; 141: column oven; 150: detector; 160: data processing device; 161: control processing section; 161a: control section; 161b: measurement condition setting section; 161c: recording section; 162: data holding section; 163: arithmetic processing section; 163a: signal processing section; 163b: arithmetic section; 163c: determination section; 170: display section DETAILED DESCRIPTION

[0021] Hereinafter, an embodiment of the present application will be described in detail with reference to the drawings.

[0022] Structure of liquid chromatograph 100

[0023] Figure 1 The outline structure of the liquid chromatograph 100 is shown. The liquid chromatograph 100 has a mobile phase container 110 which stores a liquid as a mobile phase, a pump 120 which delivers the mobile phase, an autosampler 130 which injects a sample, a column 140 which is kept at a constant temperature by a column oven 141 and separates components in the sample, a detector 150 which detects the separated components, a data processing device 160 which processes the detection results, and a display section 170 which displays the processing results. In addition, each part constituting the liquid chromatograph 100 can be configured similarly to a general device except for the processing contents of the data processing device 160, and thus detailed description is omitted.

[0024] Detailed structure of data processing device 160

[0025] As shown in FIG. 1, the data processing device 160 has a control processing section 161, a data holding section 162, and an arithmetic processing section 163. Figure 2 The control processing section 161 controls the overall operation of the liquid chromatograph 100, and is provided with a control section 161a, a measurement condition setting section 161b which sets measurement conditions according to an operation of an unillustrated operation panel or the like, and a recording section 161c which records measurement results or the like.

[0026] The data holding section 162 holds data or the like processed according to the measurement results.

[0027]

[0028] ​The processing unit 163 performs processing based on the measurement results, functioning as a hypothetical curve calculation data generation unit, a hypothetical curve calculation unit, a provisional start / end point calculation unit, a provisional feature point acquisition unit, and an actual plotted data feature point extraction unit. Specifically, for example, it includes: a signal processing unit 163a, which performs D / A conversion on the analog signal output from the detector 150; a calculation unit 163b, which extracts and analyzes feature points; and a determination unit 163c, which determines the analysis results.

[0029] (Data processing action)

[0030] In the liquid chromatograph 100 described above, for example, by measuring the action, the following is obtained: Figure 3 The waveform data shown is time on the horizontal axis and signal intensity on the vertical axis. Since the relationship between time and composition is known beforehand, the composition contained in the analytical sample is determined by the dwell time on the horizontal axis of the waveform data peak (qualitative processing). Furthermore, the amount of that composition is measured based on the peak area of ​​the waveform data (quantitative calculation processing). These processes are performed by extracting, for example... Figure 3 The diagram shows typical examples of characteristic points such as peaks, start points, end points, valleys, and shoulders, and further uses these points as a basis to set baseline segments.

[0031] Regarding the extraction of the aforementioned feature points, for example, taking the extraction of peak points, the processing by the arithmetic processing unit 163 is as follows: Figure 4 Proceed as shown.

[0032] (Data processing action - bunching)

[0033] First, when the sampling interval of detector 150 is relatively fine and the number of discrete data, i.e. plotted data, actually detected within the range of peak width w is relatively large, such as more than 65 points, the data is aggregated on the time axis to form an imaginary curve calculation data of less than 64 points, or smoothing preprocessing of the measured point group based on Savitzky-Golay method is performed.

[0034] The above aggregation processing is basically performed, for example, by simply adding every 2 points or every 3 points, etc. However, depending on the data processing device, there are cases where data points are not arranged at equal intervals of time, and aggregation processing corresponding thereto is required. For example, in a case where 4 points (aggregation of 1600 ms) are added at a sampling interval of 400 ms, and the sampling interval is changed to twice, 800 ms, thereafter, it is possible to consider performing aggregation processing of addition of every 2 points. Here, the input Peakwidth is the peak width imagined by the user. Sometimes, a shoulder peak is a superposition of 2 peaks, or a doublet looks like a single peak with a wide peak width, and it is unavoidable. There is also an influence in which a minor peak does not look like a single peak and widens a major peak. It is preferable to implement aggregation processing in which various peak shapes are also seriously considered.

