JP7241349B2 - Transient thermal characteristic analysis device, analysis method and program - Google Patents

Description

The present invention relates to technology for analyzing transient thermal characteristics of power modules.

In recent years, in the field of power electronics for vehicles, electric power systems, etc., power semiconductor devices applied to power conversion circuits and power semiconductor modules (hereinafter collectively referred to as power modules) formed by mounting one or a plurality of such power semiconductor devices have been developed. ) is becoming more and more sophisticated, the amount of heat generated is becoming a problem with such sophistication. For example, loss generated in a power module during switching operation of a power conversion circuit becomes heat, which causes a temperature rise in power devices and peripheral components such as capacitors and reactors. As a result, when the temperature difference environment between the operating time and the stopped time occurs repeatedly, there is a possibility that the joints and the like of the power module deteriorate. Also, in recent years, there is a demand for design and evaluation of transient thermal characteristics of power modules in consideration of instantaneous heat generation caused by overcurrent at the time of sudden load change or failure. Furthermore, with the progress in power module packaging technology, the thermal characteristics have been improved and the values of thermal equivalent circuit parameters have become smaller.

In the analysis of transient thermal characteristics, the thermal resistance called the structure function, which is calculated from the time-series response (time-series data) of the junction temperature measured using the temperature dependence (temperature parameter) of the electrical characteristics of the power module, is used. A thermal equivalent circuit consisting of a heat capacity is used. As a method of calculating the parameters of a thermal equivalent circuit that expresses transient thermal characteristics using deconvolution integral, the transient thermal characteristics measurement method (JESD51-14 )It has been known.

FIG. 8 shows a conventional analysis algorithm based on the JESD51-14 measurement method. In this analysis algorithm, first, time-series data of the junction temperature of the power module is sampled at regular intervals in the linear time domain, for example, in microsecond units in the transient temperature measurement step (step S101). Next, using a moving average digital filter, noise filtering processing in the linear time domain is performed to remove noise contained in the junction temperature time-series data (step S103). Next, the noise-removed junction temperature time-series data is converted into a logarithmic time domain (step S105). In the data conversion, the data is resampled by decimation, interpolation, or the like so as to have equal intervals in the logarithmic time domain. Numerical differentiation is performed as preprocessing for identifying the parameters of the thermal circuit model by deconvolution integration (step S107), followed by calculation of the thermal time constant spectrum by deconvolution integration (step S109). . Thereafter, the parameters of the Foster circuit as an example of the one-dimensional model of the thermal circuit are identified (step S111), and the identified parameters are used to calculate the structure function through Foster-Cauer transformation (step S113). ).

Further, in Patent Document 1, the heat sink is arranged in the first and second states, the forward voltage is sampled, and the transient thermal resistance value and its differential value are calculated and displayed from the junction temperature obtained in each state. A device has been proposed to display the

JP 2019-15564 A

JESD51-14, JEDEC (2010)

In recent years, advances in power module packaging technology have improved thermal characteristics and reduced the values of thermal equivalent circuit parameters. The analysis method according to the JEDEC standard does not define a specific numerical processing algorithm. Since the removal is nothing more than performing a moving average filtering process in the time domain on the time-series data of the junction temperature obtained electrically, measurement noise such as white noise and quantization errors can necessarily be effectively removed. However, in such a case, noise relatively becomes apparent in the calculation of the parameters of the thermal equivalent circuit. In addition, there is a possibility that noise components that could not be completely removed by the noise removal process may become actualized as a result of the numerical differentiation. Furthermore, although the device described in Patent Document 1 describes converting the measured forward voltage into junction temperature, no consideration is given to a method of removing noise components contained in the measured voltage.

The present invention has been made in view of the above, and is a transient heat sensor that enables more accurate analysis by removing noise components in the frequency domain from the time series data (profile) of the junction temperature of a power module. A characteristic analysis device, an analysis method, and a program are provided.

The present invention provides a transient thermal characteristic analysis device for analyzing transient thermal characteristics of a power module from time-series data of junction temperatures sampled at equal intervals of linear time during the heat dissipation process of the power module, wherein the time-series data is collected at unequal intervals. transform processing means for resampling and transforming to logarithmic time, and performing numerical differentiation on the transformed time-series data; and a noise removing means for removing noise in the frequency domain from the Fourier-transformed time-series data.

