CN117269635A

CN117269635A - Oscilloscope with principal component analyzer

Info

Publication number: CN117269635A
Application number: CN202310744512.8A
Authority: CN
Inventors: J·E·帕特森
Original assignee: Tektronix Inc
Current assignee: Tektronix Inc
Priority date: 2022-06-21
Filing date: 2023-06-21
Publication date: 2023-12-22

Abstract

An oscilloscope with a principal component analyzer is provided. A system comprising: an input for accepting an input signal from a Device Under Test (DUT); a measurement unit for generating first measurement data and second measurement data from an input signal; and one or more processors configured to: deriving at least one principal component from the first and second measurement data using principal component analysis, and remapping the first measurement data and the second measurement data to a principal component domain derived from the at least one principal component. Methods of operation and descriptions of storage media whose operation performs the above operations are also described.

Description

Oscilloscope with principal component analyzer

Cross Reference to Related Applications

The present disclosure claims the benefit of U.S. provisional application No. 63/353,950, entitled "PRINCIPAL COMPONENT ANALYSIS AS AN OSCILLOSCOPE MEASUREMENT," filed on 21, 6, 2022, the disclosure of which is incorporated herein by reference in its entirety.

Technical Field

The present disclosure relates to testing and measuring instruments, and more particularly, to measuring instruments that include tools for performing principal component analysis on measurement data gathered by the instrument.

Background

Modern oscilloscopes and other test and measurement equipment accept signals from a Device Under Test (DUT) and perform various measurements on these signals. In many cases, data is also collected from the signals, and measurements and analysis may be performed on the collected data. Tests are sometimes performed on measured parameters, such as threshold tests based on measured voltage, current or power. And sometimes perform a transformation of the input signal before performing the test or measurement. For example, the test and measurement instrument may accept an input signal in the time domain, perform a fourier transform on the signal to convert it to the frequency domain, and then perform the desired test or measurement in the frequency domain.

As described above, data may be collected from the input signal or, in some cases, the instrument may generate data describing or characterizing the input signal. While some conventional oscilloscopes may perform simple data processing on the data, such as statistical processing, or may use histograms or time series trends to plot the data, in general, data analysis tools on conventional test and measurement equipment are limited to simple tools and processing.

Embodiments in accordance with the present disclosure address these and other limitations found in conventional instruments.

Drawings

FIG. 1 is a diagram showing how an oscilloscope including principal component analysis applies such analysis to a data set collected by the oscilloscope, according to an embodiment of the present disclosure.

FIG. 2 is a diagram of a data set collected by an oscilloscope with a principal component analyzer, according to an embodiment of the present disclosure.

Fig. 3A and 3B are diagrams of raw and ordered data samples illustrating the limitations of conventional data processing in current oscilloscopes.

Fig. 4A illustrates a set of histograms showing how an oscilloscope including principal component analysis may apply the steps of data analysis, according to an embodiment of the present disclosure.

Fig. 4B illustrates a set of histograms showing how an oscilloscope including principal component analysis may apply another data analysis step, according to an embodiment of the present disclosure.

Fig. 5A and 5B are diagrams illustrating additional steps of how an oscilloscope including principal component analysis may apply data analysis according to embodiments of the present disclosure.

Fig. 6 is a diagram illustrating data regenerated using only a single principal component according to an embodiment of the present disclosure.

Fig. 7A and 7B are time trend graphs showing how an oscilloscope including principal component analysis may present the results of principal component analysis to a user according to an embodiment of the present disclosure.

Fig. 8A and 8B are spectrograms illustrating how an oscilloscope including principal component analysis may present the results of the principal component analysis to a user according to an embodiment of the present disclosure.

Fig. 9 is a functional block diagram of an oscilloscope including principal component analysis according to an embodiment of the present disclosure.