[0035] The number of data of the imaginary curve calculation data generated by the above aggregation is set to, for example, 15 points to 64 points, etc. This is because, in general, in order to accurately calculate the peak area, it is preferable to have data of 30 points to 50 points, or in order to avoid a case where a plurality of start point candidate points appear due to too many data points, it is easy to select an appropriate start point (or end point), and it is preferable to have peak formation data of 32 points to 63 points, etc.

[0036] More specifically, the above peak width w is an input variable for waveform processing given by a prescribed operation or input in the data processing system (CDS), and, for example, in a case where 0.1 minutes is input, the half width of the target peak is a reference for calculating the data point interval with 0.1 minutes as a target. For example, in a case where actual data is taken in at a sampling interval of 50 ms, 0.1 minutes is 6 s = 6000 ms, and the number of points of w is 120 points. In order to collect this to about 30 points, it is necessary to set the sampling interval to 200 ms, and as a result, it is possible to collect 4 points into 1 data point, that is, to perform aggregation processing. As can be understood from this, w is a very useful parameter. The aggregation processing based on the input value w not only reduces noise, but also as a pre-process of waveform processing, it is possible to think of a CDS of a peak waveform desired by the operator. That is, it is possible to optimize to an easy-to-process data point number that is not too much nor too little for the CDS.

[0037] Furthermore, for example, when the target peak width is w = 60s, the number of aggregated data points within a 1s time interval can be set to approximately 60. That is, for example, when the sampling period S of the original data is S = 0.4s, and the number of data points calculated from the hypothetical curve of a peak is set to N (e.g., a range of 32 to 63 points), the number of aggregated points B is calculated using B = w / (S × N). Additionally, if the value of B is not an integer, it can be rounded down or rounded to the nearest whole number. More specifically, for example, when B ≥ W / (S × N) and N = 64, B is the smallest integer satisfying the above formula.

[0038] When the number of points to be clustered is determined as described above, by calculating representative values ​​such as the average value of the measured signal strength for each of that number of plotted data points, the computational processing load of subsequent hypothetical curve calculation (curve fitting) can be easily reduced or the impact of noise can be mitigated. Furthermore, to reduce the number of data points, in addition to calculating representative values, the interval between plotted data points can be lengthened; even in this case, the computational processing load can be reduced.

[0039] Here, the peak width w can be set by user input or automatically based on the peak shape. In the latter case, it is easier to set the value for each component.

[0040] The peak width w mentioned above is provisionally calculated to determine the required number for aggregation. Therefore, compared to calculating the peak area after processing the hypothetical curve, high precision is not required. Specifically, the provisional start point and provisional end point can be obtained, for example, by calculating the provisional start and end points in the following manner. That is, for example, as follows: Figure 5 As shown, if the difference in the measured signal strength of adjacent plotted data is successively set as d1 to d4, and the specified insensible displacement is set as I, and d1≤I followed by d2 to d4≥I for three consecutive times, then the plotted point E corresponding to the initial d1 can be set as the starting point. The ending point can also be calculated in the same way.

[0041] The aforementioned imperceptible displacement I can also be as follows: Figure 6 It is set automatically as shown. For example, first, in the time period where no peak is assumed (the interval where there is no peak near the peak, i.e., the interval considered as the baseline), find the peak width w of the full width at half the value. 1 / 2 For a time interval of 20 to 30 times the normal range, the peak-to-peak magnitude of the detected signal (the maximum and minimum difference between the peaks of the noise signal) on the vertical axis is assumed to be the magnitude of the noise. Multiplying this by a pre-set coefficient (e.g., 3) allows for the setting of a non-sensitive displacement I (the threshold for identifying a peak). Here, the aforementioned coefficient does not necessarily have to be a natural number.

[0042] In addition, in a state where the aggregation processing is not performed, since the number of data points is too large or noise is not relatively suppressed, and the like, the size relationship can not be continuous even in a situation that should be recognized as a start point or the like, in which case or the like, it is only necessary to perform adjustment of increasing or decreasing the number of times of continuity, the size of the inductive displacement I, or the like, to set it to an appropriate situation according to the passage of time and repetition.

