Oscilloscope and reconstruction method of test object signal

Abstract

To select a more accurate unit interval (UI).SOLUTION: A oscilloscope 30 having Nyquist frequency lower than an analog band width includes: a port 32 configured to receive a test object signal; an ADC 38 configured to receive and sample the test object signal by a certain sample ratio to generate a digital sample; and one or more processors 42. The processors 42 are each configured to execute a program of causing the one or more processors 42 to conduct: a step of obtaining a plurality of UI candidates through generating corresponding histogram candidates using the UI candidates; a step of determining an optimal UI from the UI candidates according to a measurement of entropy of each of the histogram candidates; and a step of using the digital sample and the optimal UI to reconstruct a thing expressing the test object signal.SELECTED DRAWING: Figure 5

Description

[Technical Field]

[0001] This disclosure relates to test and measurement instruments, and more particularly to clock recovery techniques for use in test and measurement instruments. [Background technology]

[0002] As described in U.S. Patent No. 11,789,051, entitled "Real Equivalent Time Oscilloscope," filed February 22, 2021 (hereinafter "Tan"), the entire contents of which are incorporated herein by reference, high-speed signaling in data centers and other applications is moving toward ever-increasing speeds. For example, 26 Gb / s NRZ and 26 GBaud and 53 GBaud PAM4 signaling are used in 100 / 400 Gb Ethernet. For example, see "IEEE P802.3bs D3.5, Draft standard for Ethernet amendment 10: media access control parameters, physical layers, and management parameters for 200 Gb / s and 400 Gb / s operation," 2017, and "IEEE P802.3cd D3.5, Draft standard for Ethernet amendment 3: media access control parameters for 50 Gb / s and physical layers and management parameters for 50 Gb / s, 100 Gb / s, and 200 Gb / s operation," 2018. 32 GBaud PAM4 signaling is used in PCI Express Gen6. For example, see "PCI Express Base Specification 6.0, Version 0.7," specification | PCI-SIG (pcisig.com) 2021.

[0003] In these applications, high-end real-time (RT) and equivalent-time (ET) oscilloscopes are often used in research and development for debugging and characterization. ET oscilloscopes are often used in high-volume manufacturing. Real-equivalent-time (RET) oscilloscopes offer a cost-effective and power-efficient way to address the same measurement needs for high-speed signal transmission.

[0004] High-speed signaling methods have a nominal unit interval (UI) value. The nominal UI is the inverse of the nominal bit rate for NRZ or the baud rate for PAM4. For example, 32 GBaud (gigabaud) is the nominal baud rate for PCIE Gen6. However, the actual baud rate varies during data transmission. Some of the UI variation is by design. For example, in a spread-spectrum clocking (SSC) scheme, the system clock intentionally spreads down by 5000 ppm (i.e., 0.5%) of the nominal baud rate. Another portion of the UI variation is due to jitter inherent in the system clock, which is imperfect. Clock data recovery units are designed to track and reduce the effects of low-frequency jitter, including SSC, by tracking the low-frequency components of the system clock embedded in the data signal with a recovered clock. Various software clock data recovery (SCDR) techniques have been developed for real-time oscilloscopes, where the raw sampled waveform is not aliased. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] U.S. Patent No. 1,178,9051 [Patent Document 2] Japanese Patent Application Publication No. 2023-515498 [Non-patent literature]

[0006] [Non-Patent Document 1] "Tektronix oscilloscope" introduction site, Tektronix, [online], [searched February 24, 2025], Internet<https: / / www.tek.com / ja / products / oscilloscopes> [Non-patent document 2] "Entropy" article, Wikipedia (English version), [Online], [Retrieved February 24, 2025], Internet<https: / / en.wikipedia.org / wiki / Entropy> Summary of the Invention [Problem to be solved by the invention]

[0007] Because the sample rate of RET oscilloscopes is far below twice the Nyquist frequency required for real-time signal acquisition, aliasing occurs in the raw sampled waveforms acquired by RET oscilloscopes. Therefore, conventional SCDR techniques designed for real-time oscilloscopes cannot be used. Tan has presented a new SCDR for RET oscilloscopes. However, his technique faces two challenges: one is the processing speed issue, and the other is the processing of signals with larger impairments.