Detailed Description

Embodiments of the present invention include a test and measurement instrument, such as an oscilloscope, capable of performing Principal Component Analysis (PCA) on measurements or data received by the instrument from a Device Under Test (DUT). PCA operates on large data sets, such as measurement data received from DUTs. Performing PCA on these data sets allows the user to determine which variables contain most information about the data, such as measurements included in the data. In general, PCA is a matrix decomposition of data that allows users to analyze and extract insight from measurements in a principal component domain, which may be a different domain than the measurement domain that generated the measurement data. In certain aspects, the ability of PCA to re-map data from the measurement domain to the principal component domain resembles fourier transforms re-characterizing data gathered, for example, in the time domain as measurements in the frequency domain. Using PCA tools, a user may be able to discern relationships with respect to particular measurements that are not identifiable without PCA analysis. Furthermore, PCA analysis is particularly robust in analyzing multiple variables and determining which variables are related to each other.

As described above, PCA operates on the data set. Fig. 1 is a data chart 10 illustrating one basic principle of PCA. The data on chart 10 is assumed to be data having an X component and a Y component. The data is mapped on the graph 10 according to its XY component. PCA maps data from the measurement domain to the principal component domain by coordinate transformation. In order to find the principal component axis, singular value decomposition is performed on the measurement data in the following process. The principal component axis (axis 20 in this case) will always be the following: when data from a dataset is projected onto this particular axis, the axis has the greatest variance. To perform singular value decomposition on a set of data, it is conceivable to generate an axis in an arbitrary orientation of the raw data and project the dataset onto the arbitrary axis. The variance of the projection data for the current axis is recorded and then the process is repeated by projecting the original data to the new arbitrary axis. This process is repeated over all possible axis orientations. When all possible axes have been generated, the variance data for each axis is analyzed to determine which axis has the greatest variance when the raw data is projected onto it. The axis with the greatest variance is the principal component axis. In other words, the principal component axis will point in the direction where the measured data has the greatest variance. In the dataset of fig. 1, the principal axis is labeled as axis 20. Other axes, one axis for each measurement in the variable or data, may also be generated. In PCA, each principal axis is orthogonal to each other, so that the minor component axis 30 is orthogonal to the major component axis 20, as shown in fig. 1. PCA is particularly useful when the measurements are linearly related, such as feedforward equalizer taps and data carried on signals having various levels. It should be noted that when the number of measurements is three or more, visualization of the measurement data, including visualization using PCA analysis, becomes increasingly difficult, but is a useful tool for analyzing a more modest number of measurements. One of the reasons that PCA is useful in analyzing measurement data is that PCA produces a classification result of the principal components. The user may then systematically select which principal components to use for statistical analysis or rendering.

Fig. 2 shows measurement data gathered from a system with non-return-to-zero encoding with level measurement, where the levels are linearly related. The data is generated from 1000 linear correlation data. In other words, according to equation 1, the recorded measurements are simultaneously shifted from the mean value in opposite directions.

Equation (1) lvl1=x ₁ +x _n

lvl0＝x ₀ +x _n

Wherein x is ₁ Uniformly distributed in interval [.8,1]，x ₀ ＝-2x ₁ +1, and x _n Is zero-mean Gaussian noise with a standard deviation of 0.1.

A conventional analysis of the measurement data shown in fig. 2 is shown in fig. 3A and 3B. Note that the observed trend, whether measured instantaneously or at the measured level, does not reveal any important information about the recorded data. In fig. 3A and 3B, the instantaneous measurement of each sample number between 0-1000 is shown. The darker lines falling in fig. 3A and rising in fig. 3B show the measurements in ordered sequence.

However, using PCA on recorded data may reveal linear relationships within the data that are not identifiable using conventional tools, such as shown in fig. 3A and 3B.

First, in order to perform PCA, as described above, a principal component is extracted from the measurement data using singular value decomposition to determine a principal component axis. Then, after deriving the principal component, the measurements initially gathered in the measurement domain are projected into the Principal Component (PC) domain, where each PC is a linear combination of levels.

Equation (2)

For example, using equation 2, the levels [1, -1]V ] are mapped to [ -0.223, ] 0002.