[0043] (Data processing action - hypothetical curve calculation processing and feature point determination processing)

[0044] When a proper number of hypothetical curve calculation data is found by the aggregation processing described above, the hypothetical curve calculation processing (curve fitting) or the feature point determination processing can be performed with a relatively small processing load. Specifically, for example, a hypothetical curve C (a quadratic curve or the like) is found by a nonlinear least square method or the like. Figure 4 Alternatively, a hyperbolic cosine function (hyperbolic cosine: cosh) can be used, but in the case of either regression curve, the fewer the number of regression coefficients, the less likely it is to be affected by noise and deviation values. In more detail, for example, the plotted data of five adjacent points is applied to a quadratic function or a polynomial of three or more.

[0045] Here, regarding the range of the hypothetical curve calculation data that is the object of the hypothetical curve calculation processing described above, as in the case of the example described above where the provisional start point or the provisional end point is found based on the difference in the signal intensity of the plotted data adjacent to each other, when finding the peak width w for finding the prescribed number of aggregations described above, it can be set by finding the start point and the end point based on the difference in the signal intensity of the hypothetical curve calculation data adjacent to each other. In this case, it is expected that the number of points of the hypothetical curve calculation data will be made appropriate by the aggregation processing, and the vertical detection signal noise is relatively well suppressed compared to the original data, so the hypothetical curve corresponding to the appropriate start point and end point can be easily calculated.

[0046] That is, the baseline region and the peak region can also be easily recognized by using the inductive displacement I, so the peak region can be cut out before the hypothetical curve calculation processing, and the hypothetical curve calculation processing can be performed with only the data points of the peak region as the object. For example, in the case where the start point is found in the determination of the number of times of continuity being three, the first or second data point thereof can be provided to the hypothetical curve calculation processing. The end point can also be determined after being found, and provided to the hypothetical curve calculation processing (considering the signal shift before the passage of time). In addition, the method using the inductive displacement I can also contribute to the quantification of the detection signal vertical axis (determination of the reference of significant figures). The advantage thereof is that the data points for the hypothetical curve calculation processing are simplified. In addition, in the case of a display or a printout, this quantification is also effective.

[0047] Furthermore, in cases where characteristic points such as start or end points are determined based on an imaginary curve obtained through calculation and processing, the plotting data of seven adjacent points are applied to the hyperbolic function (inverse proportional function) f(t) = a / (tb) + c (for example). Figure 7 (D). Regression functions can be estimated using polynomials of degree 4 or higher, but as the number of regression coefficients increases, they become more susceptible to noise and other influences, increasing the necessity of increasing the sum of actual data points that constitute the regression object. Ideally, fewer regression coefficients make it less susceptible to deviations. The premise that peak waveforms, as natural phenomena, should be simple curves is the background of this regression. Furthermore, while exponential decay functions are non-linear, Gaussian and EMG (Exponentially Modified Gaussian) functions can also be used. Here, in cases where multiple peaks are adjacent, the characteristic length, interval, and number of points of representative peaks along the time axis, such as the peak width w of the input half-value full width, are predetermined or applied. That is, for example, the number of actual data points for the hypothetical curve regression object is determined based on the input (assigned) peak width.

[0048] Furthermore, when using exponential functions to regress hypothetical curves that approximate linearity, regression can also be performed using linear regression on logarithmic data that has undergone logarithmic operations. For example,

[0049] When f(t)-C=αe^(tT) / τ, it can be simplified to f(t)-C=Ae^t / τ, with regression coefficients A, C and time constant τ (α decreases by 1 / e when t decreases by τ).

[0050] Therefore, when taking the logarithm of both sides,

[0051] log{f(t)-C}=log A+t / τ, therefore by treating the baseline of the straight line as the horizontal asymptote y=C, with the slope on the right side being 1 / τ, the intercept can be regressed by a linear expression of t corresponding to log A.

[0052] Alternatively, nonlinear hypothetical curve calculations can be performed using C as a regression coefficient. For example,

[0053] When f(t)-C=Ae^-((t-tr)^2) / 2σ^2, it can be simplified to f(t)-C=Ae^(a0+a1×t+a2×t^2). When taking the logarithm of both sides,

[0054] log{f(t)-C}=log A+a0+a1×t+a2×t^2

[0055] log{f(t)-C} = a0' + a1xt + a2xt2, the logarithmic value log{f(t)-C} of the chromatogram waveform {f(t)-C} from which the baseline is subtracted can be regressed using the quadratic expression of the time t, and the start point and the end point can be easily searched.