The present invention also provides a transient thermal characteristic analysis method for analyzing the transient thermal characteristics of a power module from time-series data of junction temperatures sampled at equal intervals of linear time during the heat dissipation process of the power module, wherein the time-series data is undefined. A conversion step of resampling at equal intervals to convert to logarithmic time and subjecting the converted time series data to numerical differentiation, and a Fourier transform step of subjecting the numerically differentiated time series data to non-equidistant Fourier transformation. and a noise elimination step of performing noise elimination processing in the frequency domain on the Fourier-transformed time-series data.

Further, the present invention provides a program for analyzing, by a computer, the transient thermal characteristics of the power module from time-series data of junction temperature sampled at equal intervals of linear time during the heat dissipation process of the power module, wherein the time-series data is collected at unequal intervals. Transformation processing means for resampling to logarithmic time and performing numerical differentiation on the transformed time-series data, Fourier transformation means for subjecting the numerically differentiated time-series data to nonuniform Fourier transformation, and The computer is caused to function as noise removal means for performing noise removal processing in the frequency domain on the time-series data subjected to the Fourier transform.

According to these inventions, the time-series data of the junction temperature sampled at regular intervals during the heat dissipation process of the power module is obtained, and the transient thermal characteristics of the power module are analyzed from the time-series data of the junction temperature. That is, the time series data is resampled at unequal intervals and converted to logarithmic time by the conversion processing means, and the converted time series data is subjected to numerical differentiation. Further, the time-series data subjected to the numerical differentiation is subjected to nonuniform Fourier transform by the Fourier transform means. Then, noise removal processing in the frequency domain is performed on the time-series data subjected to the Fourier transform by the noise removal means.

For example, in order to obtain thermal equivalent circuit parameters that represent the transient thermal characteristics of a power module, the temperature dependence of the electrical characteristics of power semiconductor devices is used to obtain the time-series data of the junction temperature of the power module. converted from the value. At this time, if noise is superimposed on the voltage and current values, this noise becomes an error factor in the analysis of transient thermal characteristics. Therefore, instead of noise filtering in the time domain for the conventionally used time series data, that is, without filtering the obtained time series data in the time domain, once converted to logarithmic time at uneven intervals, numerical After differentiation, a Fourier transform is performed at unequal intervals to remove noise in the frequency domain, making it possible to further reduce the effects of noise. Transformation of measured time series data from the linear time domain to logarithmic time at unequal intervals, instead of applying similar data by decimating or interpolating the original data to the original measured data Makes himself fully usable. In addition, a part of the measured time-series data is extracted in addition to the entire area, and a filter is applied to appropriately remove unnecessary frequency characteristic noise for analysis of transient thermal characteristics peculiar to that period. There are also aspects. According to the above, effective noise removal such as removal of high frequency components or removal of intermediate frequency components can be performed in accordance with the frequency characteristics of noise components. Moreover, since noise can be reduced on the analysis software side, transient thermal characteristic analysis with high reproducibility is possible.

Further, the noise removing means removes high frequency components in the frequency domain, and it is particularly preferable that the noise removing means is a low-pass filter. According to such a configuration, it is possible to selectively remove frequency components, for example, high frequency components, depending on the characteristics of noise superimposed when measuring time-series data. In this case, a simple low-pass filter may be applied. preferable.

In addition, the present invention further comprises inverse Fourier transform means for resampling the time series data processed by the noise removal means at equal intervals of logarithmic time and performing inverse discrete Fourier transform, and time series data processed by the inverse Fourier transform means. and calculating means for calculating a thermal time constant spectrum by performing deconvolution integral. According to this configuration, by removing noise in the frequency domain, it is possible to reduce the influence of noise on the thermal time constant spectrum necessary for calculating the thermal equivalent circuit parameters. In addition, since the measured time-series data is data sampled at equal intervals in the linear time domain, the sampling intervals are unequal in the logarithmic time domain. Therefore, by applying the nonuniform Fourier transform in the linear time domain, we suppress the loss of the original data due to resampling in the linear time. Furthermore, resampling was performed at equal logarithmic time intervals by inverse Fourier transform. By obtaining a thermal time constant spectrum with more suppressed noise in this way, it is possible to calculate the structure function with high accuracy.

ADVANTAGE OF THE INVENTION According to this invention, the transient heat characteristic of a power module can be analyzed with high precision.

