Test and measurement instrument, method for compressively sensing signal from DUT, and array of analog-to-digital converters

Abstract

To achieve a higher bandwidth than what can be conventionally achievable.SOLUTION: A test and measurement instrument 10 provided herein comprises one or more ports 12 for receiving a signal from a device under test (DUT) 11, an array 18 of analog-to-digital converters (ADC) for receiving the signal, a data collector for outputting one sample from each ADC 16 during one ADC clock cycle, and one or more processors 24 for providing a sample clock to each ADC 16 having a different clock phase from other ADCs to cause non-uniform sample spacing below a Nyquist frequency, and for causing the ADCs to output samples with non-uniform spacing.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] FIELD OF THE DISCLOSURE The present disclosure relates to test and measurement instruments, and more particularly to test and measurement instruments that employ compressed sensing during sample acquisition. [Background technology]

[0002] Generally, test and measurement equipment measures and tests the operation and performance of a device under test (DUT) by receiving and analyzing signals from the DUT. The signals typically consist of analog signals that must be converted by one or more analog-to-digital converters (ADCs).

[0003] Analog signals must be sampled at a high enough frequency to avoid aliasing, or signal distortion. Aliasing occurs when test and measurement equipment does not sample fast enough to accurately reconstruct the signal. The Nyquist theorem, or Nyquist-Shannon theorem, states that the sampling frequency must be at least twice the highest frequency component of the signal. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Japanese Patent Application Publication No. 2023-33236 [Patent Document 2] Japanese Patent Publication No. 2022-173145 [Non-patent literature]

[0005] [Non-Patent Document 1] "Tektronix oscilloscope" introduction site, Tektronix, [online], [searched February 28, 2025], Internet<https: / / www.tek.com / ja / products / oscilloscopes> Summary of the Invention [Problem to be solved by the invention]

[0006] High frequency sampling requirements increase the complexity and cost of test and measurement equipment, and ever-increasing signal speeds require devices and methods that can accommodate higher speed signals. [Means for solving the problem]

[0007] Embodiments of the disclosed technology include test and measurement instruments, particularly oscilloscopes, that employ compressive sensing (CS), which allows oscilloscopes to achieve higher bandwidths than conventional frequencies.

[0008] CS is essentially an L1 minimization method for solving under-determined system problems, and therefore can recover the original signal from fewer samples than Nyquist sampling. [Brief explanation of the drawings]

[0009] [Figure 1] FIG. 1 shows an embodiment of a test and measurement device. [Figure 2] Figure 2 shows an embodiment of an array of analog-to-digital converters. [Figure 3] Figure 3 shows a graphical representation of the phase of an analog-to-digital converter with non-uniform sample intervals. [Figure 4] FIG. 4 shows a flowchart of a method for sampling a signal using compressed sensing. [Figure 5] FIG. 5 is a graphical representation of an embodiment of a method for reconstructing a signal from compressed sensing samples. [Figure 6] FIG. 6 is a graphical representation of an embodiment of a method for reconstructing a signal from compressed sensing samples. DETAILED DESCRIPTION OF THE INVENTION

[0010] Let's consider the following classical problem in linear algebra. [Mathematics 1] y = Φx Equation 1 clearly represents a determined system. That is, the number of equations is exactly equal to the number of unknowns. Here, y is a column vector of size n, and x is a column vector of size n. The symbol Φ represents an n×n invertible matrix. This is a classical problem of n equations and n unknowns. For example, in Nyquist sampling, since Φ is the identity matrix, y = x. y is the sampled measurement value, and x is the Nyquist band-limited signal of the original signal.

[0011] Assume Φ is an m×n reduction matrix with m < n. x is a column vector of size n. y is a column vector of size m. The above set of equations is an ill-conditioned underdetermined system (difficult to determine the solution). Even if the measurement value y and the matrix Φ are given, the original signal x cannot be restored.

[0012] However, if this underdetermined system can transform x into a k-sparse vector (sparse vector) with k non-zero components by the transformation matrix Ψ, and Φ is incoherent with respect to Ψ, then it can be solved (with a high probability). Examples of Ψ include the Discrete Cosine Transform (DCT) matrix, the Discrete Fourier Transform (DFT) matrix, etc. Ψ is unitary and thus invertible. The non-zero components are usually composed of values large enough to exceed a threshold like the noise floor. In such a case, with n > m ≧ 2k, it is possible to solve for x using L1 minimization with m measurement values y.