[0008] Real-time (RET) oscilloscopes offer a low-cost alternative to either real-time (RT) or equivalent-time (ET) oscilloscopes for available applications. RT oscilloscopes can sample the input waveform in a single pass, meaning acquisition and display can occur in the same time frame. To achieve this, traditional real-time oscilloscopes have a sampling rate high enough relative to their analog bandwidth to prevent aliasing during fast acquisition of the signal under test. ET (equivalent-time) oscilloscopes reconstruct waveforms using repetitive patterns in the signal. A clock data recovery (CDR) unit can acquire samples via the ET oscilloscope's hardware trigger. Because a repetitive signal is sampled, the ET oscilloscope's bandwidth can exceed its sample rate.

[0009] In contrast, as explained by Tan, real-time equivalent-time (RET) oscilloscopes have a sampling frequency less than twice the Nyquist frequency required for real-time acquisition, resulting in aliasing of the acquired samples. RET oscilloscopes determine the signal's bit rate or baud rate by repeatedly generating eye diagrams using multiple sample windows until the eye diagram has the widest opening. The eye diagram consists of a two-dimensional (2D) histogram of the sampled waveform. The oscilloscope adjusts the bit rate or baud rate until the widest opening is achieved. Once the oscilloscope determines the bit rate or baud rate, it can place each sample into the reconstructed signal. This reconstruction process does not require a hardware trigger to reconstruct the signal, as is the case with ET oscilloscopes.

[0010] As mentioned above, the above process is slower than required for high-speed signals and does not adequately handle signals with large impairments. Impairments can include issues such as jitter, for example. In Tan, the process operates iteratively. For each candidate eye diagram in the unit interval, the process repeatedly calculates the standard deviation of the jitter using various offsets. The process then repeats these iterations for each eye diagram. This process takes time, slowing down the overall process. [Means for solving the problem]

[0011] Instead, embodiments of the present application utilize a measure of the entropy of the waveform histogram of each eye diagram for a candidate unit interval. This process measures the entropy only once and selects the candidate unit interval with the lowest entropy. The lowest entropy indicates the highest density, which can be interpreted as selecting a more accurate unit interval. [Brief explanation of the drawings]

[0012] [Figure 1] Figure 1 shows a plot of probability versus entropy for transmitting bit 0 and bit 1. [Figure 2] Figure 2 shows a plot of entropy over a uniform probability distribution. [Figure 3] Figure 3 shows the same distribution for modulo operations at various offsets. [Figure 4] Figure 4 shows an embodiment of a neural network for an entropy-based real equivalent time oscilloscope. [Figure 5] FIG. 5 shows a block diagram of an embodiment of a real equivalent time oscilloscope using machine learning. [Figure 6] Figure 6 shows two-dimensional histogram plots based on various unit interval (UI) estimates. [Figure 7]Figure 7 shows the output from the neural network for various signals with various UI estimates. [Figure 8] Figure 8 shows a sample eye diagram on the RET oscilloscope after software clock recovery. DETAILED DESCRIPTION OF THE INVENTION

[0013] Entropy is a scientific concept, most commonly a measurable physical property associated with a state of disorder, randomness, or uncertainty. For an explanation of entropy, see https: / / en.wikipedia.org / wiki / Entropy. Entropy has been explored in many disciplines, from classical thermodynamics to statistical physics and later information theory. Signals acquired by oscilloscopes are primarily relevant to communication systems, and information theory is one of the fundamental theories.

[0014] For a given histogram, the entropy value can be calculated as follows:

number

[0015] An example of entropy is transmitting a bit with a value of 0 or 1. If the probability of transmitting a 0 bit is p, then the probability of transmitting a 1 bit is 1-p. Based on Equation 1, entropy can be calculated as a function of p, as shown in Figure 1.

[0016] Figure 1 shows that the entropy value reaches its minimum when only bit 0 or bit 1 is transmitted. The entropy value reaches its maximum when the probability of transmitting bits 0 and 1 is evenly distributed.

[0017] Another example is the entropy of a uniform distribution: if the probability is evenly (uniformly) distributed over two possible values, the entropy value is 1, as shown in Figure 1. If the probability is evenly distributed over n possible values, the corresponding entropy value is shown in Figure 2.

[0018] Figure 2 shows that the entropy value increases when the probabilities are distributed over a larger number of possible values ​​or bins. For example, if the probabilities are evenly (uniformly) distributed over four bins, the entropy value increases to 2. If the entropy value is distributed over eight bins, it increases to 3. In summary, the lower the density, the higher the entropy value.