1 is a block diagram showing an embodiment of a transient thermal characteristic analysis device according to the present invention; FIG. It is a side sectional view showing an example of a power module. 4 is a flow chart showing a transient thermal characteristic analysis algorithm according to the present invention; Time chart showing differential values of junction temperature time series data on a logarithmic time axis, (A) showing numerical differentiation of junction temperature time series data, (B) analysis method according to the present invention (example) and a noise reduction effect by a conventional analysis method (comparative example). FIG. 3 is a diagram showing thermal time constant spectra in an example and a comparative example, which are used for calculating thermal equivalent circuit parameters on a logarithmic time axis; FIG. 4 is a diagram showing a power spectrum of random noise as a sample corresponding to each level superimposed on the junction temperature time-series data (ideal). FIG. 6 is a chart showing the difference in noise reduction effect between the example and the comparative example when the sample noise shown in FIG. 6 is superimposed. 1 is a flow chart showing a conventional transient thermal characterization algorithm based on JESD51-14 measurement method;

FIG. 1 is a block diagram showing one embodiment of a transient thermal characteristic analysis apparatus according to the present invention. The transient thermal characteristic analysis device 1 samples the time-series data of the junction temperature of the power module 40, performs necessary noise removal processing, and then analyzes and evaluates the transient thermal characteristics of the structure function. processed by computer. Note that the junction temperature is measured at the junction with the semiconductor inside the power module 40 . The computer also includes a control unit 10 that performs arithmetic processing using a processor (CPU).

The transient thermal characteristic analysis apparatus 1 also includes a display unit 21, a storage unit 101, a power supply 31 on the side of the measurement system, and a driver 32 for power supply. The control unit 10 is connected to the display unit 21, the storage unit 101, and the driver 32, and is connectable to the junction unit of the analysis target power module 40 connected (set) to the measurement system.

The display unit 21 displays an image, and is provided as required. The display unit 21 displays contents set via an input unit (not shown) such as a touch panel for confirmation, and displays analysis contents in various forms. The storage unit 101 stores a processing program executed by the processor of the control unit 10, and data necessary for executing the processing program, such as various numerical calculation formulas, various conversion formulas, various functions, and the temperature of the power module 40. A work area is provided for storing parameters (temperature dependence), etc., and for temporarily storing data during processing.

The power supply 31 constitutes a power supply circuit capable of outputting a large heating current for once heating the power module 40 to a predetermined temperature and a minute small current for measuring the junction temperature during heat radiation or cooling. The power supply 31 may be configured such that a large-current power supply circuit and a small-current power supply circuit are separately provided. The driver 32 is composed of an IGBT (insulated gate bipolar transistor) or the like for switching between the large current and the small current from the power supply 31 and supplying the power module 40 (the junction thereof). The driver 32 is driven according to a drive signal from the control section 10 as will be described later, and is controlled to output a predetermined current.

The control unit 10 takes in the forward voltage and current of the junction of the power module 40, for example, the diode, via an A/D conversion unit or the like. Time-series data of the junction temperature is obtained from the measured voltage and current using the temperature parameter.

Here, the configuration of the power module 40 to be analyzed according to the present embodiment will be described with reference to FIG. In this embodiment, the power module 40 has a semiconductor package 41 mounted on a heat sink 46 via grease 45 as a heat dissipation material. The power module 40 includes a chip 42 , a die attach 43 and a die pad 44 , typically with junctions on the chip 42 . The thermal resistance can be adjusted by the material (thermal conductivity), shape and size of the package 41 and also by the material, shape and size of each member in the heat radiation path from the chip 42 to the grease 45 . In addition, the surface condition of each member may also be subject to adjustment. In some cases, the lead wire 47 should also be considered as part of the heat dissipation path.

The control unit 10 functions as a power supply drive unit 11 , a measurement processing unit 12 , a calculation unit 13 and a structure function calculation unit 14 by executing a processing program stored in the storage unit 101 with a processor. The calculation unit 13 includes a conversion processing unit 131 , a noise removal unit 132 and a thermal time constant spectrum calculation unit 133 .

The power supply driving unit 11 controls the level of current supplied to the power module 40. Upon receiving an instruction to start the analysis algorithm, the power supply driving unit 11 first outputs a large current to the driver 32, and when a predetermined temperature is reached, a transient current is generated. After the temperature measurement step, the output is switched to a small current of a predetermined level.