[0013] L1 minimization can be achieved using various algorithms such as Matching Pursuit (MP), Orthogonal Matching Pursuit (OMP), and Belief Propagation (BP). Transforming x into a sparse vector s using the Ψ matrix is ​​s = Ψx. Equation 1 contains x = Ψ -1 s can be substituted. [Number 2] x=Ψ -1 s [Number 3] y=ΦΨ -1 s By associative law, A=ΦΨ -1 Then, [Number 4] y=As Since y and A are known, we can solve for s via L1 minimization. Furthermore, x=Ψ -1 s. The dimensions of Ψ are n×n, Φ are m×n, and A is m×n.

[0014] In CS, certain conditions must be met to reconstruct x from y. First, the vector x must be compressible, i.e., k-sparse (having at most k non-zero elements) in some basis. For example, s=Ψx, where s is k-sparse and Ψ is a DCT or DFT.

[0015] Second, Φ must be incoherent with respect to Ψ. This means that for a matrix coherence μ, μ(Φ,Ψ)=max 1≦i≦m max 1≦j≦n |<Φ i Ψ j>| → 1.0. A random matrix Φ approximately satisfies the above conditional relations, but not with absolute certainty. Φ is an independent and identically distributed (IID) random variable. Multiplying an IID matrix Φ by an orthonormal matrix Ψ still results in an IID matrix. A matrix is ​​orthonormal if its columns form an orthonormal set, where each column has length 1 and is orthogonal to all other column vectors.

[0016] Third, the matrix Φ should exhibit the Restricted Isometry Property (RIP), in that it should behave approximately orthonormally. In this case, the probabilities contained in the CS give a high probability, but not an absolute probability, that the columns are all length 1 and orthogonal to all other columns, such that multiplying the matrix by the matrix Φ is approximately isometric (L2 minimization preserves distances). [Number 5] (1-δ k )||s|| L2 2 ≦||Φs|| L2 2 ≦(1+δ k )||s|| L2 2

[0017] Equation 5 is true because Φ is a function of the restricted isometry constant δ k∈(0, 1), which means that the RIP condition is satisfied. A random matrix Φ and a k-sparse vector s approximately satisfy this RIP condition, which means that there is a high probability that these matrices and vectors satisfy the RIP condition. Constructing a RIP is NP-hard, meaning that constructing a RIP is one of the most difficult computational puzzles to solve, but if Φ is random, the RIP can be satisfied with a high probability. The inability to satisfy the RIP with absolute probability is what makes it almost satisfy the RIP. The randomness of Φ leads to incoherence, which almost satisfies the RIP.

[0018] Fourth, for exact reconstruction, the condition m ≥ cklog(n / k) must be satisfied, such that m ≥ 2k is true for some small constant c > 0. c is coherent between Ψ and Φ and approximates the non-zero coefficients. Meeting these requirements allows us to solve for s in Equation 4. Let s' be the reconstructed version of s as follows: [Number 6] s'=min||y-As||1 where s is a sparse vector of x, which is the inferred (or imaged) ideal Nyquist samples. If the minimization of Equation 6 is perfect, then s = s'. Equation 6 can be solved using various iterative algorithms, such as Matching Pursuit (MP), Orthogonal Matching Pursuit (OMP), and Belief Propagation (BP).

[0019] Now that we have defined the terms used in compressed sensing as described in this application, we will explain how compressed sensing is used to obtain samples. -1 Given the relationship between s, equation 2 is x=Ψ -1 gives the relationship between s. Without loss of generality, the variables are defined as follows: x: n×1 signal sampled at the Nyquist rate in the time domain s: An n×1 x DCT transform that is k-sparse (has at most k nonzero components) in the frequency domain. Ψ: n×n DCT transformation matrix. Φ: m×n measurement matrix. where s is unknown. Ψ is simply the DCT of the identity matrix. The assumption in this disclosure is that x is sparse in the frequency domain. In the implementation of the CS sampling technique, the measurement matrix Φ is the key component variable that the acquisition system needs to generate.

[0020] The measurement matrix Φ precisely controls the time location of the samples. y are the samples acquired at these times. Φ is an m-by-n matrix. Size n is the length of the reconstructed acquisition sample record as if the acquisition (acquired waveform data) were sampled at the Nyquist rate, and m is the number of acquired samples, which is less than n, to reconstruct the record. In the discrete-time sampling situation, the matrix Φ is a binary matrix with elements either 1 or 0. An element 1 indicates one sample, and 0 means no sample. There is exactly one sample per row. For example, in traditional Nyquist sampling, Φ would be an n-by-n identity matrix.