[0019] RET's software clock and data recovery relies on actual measurements, but the less accurate the unit interval estimation, the greater the timing dispersion after modulo operations based on the unit interval, which means the samples will be less dense and the eye diagram will be less clear.

[0020] In one embodiment, an entropy measure can be used to determine which unit interval estimate is the most accurate, or "best," unit interval estimate. First, a 2D histogram is calculated from the RET samples for each of Tan's candidate unit interval estimates. Tan's process selects a set of multiple unit interval estimates based on the eye diagrams of each candidate unit interval. Based on the 2D histogram, an entropy value can be calculated for all these candidate unit intervals.

[0021] For a 2D histogram, the 2D entropy can be calculated as a single value using the same formula as in Equation 1, and its index covers all the grids of the 2D histogram. The 2D entropy represents the randomness of the 2D histogram. The 2D entropy can be used for software clock recovery in RET.

[0022] Alternatively, a vertical range can be selected for each 2D histogram and a 1D histogram can be created using this vertical range. The vertical range can be selected, for example, 5% or some other percentage of the signal amplitude, centered around the point in the 2D histogram corresponding to the average power level or average voltage level. Next, the entropy is calculated from the 1D histogram, and the unit interval corresponding to the 1D histogram with the lowest entropy value is selected. As mentioned above, lower entropy indicates higher density and corresponds to a better unit interval estimate. While not limiting, an example may be helpful for clarity. Consider a signal with values ​​between 0V and 1V. A mean value such as (0 + 1) / 2 = 0.5V can be selected. Then, [-2.5%, +2.5%] can be selected around 5%, i.e., 0.5V. The amplitude is 0.5. The vertical range is [0.5-2.5%*0.5, 0.5+2.5%*0.5]=[0.4875, 0.5125]. Alternatively, a 1D histogram can be used as a candidate histogram to send to machine learning. In this embodiment, the vertical range is determined based on the digital samples. The one or more processors then select samples that fall within the selected vertical range, perform a modulo operation on the sampling timing with the estimated unit interval, and use the result of this operation as the bin location to place the timing of the selected samples into bins in the 1D histogram.

[0023] In comparison, the process disclosed in Tan uses the standard deviation to determine the optimal unit interval. Because the standard deviation is sensitive to the offset of the 1D histogram, it must be calculated multiple times. For example, due to the nature of modulo arithmetic based on the unit interval of the 1D histogram shown above, samples may be concentrated in the center (horizontal direction) of the eye diagram. However, due to modulo arithmetic, the time offset of the 1D histogram can also be used to distribute samples to both ends (horizontal direction). In these two cases, even if the unit interval estimate is the same, the standard deviation is different. The only difference is the time offset, as shown in Figure 3. To obtain the correct standard deviation value used to determine the accuracy of the unit interval estimate, multiple standard deviation calculations using various time offsets yield the correct standard deviation value. The optimal time offset yields the smallest standard deviation. This iterative process slows down the calculation process.

[0024] In contrast, for the two distributions 10 and 12 in Figure 3, their entropy values ​​are identical based on Equation 1. The time offset does not affect the entropy measurement, making it faster to compute than standard deviation-based methods. Entropy-based methods also emphasize randomness, making them work well when the signal is highly impaired, such as with jitter, noise, or inter-symbol interference. A poorly estimated unit interval results in a more random 1D histogram than a highly accurate unit interval estimate.

[0025] When the signal is severely impaired, entropy-based software clock recovery cannot readily determine which unit interval estimate is better, based on the 2D or 1D histogram approach described above. In this case, machine learning can help.

[0026] Machine learning using neural networks provides a powerful tool. Neural networks can efficiently utilize more information and therefore can look at a full 2D histogram rather than a 1D histogram. Figure 4 shows an embodiment of a neural network structure. The neural network 20 receives the 2D histogram as its input. The neural network's labels for training are based on entropy. In various training cases, increasing disturbances increases entropy. Poor unit interval estimates also increase entropy. Entropy-based labels may be interpolated and extrapolated for training based on estimates of disturbances and unit intervals.

[0027] If the disturbances are very large, software clock recovery may fail even on real-time oscilloscopes. In this case, machine learning has a unique advantage. Because the training data is known, training data with large disturbances can be created. The unit interval (UI) of the training data is known and can be labeled accordingly. This is where machine learning excels. After training, machine learning can determine which UI estimate is appropriate based on the model it has learned.