Hereinafter, the description from the measurement processing unit 12 to the structure function calculation unit 14 will be given with reference to the analysis algorithm shown in FIG. Upon receiving the instruction to start the transient temperature measurement process, the measurement processing section 12 measures the voltage value from the junction section of the power module 40 at regular intervals in a predetermined period, for example, in microsecond units, that is, the current value at that time. Also, the time-series data of the junction temperature is sampled (stored in the storage unit 101) by A/D conversion and periodic reading, and conversion using the temperature parameter (see step S1 in FIG. 3). The measurement processing unit 12 also performs preprocessing for processing by the calculation unit 13 . The preprocessing includes, for example, thinning processing, offset processing (initial data cutting processing, see FIG. 4A), and transient thermal resistance calculation processing.

The conversion processing unit 131 executes various conversion processes, which will be described later. In the present embodiment, the conversion processing unit 131 performs resampling at unequal intervals when converting the time-series data of the junction temperature sampled at equal intervals in the linear time domain into data in the logarithmic time domain ( (see step S3 in FIG. 3). By resampling at unequal intervals, all measured time-series data can be used to eliminate missing data and maintain accuracy. In addition, the conversion processing unit 131 performs numerical differentiation processing on the time-series data resampled at unequal intervals in the logarithmic time domain (see step S5 in FIG. 3). Note that the conversion processing unit 131 uses the acquired time-series data itself for numerical differentiation processing, so accuracy is maintained, and as a result, higher noise reduction performance can be exhibited.

Further, the transformation processing unit 131 performs a nonuniform variance Fourier transform on the numerically differentiated time series data to transform the time series data into the frequency domain (see step S7 in FIG. 3). Furthermore, the transform processing unit 131 performs resampling processing at regular intervals in the logarithmic time domain on the time-series data subjected to noise removal processing by noise filtering, and performs an inverse discrete Fourier transform (see step S11 in FIG. 3). ).

The noise removal unit 132 performs noise filtering in the frequency domain on the time-series data subjected to the nonuniform discrete Fourier transform (see step S9 in FIG. 3). In this embodiment, the noise filtering is preferably a low-pass filter that effectively removes high-frequency component noise such as white noise mixed from the power module 40 side and the measurement system side when acquiring junction temperature data. . For example, a Fermi-Dirac filter function can be employed. In addition, in a mode in which a cooler is employed during measurement, it is preferable to remove cooling noise as well. A band-pass filter can also be applied as one having a high-frequency removal (low-pass filter) function.

The thermal time constant spectrum calculation unit 133 calculates a thermal time constant spectrum by deconvolution integral for the time constant data that has undergone the inverse discrete Fourier transform in step S11 of FIG. 3 (see step S13 of FIG. 3).

The structure function calculator 14 identifies parameters of a Foster circuit as an example of a one-dimensional model of a thermal circuit from the calculated thermal time constant spectrum (see step S15 in FIG. 3). Further, the structure function calculator 14 uses the identified parameters to calculate a structure function (thermal resistance, heat capacity) through Foster-Cauer transformation (see step S17 in FIG. 3). From the contents of the obtained structure function, it becomes possible to easily identify the improvements and items to be improved for each member.

Next, the analysis algorithm according to the present invention will be explained using the flow chart of FIG.

In FIG. 3, the analysis device T3Ster manufactured by Mentor Graphics is applied to the processing portion common to that in FIG. 4 and 5 are created based on the analysis device T3Ster and by applying the processing procedure of the analysis device T3Ster to the procedure shown in FIG.

In FIG. 3 , first, the power module 40 to be analyzed is set in the transient thermal characteristic analysis device 1 . When the measurement processing unit 12 receives an instruction to start the transient temperature measurement process, the measurement processing unit 12 A/D converts and reads the voltage and current values from the junction of the power module 40 at equal intervals in a linear time domain of, for example, 1 μs. Time-series data of the junction temperature is sampled by conversion using parameters (step S1). The measurement processing unit 12 then performs preprocessing for processing by the calculation unit 13 .

Subsequently, the conversion processing unit 131 converts the junction temperature time-series data obtained in step S1 into logarithmic time domain data (step S3). At this time, the time-series data is resampled as it is, that is, at unequal intervals in the logarithmic time domain. Since the acquired time-series data itself is used, accuracy is maintained, and as a result, higher noise reduction performance is exhibited.