The principal component 1 axis (PC 1) and principal component 2 axis (PC 2) are shown in fig. 2, which are determined by performing this PC analysis on the measurement data in fig. 2. Note that the PC2 axis is orthogonal to the PC1 axis.

After deriving the principal component and thus the PC domain, and after the raw measurement data has also been projected onto the PC domain, data analysis may be performed which is not possible with the raw data alone. For example, a measurement histogram may be generated that allows a user to investigate the behavior of the data being measured. Fig. 4A shows the measurement histograms of level 1 and level 0 data in the measurement domain, while fig. 4B shows the histograms of the measurement data after the measurement data has been projected onto the first two principal component domains PC1 and PC 2. Fig. 4B shows two separate histograms, one of which projects the measurement data onto the first principal component PCI and is divided into bins (bins), while the other shows the measurement data projected onto the second principal component PC2 and divided into bins. Recall that PC2 is orthogonal to PC 1.

Unlike the plots of fig. 3A and 3B, which provide little information about the raw measurement data, the histogram shown in fig. 4B provides useful information about the measurement data, such as the patterns revealed when binning the transformed data. The binning data of PC1 shows that most of the center bins have approximately the same measurements per bin, while the binning data of PC2 looks more like a gaussian distribution.

Furthermore, the singular values mapped in fig. 5A and 5B reveal the power captured in the principal component. Fig. 5A plots two singular values from a Sigma matrix, which is calculated during the singular value decomposition process. The Sigma matrix provides the variance or standard deviation along the PC axis. It can be considered as the "power" captured in the PC. Fig. 5B is a graph of normalized accumulated power or "energy". The first data point in FIG. 5B has a value of.92, which can be calculated from the data depicted in FIG. 5A. In fig. 5A, the total is 4.3. The first data point of the accumulated power in fig. 5B is then determined as the first value 4 divided by the total number 4.3, yielding approximately.92. The second data point of the accumulated power in fig. 5B is determined by summing the first and second values by 4+.3 and dividing the sum by the total (which is also 4.3) to yield 1.0, which is plotted as the second value in fig. 5B. Thus, in this example, 92% of the measurement variance is captured in the first PC 1. This means that the two measurements, i.e. the data originally mapped in fig. 2, are linearly related to each other. The standard deviation of PC2 is exactly the standard deviation of noise in equation (1) above. It is related to singular values asWhere N is the number of observations. Therefore, if the measurement is reconstructed only from the PC1, this has the effect of removing noise in the observation, which is shown in fig. 6.

Specifically, in fig. 6, the raw data is shown as a number of singular points, while the data reconstructed using only PC1 and not PC2 is shown as a much tighter data set. As described above, to generate reconstructed data, the raw measurement data is remapped to the PC domain. Then, the contribution to the data from PC2 is removed and the remaining data is remapped back to the measurement domain again. Since noise is present in PC2, which can be observed by noting that the PC2 bins in fig. 4B approximate gaussian curves, removing the PC2 component eliminates this noise when remapping data from the PC domain back to the original measurement domain. Note that the reconstructed data in fig. 6 appears to be much more linear than the original data.

In general, PCA is performed on a population of two or more measurements. The population may be from a single acquisition or multiple acquisitions. In this case, the user may query the measurement through a standard user interface of the test and measurement device, as described below.

If N measurements are configured in a global PCA measurement, up to N PCs can be analyzed, but the same number of PCs must be equal to the number of measurements, which is not strictly necessary. For example, the number of the cells to be processed,

measa (in measurement domain)

Measb (in measurement domain)

Measc (in measurement domain)

PCA (configured to use measA and measB)

Pc1=v11+v12_measb (in PC domain)

Pc2=v21+v22_measb (in PC domain)

After the user has performed the PC1 and PC2 analyses, embodiments in accordance with the present disclosure allow the user to observe the PCA results through statistics and plots familiar to the user of the measurement device. In this example, measurement C remains in the measurement domain, which indicates that not all measurements need to be part of the PCA. Instead, the user may use a combination of measurements made in the measurement domain and data analyzed in the PC domain for overall analysis.