[0028] The impairments in the training data sets have known values. For example, the jitter, noise, and ISI values ​​of each training data set are known. Labels may be interpolated or extrapolated based on these impairments. For example, the entropy value of training data 1, which has a jitter value of J1, a noise value of N1, and an ISI value of I1, is H1. The entropy value of training data 2, which has a jitter value of J2, a noise value of N2, and an ISI value of I2, is H2. The entropy values ​​H1 and H2 of training data 1 and training data 2 are appropriate labels because they can be used to reliably determine the best UI estimate. If the entropy value of training data 3 cannot be used to reliably determine the best UI estimate, the label of training data 3 may be estimated by interpolation or extrapolation based on the labels from training data 1 and training data 2, the impairments of training data 3, which has a jitter value of J3, a noise value of N3, and an ISI value of I3, and the impairments of training data 1 and training data 2.

[0029] After training, the neural network can determine which unit interval estimate is the best. During the testing phase, a 2D histogram based on various unit interval estimates is fed to the neural network. The neural network's output indicates which estimate is the best. The lower the entropy measure for the selected unit interval, the better the unit interval estimate. Having the most accurate unit interval estimate ensures a correct evaluation of the signal under test. An inaccurate unit interval estimate can result in a false fail or pass of the signal under test when compared to the desired signal characteristics and test criteria.

[0030] FIG. 5 illustrates an embodiment of an oscilloscope that can implement the above-described process based on a signal under test received from a device under test (DUT). FIG. 5 illustrates a block diagram of an example real-time test and measurement instrument 30 according to some aspects of the present disclosure. The test and measurement instrument 30 has one or more ports 32, which may be any electrical signal transmission medium. The ports 32 may include a receiver, a transmitter, or a transceiver. Each of the ports 32 is a channel of the test and measurement instrument 30.

[0031] The signals from the ports are then sent to a vertical gain / offset section 34, which can adjust the offset or baseline of the received signal and scale the received signal. In some configurations or embodiments, the vertical gain / offset section 34 may not include vertical gain adjustment. The absence of vertical gain adjustment can reduce vertical noise, but also reduces dynamic range. To address this, some embodiments may use external attenuators or amplifiers to attenuate or amplify the incoming signal under test. From the vertical gain / offset section 34, the signals are sent to a sampler track-and-hold circuit 36. The track-and-hold circuit 36 ​​holds each signal stable long enough to allow digitization by a high-resolution analog-to-digital converter (ADC) 38.

[0032] The ADC 38 converts the analog signal from the track-and-hold circuit 36 ​​into a digital signal. The sampling rate of the ADC 38 is greater than that of equivalent-time test and measurement instruments, but less than that of real-time test and measurement instruments. For example, the ADC 38 can sample signals from a few gigasamples per second (GS / s) to tens of GS / s. In some configurations, the ADC 38 can sample analog signals between 1 GS / s and 100 GS / s. In other configurations, the ADC can sample analog signals between 2 GS / s and 25 GS / s. The digitized signal from the ADC 38 can then be stored in an acquisition memory 40.

[0033] One or more processors 42 may be configured to execute instructions from memory and perform any method or associated steps indicated by such instructions, such as receiving acquired signals from acquisition memory 40 and reconstructing the signal under test without the use of a hardware trigger or acquiring samples at a high acquisition rate.

[0034] Memory 40, or any other memory on test and measurement instrument 30, may be implemented as processor cache, random access memory (RAM), read-only memory (ROM), solid state memory, a hard disk drive, or any other form of memory. Memory serves as a medium for storing data, computer program products, and other instructions.

[0035] A user input 44 is coupled to the one or more processors 42. The user input 44 may include a keyboard, mouse, trackball, touchscreen, or any other control device available to allow a user to interact with the GUI on the display 46. The display 46 may be a digital screen or any other monitor for displaying waveforms, measurements, and other data to a user. While the components of the test and measurement instrument 30 are depicted as being integrated within the test and measurement instrument 30, one skilled in the art will appreciate that any of these components may be external to the test and measurement instrument 30 and may be coupled to the test and measurement instrument 30 in any conventional manner. For example, in some embodiments, one or more neural networks 50 may be remote from the test and measurement instrument 30.