[0056] In addition, the square root of the quadratic curve can also be taken as the plotting data and regressed using a straight line in the same idea.

[0057] y - C = (t + R)2, SQRT(y - C) = t + R

[0058] In addition, as the characteristic point of the shoulder peak, an inflection point is sometimes used. In this case, the regression analysis can be a polynomial of three or more or a hyperbolic sine function. The cubic polynomial does not have an extreme value but has an inflection point.

[0059] The coordinates of the vertex O and the like of the above-mentioned imaginary curve C( Figure 4 ) can be easily found by algebraic operation and the like in most cases. Specifically, for example, when the imaginary curve is represented by a quadratic curve f(t) = at2+ bt + c, the time coordinate value of the vertex O is given by -b / 2a.

[0060] Alternatively, in the case of an imaginary curve D( Figure 7 ) of an inverse proportional function and the like, the provisional height of the peak i can be set as H, 0.01H multiplied by a value that can be set in advance or thereafter, 0.01, can be set as the threshold, and the provisional start point (for example, R of Figure 7 ) or the provisional end point from the provisional baseline and the provisional vertex can be found to the left and right.

[0061] In addition, when the hypothetical curve is represented by a cubic curve f(t) = at3+ bt2+ ct+ d, the time coordinate value tl of the shoulder point S is assigned by -b / 3a. In addition, it can also be found that the change amount of the adjacent data points is below the threshold value. Here, in the regression analysis, the discriminant of the quadratic function can also be used to confirm that there are no two real solutions (monotonically increasing, monotonically decreasing), and thus the processing of the provisional feature points is performed. In addition, in the case where the real solutions are significantly regressed to two, the usual peak top detection processing can also be performed. In addition, the regression can also be performed under the constraint condition related to the coefficients a, b, c, d to limit the regression cubic to one real solution. In addition, even in the case where the real solutions are two, in the case where the time coordinate value of the inflection point as the shoulder point is very likely to be appropriately found, the hypothetical curve itself can not necessarily coincide with the most appropriate curve, and the provisional shoulder point can also be found from the inflection point. In addition, the interval of the regression analysis is set to be designated by the waveform processing terminology table. In the automatic execution, for example, the provisional retention time tR and the input peak half-width w can be used to set tR-2w ~ tR-1 / 4w as the interval and perform the regression analysis. Here, the above interval tR-2w ~ tR-1 / 4w needs to have flexibility, and in particular, when the adjacent peaks are close, it is preferable to be set to be unaffected thereby.

[0062] In addition, the Savitzky-Golay method can also be used in the differential coefficient determination method of the regression curve to temporarily find the hypothetical feature points such as the start point, the end point, the valley point, the peak top point, the shoulder point, and the like. That is, the Savitzky-Golay method is also effective for calculating the differential coefficient, and not only the regression coefficient but also the differential coefficient of the polynomial can be determined. Therefore, the differential coefficient can also be used to find each hypothetical feature point.

[0063] (Extraction of Actual Plot Data Feature Points)

[0064] The coordinates of the top point O and the like found as described above are usually the coordinates of the hypothetical points. Therefore, the feature points found as such from the hypothetical curve C and the like are extracted and selected as the actual plot data feature points from the actually measured plot data. Specifically, as the actual plot data feature points, for example, the plot data closest to the provisional feature points in time (for example, the plot data P), the plot data closest in distance to the provisional feature points, or the plot data (for example, the plot data Q) or the like that takes an extreme value within a predetermined time range from the provisional feature points or the point with the smallest slope between the adjacent plot data can be extracted and selected.

[0065] That is, according to a certain rule of selecting the plotting data and the like that are short in time from the provisional feature point, the actual data point and various imaginary feature points can be associated. This argument is the gist of the present application, but in addition to the rule of selecting the side that is short in time between two time points, it is also possible to consider selecting the side that is early in time or the side that is late in time. In addition, it is also possible to consider a rule of considering the information in the vertical axis direction (detection intensity) of the two-dimensional chromatogram.