The statistics of the PC1 and PC2 analyses may include statistical processing and results such as mean, standard deviation, and maximum and minimum values. The plots showing PCA analysis may include typical plots familiar to the user, such as, for example, histograms such as shown in fig. 4B, time trend plots such as shown in fig. 7A and 7B, and spectrograms such as shown in fig. 8A and 8B. In these figures, the histogram of fig. 4B is in the PC domain, while the time trend graph and the spectrogram are in the measurement domain, although the user may select any plot from the measurement domain or the PC domain for analysis and viewing.

Embodiments of the present disclosure operate on specific hardware and/or software to achieve the PCA operations described above. Fig. 9 is a block diagram of an example test and measurement instrument 900, such as an oscilloscope or spectrum analyzer for implementing embodiments disclosed herein. The test and measurement instrument 900 includes one or more ports 902, which may be any signaling medium. The port 902 may include a receiver, a transmitter, and/or a transceiver. Each port 902 is a channel of the test and measurement instrument 900. The port 902 is coupled to one or more processors 916 to process signals and/or waveforms received at the port 902 from one or more Devices Under Test (DUTs) 990. In some embodiments, a port accepts multiple signals from DUT 990 or from one or more DUTs. Although a dual signal DUT 990 is shown in fig. 9, the test and measurement instrument 900 may accept any number of input signals up to the number of ports 902. Further, although only one processor 916 is shown in FIG. 9 for ease of illustration, those skilled in the art will appreciate that multiple processors 916 of different types may be used in combination in the instrument 900 instead of a single processor 916.

The port 902 may also be connected to a measurement unit 908 in the test instrument 900. Measurement unit 908 may include any component capable of measuring aspects (e.g., voltage, amperage, amplitude, power, energy, etc.) of a signal received through port 902. The test and measurement instrument 900 may include additional hardware and/or processors, such as conditioning circuitry, analog-to-digital converters, and/or other circuitry, to convert the received signals into waveforms for further analysis. The resulting waveforms may then be stored in memory 910 and displayed on display 912.

The one or more processors 916 may be configured to execute the instructions from the memory 910 and may perform any methods and/or associated steps indicated by the instructions, such as displaying and modifying input signals received by the instrument. Memory 910 may be implemented as processor cache, random Access Memory (RAM), read Only Memory (ROM), solid state memory, hard disk drive(s), or any other memory type. Memory 910 acts as a medium for storing data such as acquired sample waveforms, computer program products, and other instructions.

User input 914 is coupled to processor 916. User inputs 914 may include a keyboard, mouse, touch screen, and/or any other control device that a user may use to set up and control instrument 900. User input 914 may include a graphical user interface or text/character interface that operates in conjunction with display 912. User input 914 may receive remote commands or commands in the form of programs on the instrument 100 itself or from a remote device. Display 912 may be a digital screen, cathode ray tube based display, or any other monitor to display waveforms, measurements, and other data to a user. Although the components of the test instrument 900 are depicted as being integrated within the test and measurement instrument 900, one of ordinary skill in the art will appreciate that any of these components may be external to the test instrument 900 and may be coupled to the test instrument 900 in any conventional manner (e.g., wired and/or wireless communication medium and/or mechanism). For example, in some embodiments, the display 912 may be remote from the test and measurement instrument 900, or the instrument may be configured to send output to a remote device in addition to displaying the output on the instrument 900. In further embodiments, the output from the measurement instrument 900 may be sent to or stored in a remote device (e.g., a cloud device), which is accessible from other machines coupled to the cloud device.