[0036] In one embodiment, the oscilloscope utilizes a neural network 50 to determine the optimal unit interval for clock recovery. The neural network may be implemented on-board the oscilloscope or as software executed by the same processor(s) that operate the oscilloscope. Alternatively, the neural network may reside in a separate component within the oscilloscope or on an external computing device connected to the oscilloscope. In either case, the processor(s) execute a program to operate or interface with the neural network.

[0037] Machine learning implementations, including neural networks 50, one embodiment of which is shown in Figure 4, can improve both the speed and accuracy of selecting the best (i.e., most accurate) unit interval. The clock recovery process used in RET oscilloscopes incorporating embodiments of the present application overcomes conventional problems.

[0038] Figure 6 shows three different histogram plots for various unit intervals. The top plot 60 has the least accurate unit interval estimate, the bottom plot 64 has the highest, and plot 62 is somewhere in between. Each unit interval has a time offset. The time offset shown in the histogram plots does not affect the entropy values. Certain neural networks, such as convolutional neural networks (CNNs), are not affected by 2D histogram rotation.

[0039] Figure 7 shows the test case results for RET's software clock recovery using a ResNet34 neural network structure based on a trained CNN model. In this particular embodiment, each of the 201 points along the horizontal axis represents one signal with 201 estimates of the unit interval. Each "V" shape constitutes one signal. The center point 66 of these 201 points has the best unit interval estimate when multiple test cases are created. Figure 7 shows that the neural network outputs the lowest value in the 2D histogram, corresponding to the best unit interval estimate. As each of the 201 points in Figure 7 indicates, different signals have different entropy levels.

[0040] Once the unit interval is correctly estimated, the rest of the software clock recovery can be handled in the same way as described by Tan. The sample rate and frequency can be used to recover the clock. The recovered clock is used to retime the waveform's samples, ensuring that the samples are at the correct timing positions in the pattern, thereby generating the original waveform. The pattern waveform can then be interpolated and resampled to ensure evenly spaced timing. An evenly spaced pattern waveform eliminates aliasing.

[0041] Figure 8 shows the eye diagram on the RET oscilloscope after the samples have undergone clock recovery and resampling. As can be seen, there is a clear opening in the eye diagram.

[0042] In this way, you can enjoy the benefits of a RET oscilloscope without the penalty of processing delays and less accurate unit intervals.

[0043] Aspects of the disclosed technology may operate on specially created hardware, firmware, digital signal processors, or specially programmed general-purpose computers, including processors that operate according to programmed instructions. The terms "controller" or "processor" herein contemplate microprocessors, microcomputers, ASICs, and dedicated hardware controllers, among others. Aspects of the disclosed technology may be implemented with computer-usable data and computer-executable instructions, such as one or more program modules, executed by one or more computers (including a monitoring module) or other devices. Generally, program modules include routines, programs, objects, components, data structures, etc., which, when executed by a processor in a computer or other device, perform particular tasks or implement particular abstract data types. Computer-executable instructions may be stored in computer-readable storage media, such as hard disks, optical disks, removable storage media, solid-state memory, RAM, etc. Those skilled in the art will appreciate that the functionality of the program modules may be combined or distributed as desired in various embodiments. Furthermore, such functionality may be embodied in whole or in part in firmware or hardware equivalents, such as integrated circuits, field programmable gate arrays (FPGAs), etc. Certain data structures may be used to more effectively implement one or more aspects of the disclosed technology, and such data structures are considered within the scope of the computer-executable instructions and computer-usable data described herein.

[0044] The disclosed aspects may, in some cases, 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 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 used herein, computer-readable media refers to any medium that can be accessed by a computing device. By way of example, and not limitation, computer-readable media may include computer storage media and communication media.

[0045] "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 random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory and other memory technologies, compact disc read-only memory (CD-ROM), digital video disc (DVD) and other optical disk storage, magnetic cassettes, magnetic tape, magnetic disk storage and other magnetic storage devices, and any other volatile or nonvolatile, removable or non-removable medium implemented in any technology. "Computer storage media" excludes signals themselves and transitory forms of signal transmission.

[0046] A communication medium means any medium usable for communicating computer-readable information. By way of example, and not limitation, communication media may include coaxial cable, fiber optic cable, air, or any other medium suitable for communicating electrical, optical, radio frequency (RF), infrared, acoustic, or other types of signals. Example

[0047] The following examples are provided to aid in understanding the technology disclosed in this application. Embodiments of the technology may include one or more of the examples described below, and any combination thereof.