Further, the conversion processing unit 131 performs numerical differentiation processing on the time-series data resampled at unequal intervals in the logarithmic time domain (step S5). FIG. 4A shows an example of numerical differentiation of the preprocessed junction temperature time-series data. In FIG. 4, the horizontal axis is logarithmic time, and the vertical axis is the normalization level of numerical differentiation.

Next, the transform processing unit 131 performs unequal spaced variance Fourier transform on the numerically differentiated time series data to transform the time series data into the frequency domain (step S7).

Next, the noise removal unit 132 performs noise filtering in the frequency domain on the time-series data subjected to the unequal discrete Fourier transform (step S9). In this embodiment, noise filtering is a low-pass filter that effectively removes high-frequency component noise such as white noise mixed from the power module 40 side and the measurement system side when acquiring junction temperature data.

Next, the transform processing unit 131 performs resampling processing at regular intervals in the logarithmic time domain on the time-series data from which noise has been removed by noise filtering, and performs inverse discrete Fourier transform (step S11).

FIG. 4(B) shows an example (working example) of the result of performing the inverse discrete Fourier transform in step S11 based on FIG. 4(A). In FIG. 4(B), the comparative example is obtained by applying the conventional analysis algorithm shown in FIG. 8, and performing the inverse discrete Fourier transform of the numerical differentiation of FIG. 4(A) as it is. As can be seen from FIG. 4B, high frequency components corresponding to noise components remain in the figure shown in the comparative example, while the figure shown in the example is a curve in which almost no residual high frequency components are observed. , that is, the noise component is effectively removed. In addition, the vertical axis of FIG. 4(B) is enlarged as compared with that of FIG. 4(A).

Next, the thermal time constant spectrum calculation unit 133 calculates a thermal time constant spectrum by deconvolution integral for the time constant response that has undergone the inverse discrete Fourier transform in step S11 (step S13). FIG. 5 is a diagram showing a thermal time constant spectrum. The figure of the thermal time constant spectrum shown in the comparative example is generally gentle, and the level change is small especially on the initial time side. On the other hand, the figure of the thermal time constant spectrum shown in the example shows a relatively wavy waveform, and in particular, the peak shows a relatively high level, and a thermal time constant spectrum with more noise removed is obtained. Furthermore, it can be seen that the noise is further removed as a whole from the fact that the waving tendency is remarkable (the level change is large) on the initial time side.

Next, from the calculated thermal time constant spectrum, the structure function calculator 14 identifies the parameters of the Foster circuit as an example of the one-dimensional model of the thermal circuit (step S15). , and Foster-Cauer transformation to calculate the structure function (thermal resistance, heat capacity) (step S17). Then, the calculated structure function of each member is displayed on the display unit 21 .

Next, an example of the difference in noise reduction effect between the embodiment and the comparative example will be described using sample noise with reference to FIGS. 6 and 7. FIG. The numerical values in FIG. 7 are the numerical values when sample noise of each level is applied to the analysis device T3Ster manufactured by Mentor Graphics. It is based on the implementation of the algorithm of FIG.

In FIG. 6, for example, -60 dB (noise level: 0.1%), -46 dB (noise level: 0.5%), -40 dB (noise level: 1.0 %), the power spectrum of sample random noise at a level of -26 dB (noise level: 5.0%) is superimposed. The RMS (Root Mean Square) values from the true value when ^each noise ^shown in FIG. ×10 ⁻³ , 1.01×10 ⁻² , whereas the examples are 25.02×10 ⁻⁵ , 2.40×10 ⁻⁴ , 3.39×10 ⁻⁴ , 8.02×10 ⁻³ . As described above, it is recognized that the embodiment can eliminate noise by approximately one digit to several times for any level of noise. In particular, the actual noise level is considered to be about -40dB (noise level: 1.0%), but even for noise that is five times higher (-26dB (noise level: 5.0%)), the noise removal effect is higher. is obtained.

^It _{should be} noted that ^the _data ^shown in _FIG ^. ₃ = 5.98 × 10 ^-3 , C ₃ = 2.22 × 10 ^-2 ), the temperature response data assuming 1 µs sampling, which is numerically calculated from the three-stage Foster circuit, is used as the ideal. This data is subjected to analysis with noise level (amplitude) as a parameter, and random noise is superimposed on the data.

The present invention can include the following aspects.