The instrument 900 may include a principal component processor 920, which may be a separate processor from the one or more processors 916 described above, or the functionality of the principal component processor 920 may be integrated into the one or more processors 916. In addition, principal component processor 920 can include separate memory, using memory 910 described above, or any other memory accessible to instrument 900. The principal component processor 920 can include a dedicated processor or operations to perform the functions described above. For example, the principal component processor 920 can include a principal component extractor 922 for performing principal component analysis on two or more sets of measurement data. The principal component processor 920 may perform a singular value decomposition process on the raw data set as described above. PC domain mapper 924 may then map the measurement data from the original measurement domain to a principal component domain derived by principal component extractor 922. Once the measurement data has been mapped to the principal component domain, various statistics and plots can be generated on the remapped data. For example, the PC statistics processor 926 may generate statistics derived from the remapped data, including mean, standard deviation, maximum and minimum processing. Further, the PC plotter 928 may generate histograms, temporal trend graphs, and spectrograms, which facilitate user analysis of the measurement data.

Any or all of the components of the principal component processor 920, including the principal component extractor 922, the PC domain mapper 924, the PC statistics processor 926, and the PC plotter 928, may be embodied in one or more separate processors, and the separate functions described herein may be implemented as specific preprogrammed operations for dedicated or general-purpose processors. Further, as described above, any or all of the components or functions of the principal component processor 920 may be integrated into one or more processors 916 of the operational instrument 900.

Aspects of the disclosure may operate on specially created hardware, firmware, digital signal processors, or specially programmed general-purpose computers comprising processors operating according to programmed instructions. The term controller or processor as used herein is intended to include microprocessors, microcomputers, application Specific Integrated Circuits (ASICs), and special purpose hardware controllers. One or more aspects of the present disclosure may be embodied in computer-usable data and computer-executable instructions, such as in one or more program modules, executed by one or more computers (including monitoring modules) or other devices. Generally, program modules include routines, programs, objects, components, data structures, and the like. Which when executed by a processor in a computer or other device performs certain tasks or implements certain abstract data types. The computer-executable instructions may be stored on a non-transitory computer-readable medium such as a hard disk, an optical disk, a removable storage medium, a solid state memory, random Access Memory (RAM), and the like. As will be appreciated by one of skill in the art, the functionality of the program modules may be combined or distributed as desired in various aspects. Furthermore, the functionality may be embodied in whole or in part in firmware or hardware equivalents such as integrated circuits, FPGAs, and the like. Particular data structures may be used to more effectively implement one or more aspects of the present disclosure, and such data structures are considered to be within the scope of computer-executable instructions and computer-usable data described herein.

In some cases, the disclosed aspects may be implemented in hardware, firmware, software, or any combination thereof. The disclosed aspects may also be implemented as instructions carried by or stored on one or more non-transitory computer-readable media, which may be read and executed by one or more processors. Such instructions may be referred to as a computer program product. As discussed herein, computer-readable media means any medium that can be accessed by a computing device. By way of example, and not limitation, computer readable media may comprise computer storage media and communication media.

Computer storage media means any medium that can be used to store computer readable information. By way of example, and not limitation, computer storage media may include RAM, ROM, electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, compact disk read-only memory (CD-ROM), digital Video Disk (DVD) or other optical disk storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, and any other volatile or non-volatile, removable or non-removable media implemented in any technology. Computer storage media does not include signals themselves and the transitory form of signal transmission.

Communication media means any medium that can be used for communication of computer readable information. By way of example, and not limitation, communication media may include coaxial cables, fiber optic cables, air, or any other medium suitable for communication of electrical, optical, radio Frequency (RF), infrared, acoustic, or other types of signals.

Example

Illustrative examples of the disclosed technology are provided below. Embodiments of these techniques may include one or more of the following examples, as well as any combination.

Example 1 is a system, comprising: an input for accepting an input signal from a Device Under Test (DUT); a measurement unit for generating first measurement data and second measurement data from an input signal; and one or more processors configured to derive at least one principal component from the first and second measurement data using principal component analysis, and remap the first measurement data and the second measurement data to a principal component domain derived from the at least one principal component.