[0048] Example 1 is an oscilloscope having a Nyquist frequency lower than an analog bandwidth, comprising an input configured to receive a signal under test, an analog-to-digital converter (ADC) that receives the signal under test and samples the signal under test at a sample rate to generate digital samples of the signal under test, and one or more processors, the one or more processors being configured to execute a program that causes the one or more processors to perform the following processes: determine a plurality of candidate unit intervals by using candidate unit intervals to generate corresponding candidate histograms; determine a best unit interval from the candidate unit intervals based on an entropy measurement of the candidate histograms; and reconstruct a representation of the signal under test using the digital samples and the best unit interval.

[0049] Example 2 is the oscilloscope of Example 1, wherein the one or more processors are further configured to execute a program that causes the one or more processors to perform processing to determine whether a representation of the signal under test satisfies a test criterion.

[0050] Example 3 is an oscilloscope of either Example 1 or 2, further comprising one or more neural networks, wherein the program that causes the one or more processors to perform the process of determining the best unit interval includes a program that causes the one or more processors to perform the process of sending candidates for the histogram to the one or more neural networks and the process of receiving specific information for the candidates for the best unit interval from the one or more neural networks.

[0051] Example 4 is the oscilloscope of Example 3, wherein the one or more processors are further configured to execute a program that causes the one or more processors to perform a process of training the one or more neural networks.

[0052] Example 5 is the oscilloscope of Example 4, wherein the one or more processors are configured to execute a program that causes the one or more processors to perform a process of training the one or more neural networks by creating one or more training data sets consisting of histograms and entropy values ​​associated with each of the histograms.

[0053] Example 6 is the oscilloscope of Example 4, wherein the one or more processors are further configured to execute a program that causes the one or more processors to generate a training set for the histogram from signals that have impairments that are too large to allow a histogram to be used in the data set by interpolation using a nearby training set.

[0054] Example 7 is an oscilloscope of any of Examples 1 to 6, wherein the program that causes the one or more processors to perform the process of determining the best unit interval includes a program that causes the one or more processors to perform the processes of generating two-dimensional histograms as candidates for the histogram, and calculating the entropy value of each of the two-dimensional histograms and selecting the unit interval corresponding to the two-dimensional histogram having the lowest entropy value as the best unit interval.

[0055] Example 8 is an oscilloscope of any of Examples 1 to 7, wherein the program that causes the one or more processors to perform the process of determining the best unit interval includes a program that causes the one or more processors to perform the processes of calculating two-dimensional histograms as candidates for the histogram, calculating one-dimensional histograms for each of the two-dimensional histograms within a certain vertical range of the two-dimensional histograms, calculating entropy values ​​for each of the one-dimensional histograms, and selecting the unit interval corresponding to the one-dimensional histogram with the lowest entropy value as the best unit interval.

[0056] Example 9 is an oscilloscope of Example 8, wherein the program that causes the one or more processors to perform a process of calculating the one-dimensional histogram within the vertical range causes the one or more processors to perform a process of selecting a vertical range that includes a point in the two-dimensional histogram corresponding to either an average signal power level or an average voltage level, plus or minus a certain percentage of the signal amplitude.

[0057] Example 10 is an oscilloscope according to any one of Examples 1 to 9, wherein the program causing the one or more processors to perform the process of determining the best unit interval includes a program causing the one or more processors to perform the processes of determining a vertical range based on the digital samples, selecting samples within the selected vertical range, and performing a modulo operation (modulo operation) on the timing of the samples selected based on the best unit interval and arranging the results at bin positions of a one-dimensional histogram.

[0058] Example 11 is a method for reconstructing a signal under test using an oscilloscope having a Nyquist frequency lower than an analog bandwidth, comprising: receiving the signal under test; sampling the signal under test to generate digital samples of the signal under test; determining a plurality of candidate unit intervals for the digital samples by using the candidate unit intervals to generate corresponding candidate histograms; determining a best unit interval from the candidate unit intervals based on a measurement of the entropy of the candidate histograms; and reconstructing a representation of the signal under test using the digital samples and the best unit interval.

[0059] Example 12 is the method of example 11, further comprising determining whether the representation of the signal under test meets a test criterion.