(1) The power module to be analyzed may include not only power conversion, but also general semiconductor devices that cause heat generation, and LEDs for light emission.

(2) The transient thermal characteristic analysis apparatus 1 may include up to the structure function calculator 14, or may be divided into a configuration up to the calculation of the thermal time constant spectrum and a configuration for calculating the structure function.

(3) The transient thermal characteristic analysis device 1 does not need to be in a mode including all the above-mentioned parts, but in a mode including up to the calculating part 13, or in a mode including at least the configuration up to the noise removing part 132 of the calculating part 13. In these cases, the remaining units up to the structure function calculator 14 may be executed by separate devices.

(4) Furthermore, the transient thermal characteristic analysis device according to the present invention may employ the following aspects. That is, in the transient thermal characteristic analysis device for analyzing the transient thermal characteristic of the power module from the time series data of the junction temperature sampled at equal intervals of linear time in the heat dissipation process of the power module, the time series data is converted into logarithmic time. , transformation processing means for performing numerical differentiation on the transformed time-series data; Fourier transformation means for performing Fourier transformation on the time-series data subjected to the numerical differentiation; and frequency domain for the Fourier-transformed time-series data. and noise removal means for performing noise removal processing in the above. By performing noise removal processing in the frequency domain on the time-series data in this way, it becomes possible to calculate a thermal time constant spectrum with higher accuracy than in the conventional apparatus.

In the above configuration, the conversion processing means resamples the time series data at unequal intervals, converts it to logarithmic time, and numerically differentiates the converted time series data, and the Fourier transform means The numerically differentiated time-series data may be subjected to nonuniform Fourier transform. In this case, if the logarithm- and Fourier-transformed time-series data are set at unequal intervals, a more accurate analysis of the transient thermal characteristics can be expected than in the case of resampling at equal intervals.

1 transient thermal characteristic analysis device 10 control unit 12 measurement processing unit 13 calculation unit 131 conversion processing unit (conversion processing means, Fourier transform means, inverse Fourier transform means)
132 noise elimination unit (noise elimination means)
133 Thermal time constant spectrum calculation unit (calculation means)
14 structure function calculator 40 power module

Claims (6)

A transient thermal characteristic analysis device for analyzing the transient thermal characteristic of the power module from time-series data of junction temperature sampled at equal intervals of linear time during the heat dissipation process of the power module,
conversion processing means for resampling the time-series data at unequal intervals to convert it into logarithmic time, and performing numerical differentiation on the converted time-series data;
Fourier transform means for performing a nonuniform Fourier transform on the numerically differentiated time-series data;
A transient thermal characteristic analysis apparatus comprising noise removal means for performing noise removal processing in the frequency domain on the Fourier-transformed time-series data. 2. The transient thermal characteristic analysis apparatus according to claim 1, wherein said noise removing means removes high frequency components in the frequency domain. 3. The transient thermal characteristic analysis apparatus according to claim 2, wherein said noise removing means is a low-pass filter. an inverse Fourier transform means for resampling the time-series data processed by the noise removal means at equal intervals of logarithmic time and performing an inverse discrete Fourier transform;
4. The transient thermal characteristic analysis apparatus according to claim 1, further comprising calculation means for calculating a thermal time constant spectrum by applying deconvolution integral to the time-series data processed by said inverse Fourier transform means. In a transient thermal characteristic analysis method for analyzing the transient thermal characteristic of the power module from time-series data of junction temperature sampled at equal intervals of linear time during the heat dissipation process of the power module,
a conversion step of resampling the time-series data at unequal intervals to convert it into logarithmic time, and performing numerical differentiation on the converted time-series data;
a Fourier transform step of performing a nonuniform Fourier transform on the time-series data subjected to the numerical differentiation;
and a noise elimination step of performing noise elimination processing in the frequency domain on the Fourier-transformed time-series data. A program for analyzing, by a computer, the transient thermal characteristics of the power module from time-series data of the junction temperature sampled at equal intervals of linear time during the heat dissipation process of the power module,
conversion processing means for resampling the time-series data at unequal intervals to convert it into logarithmic time, and performing numerical differentiation on the converted time-series data;
Fourier transform means for applying a nonuniform Fourier transform to the numerically differentiated time-series data, and noise removal means for removing noise in the frequency domain from the Fourier-transformed time-series data. program that makes it work.

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