Example 2 is the system of example 1, wherein the one or more processors are further configured to perform a statistical analysis on the remapped data.

Example 3 is a system according to any of the preceding examples, wherein the statistical analysis includes mean and standard deviation analysis.

Example 4 is the system of example 2 or example 3, wherein the one or more processors are further configured to show results of the statistical analysis on the output display.

Example 5 is a system according to any of the preceding examples, wherein the one or more processors are further configured to generate a plot from the remapped data and to show the plot on the output display.

Example 6 is the system of example 5, wherein the plot is a histogram, a time trend graph, or a spectral display.

Example 7 is a system according to any of the preceding examples, wherein the one or more processors are further configured to re-map the first measurement data and the second measurement data from the primary component domain back to the measurement domain using information from only a single primary component.

Example 8 is a system according to any of the preceding examples, wherein the one or more processors are further configured to remap the first measurement data and the second measurement data from the domain of the primary component back to the measurement domain using information from less than all components in the domain of the primary component.

Example 9 is the system according to any of the preceding examples, wherein the measurement unit generates N sets of measurement data, and wherein the one or more processors are configured to derive M principal components from the N sets of measurement data, wherein M is in the range [1, N ].

Example 10 is a method, comprising: receiving an input signal from a Device Under Test (DUT); generating first measurement data from an input signal; generating second measurement data from the input signal; deriving at least one principal component from the first and second measurement data using principal component analysis; and remapping the first measurement data and the second measurement data to a principal component domain derived from the at least one principal component.

Example 11 is the method of example 10, further comprising performing a statistical analysis on the remapped data.

Example 12 is the method of example 11, wherein the statistical analysis includes mean and standard deviation analysis.

Example 13 is the method of example 11 or example 12, further comprising showing results of the statistical analysis on an output display.

Example 14 is a method according to any one of the preceding example methods, further comprising: generating a plot from the remapped data; and showing the plot on an output display.

Example 15 is the method of example 14, wherein the plot is a histogram, a time trend graph, or a spectral display.

Example 16 is a method according to any one of the preceding examples, further comprising remapping the first measurement data and the second measurement data from the principal component domain back to the measurement domain using information from only a single principal component.

Example 17 is a method according to any of the preceding examples, further comprising remapping the first measurement data and the second measurement data from the principal component domain back to the measurement domain using information from less than all components in the principal component domain.

Example 18 is a method according to any one of the preceding examples, further comprising generating N sets of measurement data from the input signal, and deriving M principal components from the N sets of measurement data, wherein M is in the range [1, N ].

Example 19 is a non-transitory computer-readable storage medium storing one or more instructions that, when executed by one or more processors of a computing device, cause the computing device to: receiving an input signal from a Device Under Test (DUT); generating first measurement data from an input signal; generating second measurement data from the input signal; deriving at least one principal component from the first and second measurement data using principal component analysis; and remapping the first measurement data and the second measurement data to a principal component domain derived from the at least one principal component.

Example 20 is the non-transitory computer-readable storage medium of example 19, wherein execution of the one or more instructions further causes the computing device to perform statistical analysis on the remapped data.

Example 21 is the non-transitory computer-readable storage medium of any one of examples 19-20, wherein execution of the one or more instructions further causes the computing device to remap the first measurement data and the second measurement data from the principal component domain back to the measurement domain using information from only a single principal component.

Example 22 is the non-transitory computer-readable storage medium of any of examples 19-20, wherein execution of the one or more instructions further causes the computing device to remap the first measurement data and the second measurement data from the principal component domain back to the measurement domain using information from less than all components in the principal component domain.

The previously described versions of the disclosed subject matter have many advantages that have been described or will be apparent to those of ordinary skill. Nevertheless, not all versions of the disclosed devices, systems, or methods are required for these advantages or features.

Furthermore, the written description references specific features. It should be understood that the disclosure in this specification includes all possible combinations of those particular features. Where a particular feature is disclosed in the context of a particular aspect or example, that feature may also be used in the context of other aspects and examples as much as possible.