[0060] Example 13 is a method of either Example 11 or 12, wherein the process of determining the best unit interval includes a process of sending candidates for the two-dimensional histogram to one or more neural networks, and a process of receiving identification information of the candidates for the best unit interval from the one or more neural networks.

[0061] Example 14 is the method of example 13, further comprising training the one or more neural networks.

[0062] Example 15 is the method of Example 14, wherein the process of training the one or more neural networks includes creating one or more training data sets consisting of two-dimensional histograms and entropy values ​​associated with each of the two-dimensional histograms.

[0063] Example 16 is the method of example 14, further comprising generating the histogram training set from signals with impairments that are too large to allow histograms to be used in the data set by estimating the training set using a nearby training set.

[0064] Example 17 is a method of any of Examples 11 to 16, wherein the process of determining the best unit interval includes a process of calculating the entropy value of each of the two-dimensional histograms and selecting the unit interval corresponding to the two-dimensional histogram having the lowest entropy value as the best unit interval.

[0065] Example 18 is a method of any of Examples 11 to 17, wherein the process of determining the best unit interval includes a process of calculating a one-dimensional histogram for each of the two-dimensional histograms using a vertical range of the two-dimensional histograms, a process of calculating an entropy value for each of the one-dimensional histograms, and a process of selecting the unit interval corresponding to the one-dimensional histogram having the lowest entropy value as the best unit interval.

[0066] Example 19 is the method of example 18, wherein the process of calculating the one-dimensional histogram using the vertical range includes a process of selecting a vertical range that includes a point in the two-dimensional histogram that corresponds to either an average signal power level or an average voltage level, plus or minus a certain percentage of the signal amplitude.

[0067] Example 20 is a method of any of Examples 11 to 20, wherein the process of determining the best unit interval includes a process of determining a vertical range based on the digital samples, a process of selecting samples within the selected vertical range, and a process of performing a modulo operation on the timing of the selected samples based on the best unit interval, and then arranging the results in bin positions of a one-dimensional histogram.

[0068] Although the above-described versions of the presently disclosed subject matter have many advantages that have been described or that will be apparent to those skilled in the art, not all of these advantages or features are required in every version of the disclosed devices, systems, or methods.

[0069] Additionally, the description of this application refers to specific features. It should be understood that the disclosure herein includes all possible combinations of these specific features. When a specific feature is disclosed in connection with a particular aspect or example, that feature can also be used in connection with other aspects and examples, to the extent possible.

[0070] Furthermore, when this application refers to a method having two or more defined steps or processes, these defined steps or processes may be performed in any order or simultaneously, unless the circumstances do not preclude this possibility.

[0071] All features disclosed in the specification, claims, abstract and drawings, and all steps in any disclosed method or process, may be combined in any combination, except where at least some of such features or steps are mutually exclusive combinations. Each feature disclosed in the specification, abstract, claims and drawings may be replaced by an alternative feature serving the same, equivalent or similar purpose, unless expressly stated otherwise.

[0072] Although specific embodiments of the invention have been illustrated and described for purposes of illustration, it will be appreciated that various modifications can be made therein without departing from the spirit and scope of the invention. Accordingly, the invention should not be limited except as by the appended claims. [Explanation of symbols]

[0073] 30 Real-time equivalent time test and measurement device 32 ports 34 Vertical Gain / Offset Section 36 Sampler Track and Hold Circuit 38 Analog-to-Digital Converter (ADC) 40 Acquisition Memory 42 processors 44 User Input Section 46 Display section 50 Neural Networks

Claims

1. 1. An oscilloscope having a Nyquist frequency lower than the analog bandwidth, an input configured to receive a signal under test; an analog-to-digital converter (ADC) that receives the signal under test and samples the signal under test at a sample rate to generate digital samples of the signal under test; one or more processors Equipped with the one or more processors determining a plurality of candidate unit intervals by using the candidate unit intervals to generate corresponding candidate histograms; determining a best unit interval from among the candidate unit intervals based on an entropy measure of the candidate histograms; reconstructing a representation of said signal under test using said digital samples and said best unit interval; an oscilloscope configured to execute a program that causes the one or more processors to perform the following:

2. The program for causing the one or more processors to perform the process of determining the best unit interval further comprises one or more neural networks, sending the candidate histograms to the one or more neural networks; receiving identification of the best candidate unit intervals from the one or more neural networks; 2. The oscilloscope of claim 1, further comprising a program that causes said one or more processors to perform the steps of:

3. 10. The oscilloscope of claim 1, wherein one or more processors are configured to execute a program that causes the one or more processors to train the one or more neural networks by creating one or more training data sets comprising histograms and entropy values ​​associated with each of the histograms.