[0066] The plotting data feature point calculated as described above is a point that has a high possibility of being a feature point or a point closest to a feature point in the actually measured plotting data, and thus, it is expected that an appropriate coordinate value of a feature point will be obtained. Furthermore, compared to the provisional feature point based on the imaginary curve, it is possible to make it difficult to be affected by other plotting data such as distant plotting data. Therefore, by performing a qualitative process using the above-described plotting data feature point, or by performing setting of a baseline, or by further performing a quantitative process, it is possible to easily improve the detection accuracy. In addition, even in a case where a blank sample is not prepared, or the like, it is possible to perform a quantitative process or the like using a line segment connecting the plotting data feature points as a baseline. In addition, even in a case where there is blank data, it is possible to perform a more accurate process using the plotting data feature point even in a case where the influence of noise on the blank data is large. Furthermore, even if a blank sample is used, it is possible to perform a more accurate process in a case where the valley point does not decrease to the baseline.

[0067] (Other matters)

[0068] In addition, in the above-described example, a liquid chromatograph is exemplified, but it is not limited thereto, and the same process can be applied to various chromatographs.

[0069] In addition, the method of using the above-described provisional feature point and the plotting data feature point does not exclude a general method of directly calculating a feature point based on an imaginary curve, and these methods and the method of the present application can be selectively used. Furthermore, it is also possible to display analysis results based on various methods in a manner that can be compared.

[0070] Here, the main difference between time and time is explained. Time indicates each point of time of a clock that advances from time to time. Time has a prescribed origin, time zero. For example, a time point such as 2020 / 4 / 1 16:10:10 is time. On the other hand, time indicates the length of time, such as 10 seconds, 1.2 minutes, the difference between time A and time B, a period. Retention time is also a kind of time.

[0071] In addition, it is also possible to perform a process of removing by blank subtraction and / or offset before each process including the above-described aggregation process.

Claims

1. A data processing apparatus of a chromatograph that performs data processing based on plot data measured by the chromatograph, characterized by comprising: a hypothetical curve calculation data generating section that obtains hypothetical curve calculation data that is less in number than the plot data measured; and a hypothetical curve calculation section that obtains a hypothetical curve based on the hypothetical curve calculation data, wherein the hypothetical curve calculation data generating section obtains a representative value for each of a prescribed number of the plot data and sets the representative value as the hypothetical curve calculation data, the prescribed number being obtained based on a set peak width, wherein the prescribed number is the smallest integer that satisfies the following equation (1), B ≥ w / (S x N) (1), wherein B is the prescribed number, w is the peak width, S is a sampling interval, and N is the number of points of the hypothetical curve calculation data for one peak.

2. The data processing apparatus of a chromatograph according to claim 1, characterized in that the peak width is set for each component.

3. The data processing apparatus of a chromatograph according to claim 2, characterized in that the data processing apparatus further comprises a tentative start / end point calculation section that obtains a tentative start point and a tentative end point for each peak waveform in a measurement result of the chromatograph, wherein the tentative start / end point calculation section obtains the tentative start point and the tentative end point based on whether a difference between measured signal intensities of mutually adjacent plot data becomes a prescribed non-sensitively displaced or more for a prescribed number of times in succession, and wherein the peak width is obtained based on the tentative start point and the tentative end point.

4. A chromatograph comprising: a chromatograph unit that separates and measures components included in a sample; and the data processing apparatus of a chromatograph according to claim 1.

5. A data processing method of a chromatograph that performs data processing based on plot data measured by the chromatograph, characterized by comprising: a hypothetical curve calculation data generating step of obtaining hypothetical curve calculation data that is less in number than the plot data measured; and a hypothetical curve calculation step of obtaining a hypothetical curve based on the hypothetical curve calculation data, wherein in the hypothetical curve calculation data generating step, a representative value is obtained for each of a prescribed number of the plot data and set as the hypothetical curve calculation data, the prescribed number being obtained based on a set peak width, wherein the prescribed number is the smallest integer that satisfies the following equation (1), B ≥ w / (S x N) (1), wherein B is the prescribed number, w is the peak width, S is a sampling interval, and N is the number of points of the hypothetical curve calculation data for one peak. ​ ​ ​ ​ ​ ​ ​ ​ ​ 4. A chromatograph characterized by, ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​

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