Furthermore, when a method having two or more defined steps or operations is referred to in this application, the defined steps or operations may be performed in any order or simultaneously unless the context excludes those possibilities.

While specific examples of the invention have been shown and described for purposes of illustration, it will be understood that various modifications may be made without deviating from the spirit and scope of the invention. Accordingly, the invention should not be limited except as by the appended claims.

Claims

1. A system, comprising:

an input for accepting an input signal from a Device Under Test (DUT);

a measurement unit for generating first measurement data and second measurement data from an input signal; and

one or more processors configured to:

deriving at least one principal component from the first and second measurement data using principal component analysis, an

The first measurement data and the second measurement data are remapped to a principal component domain derived from the at least one principal component.

2. The system of claim 1, wherein the one or more processors are further configured to perform a statistical analysis on the remapped data.

3. The system of claim 2, wherein the statistical analysis comprises mean and standard deviation analysis.

4. The system of claim 2, wherein the one or more processors are further configured to show results of the statistical analysis on the output display.

5. The system of claim 1, wherein the one or more processors are further configured to generate a plot from the remapped data and to show the plot on the output display.

6. The system of claim 5, wherein the plot is a histogram, a time trend graph, or a spectral display.

7. The system of claim 1, wherein the one or more processors are further configured to:

the first measurement data and the second measurement data from the domain of the primary components are re-mapped back to the measurement domain using information from only a single primary component.

8. The system of claim 1, wherein the one or more processors are further configured to:

the first measurement data and the second measurement data from the domain of the primary components are remapped back to the measurement domain using information from less than all of the components in the domain of the primary components.

9. The system of claim 1, wherein the measurement unit generates N sets of measurement data, and wherein the one or more processors are configured to derive M principal components from the N sets of measurement data, wherein M is in the range [1, N ].

10. A method, comprising:

receiving an input signal from a Device Under Test (DUT);

generating first measurement data from an input signal;

generating second measurement data from the input signal;

deriving at least one principal component from the first and second measurement data using principal component analysis; and

11. The method of claim 10, further comprising performing a statistical analysis on the remapped data.

12. The method of claim 11, wherein the statistical analysis comprises mean and standard deviation analysis.

13. The method of claim 11, further comprising showing results of the statistical analysis on an output display.

14. The method of claim 10, further comprising:

generating a plot from the remapped data; and

a drawing is shown on the output display.

15. The method of claim 14, wherein the plot is a histogram, a time trend graph, or a spectral display.

16. The method of claim 10, further comprising remapping the first measurement data and the second measurement data from the principal component domain back to the measurement domain using information from only a single principal component.

17. The method of claim 10, further comprising remapping the first measurement data and the second measurement data from the principal component domain back to the measurement domain using information from less than all of the components in the principal component domain.

18. The method of claim 10, further comprising:

generating N sets of measurement data from the input signal; and

m principal components are derived from N sets of measurement data, where M is in the range [1, N ].

19. A non-transitory computer-readable storage medium storing one or more instructions that, when executed by one or more processors of a computing device, cause the computing device to:

receiving an input signal from a Device Under Test (DUT);

generating N sets of measurement data from the input signal;

deriving M principal components from the N sets of measurement data using principal component analysis, wherein M is in the range [1, N ]; and

the first measurement data and the second measurement data are remapped to principal component domains derived from the M principal components.

20. The non-transitory computer-readable storage medium of claim 19, wherein execution of the one or more instructions further causes the computing device to:

statistical analysis is performed on the remapped data.

21. The non-transitory computer-readable storage medium of claim 19, wherein execution of the one or more instructions further causes the computing device to remap at least one set of measurement data from the principal component domain back to the measurement domain using information from only a single principal component.

22. The non-transitory computer-readable storage medium of claim 19, wherein execution of the one or more instructions further causes the computing device to remap at least one set of measurement data from the principal component domain back to the measurement domain using information from less than all components in the principal component domain. .