4. 4. The oscilloscope of claim 3, further configured to execute a program that causes the one or more processors to train the one or more neural networks by generating a training set of histograms from signals with impairments that are too large to allow histograms to be used in a data set by interpolation using nearby training sets.

5. The program that causes the one or more processors to perform the process of determining the best unit interval comprises: generating a two-dimensional histogram as a candidate for the histogram; calculating an entropy value for each of the two-dimensional histograms and selecting the unit interval corresponding to the two-dimensional histogram having the lowest entropy value as the best unit interval; 2. The oscilloscope of claim 1, further comprising a program that causes said one or more processors to perform the steps of:

6. The program that causes the one or more processors to perform the process of determining the best unit interval comprises: calculating a two-dimensional histogram as a candidate for said histogram; calculating a one-dimensional histogram for each of said two-dimensional histograms within a vertical range of said two-dimensional histograms; calculating an entropy value of each of the one-dimensional histograms; selecting the unit interval corresponding to the one-dimensional histogram with the lowest entropy value as the best unit interval; 2. The oscilloscope of claim 1, further comprising a program that causes said one or more processors to perform the steps of:

7. 7. The oscilloscope of claim 6, wherein the program that causes the one or more processors to calculate the one-dimensional histogram within the vertical range causes the one or more processors to select a vertical range that includes points in the two-dimensional histogram that correspond to either an average signal power level or an average voltage level, plus or minus a certain percentage of signal amplitude.

8. The program that causes the one or more processors to perform the process of determining the best unit interval comprises: determining a vertical range based on the digital samples; Selecting samples that fall within a selected vertical range; performing a modulo operation on the timing of the sample selected based on the best unit interval and placing the result in a bin position of a one-dimensional histogram; 2. The oscilloscope of claim 1, further comprising a program that causes said one or more processors to perform the steps of:

9. 1. A method for reconstructing a signal under test using an oscilloscope having a Nyquist frequency lower than the analog bandwidth, comprising: receiving a signal under test; sampling the signal under test to generate digital samples of the signal under test; determining a plurality of candidate unit intervals for the digital samples by using the candidate unit intervals to generate corresponding candidate histograms; determining a best unit interval from among the candidate unit intervals based on a measure of entropy of the candidate histograms; reconstructing a representation of said signal under test using said digital samples and said best unit interval; 10. A method for reconstructing a signal under test, comprising:

10. The process of determining the best unit interval is as follows: sending the candidate two-dimensional histograms to one or more neural networks; receiving information from said one or more neural networks identifying said best candidate unit intervals; 10. The method for reconstructing a signal under test according to claim 9, comprising:

11. 11. The method of claim 10, further comprising training the one or more neural networks by creating one or more training data sets comprising two-dimensional histograms and entropy values ​​associated with each of the two-dimensional histograms.

12. 11. The method of claim 10, further comprising training the one or more neural networks by generating a training set of histograms from signals with impairments that are too large to use a histogram in a data set by estimating the training set using a nearby training set.

13. 10. The method for reconstructing a signal under test according to claim 9, wherein the process of determining the best unit interval comprises a process of calculating an entropy value of each of the two-dimensional histograms and selecting the unit interval corresponding to the two-dimensional histogram having the lowest entropy value as the best unit interval.

14. The process of determining the best unit interval is as follows: calculating a one-dimensional histogram for each of said two-dimensional histograms using a vertical range of said two-dimensional histograms; Calculating an entropy value for each of the one-dimensional histograms; selecting the unit interval corresponding to the one-dimensional histogram having the lowest entropy value as the best unit interval; 10. The method for reconstructing a signal under test according to claim 9, comprising:

15. The process of determining the best unit interval is as follows: determining a vertical range based on the digital samples; Selecting samples that fall within a selected vertical range; performing a modulo operation on the timing of said sample selected based on said best unit interval and placing the result in a bin position of a one-dimensional histogram; 10. The method for reconstructing a signal under test according to claim 9, comprising:

Images