[0021] In the following description, a 3x8 measurement matrix is ​​used as an example.

number

[0022] Let's assume the sample size is m ≥ cklog(n / k), c ≈ 3 to 5 (smaller is better), and c is the coherence value between Ψ and Φ. For example, if n = 1000, k = 10, and c ≈ 4, then m ≥ 184. Therefore, in this example, Φ will have a target of 184 times 1000 columns. If m = 200, the number of samples taken will be 200 / 1000, which is 20% of Nyquist sampling. The components of Φ are given by Φ in a random row i and column j. i,j =1. Randomness increases the chance of meeting RIP requirements. Sorting the rows does not affect the results or coherence.

[0023] In the case of sample acquisition, m is the acquisition size, but the sample time interval is not constant. Generally, the maximum average sample rate of the acquisition is f s As mentioned above, n is the length of the reconstructed record, which has a constant sample time. This allows f s *(n / m) sample rate is obtained.

[0024] FIG. 1 illustrates a test and measurement instrument 10, such as an oscilloscope, that can perform the above processing based on signals received from a device under test (DUT) 11. FIG. 1 illustrates a block diagram of an example test and measurement instrument 10 according to some aspects of the present disclosure. The test and measurement instrument 10 includes one or more ports 12, which may be any electrical signal transmission medium. The ports 12 may include receivers, transmitters, and transceivers. Each port 12 corresponds to a channel of the test and measurement instrument 10. Note that reference numbers for components of the test and measurement instrument 10 are used where appropriate in the following figures.

[0025] The signals from port 12 are then sent to a sampler track and hold circuit 14, which holds each signal stable long enough to allow it to be digitized by an array of analog-to-digital converters (ADCs) 18, which are made up of individual ADCs, such as ADC 16.

[0026] The array of ADCs 18 converts the analog signals from the sampler, track and hold circuit 14 to digital signals. As described in more detail with respect to Figures 2 and 3, the array of ADCs 18 performs compressed sensing based on the clock phase of each ADC 16 in the array of ADCs 18. The digitized signals from the array of ADCs 18 may then be stored in memory 20, which may include an acquisition memory and represent one or more memory structures within the test and measurement instrument 10.

[0027] The one or more processors 24 may be configured to execute instructions from the memory 20 and may perform any method or associated steps indicated by such instructions (e.g., receiving an acquired signal from the acquisition memory 20 and reconstructing a signal under test). In some embodiments, the one or more processors 24 control the clock phase of each ADC 16 in the array of ADCs 18 to generate non-constant sampling times for the array of ADCs 18, which have an ending sample frequency that is lower than the Nyquist frequency of the bandwidth of interest, but higher than the Nyquist frequency of the ADCs in the array of ADCs 18. This enables compressed sensing in the test and measurement instrument.

[0028] Memory 20 represents any memory within test and measurement instrument 10 and 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 20 serves as a medium for storing data, computer program products, and other instructions.

[0029] The user interface 26 receives and couples user input to the one or more processors 24. The user input 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 28. The display 28 may be a digital screen or any other monitor for displaying waveforms, measurements, and other data to the user. While the components of the test and measurement instrument 10 are depicted as being integrated within the test and measurement instrument 10, those skilled in the art will understand that any of these components may be external to the test and measurement instrument 10 and may be coupled to the test and measurement instrument 10 in any conventional manner.

[0030] The resulting signal samples are sparse because they were obtained by compressive sensing. One or more processors 24 may execute programs to reconstruct the signal from the sparse samples. As described in more detail below, reconstructing the signal from the sparse samples may involve the use of machine learning. The machine learning block 30 may take the form of a program executed by the processor to perform the machine learning process or may include access to a separate machine learning system.

[0031] FIG. 2 shows a more detailed diagram of an embodiment of an array of ADCs 18. The parallel array of ADCs 18 samples at non-uniform times. One or more processors 24 can control the array of ADCs 18 at specific phases to achieve non-uniform sampling. With an array of m ADCs 16, each ADC 16 uses a sample clock 40 to generate a frequency f s If there are m ADCs in the array of ADCs 18, each ADC 16 samples the same input signal with a phase delay of 2π / m. This system constitutes an interleaved system, and mf sThe ADCs 16 are sampled at a rate of 1 / 2 m. The multiplexer 42 outputs one sample from each ADC 16 at a time, for all m ADCs 16 during one ADC clock cycle, outputting m samples per ADC clock cycle. Alternatively, a FIFO (first-in, first-out) buffer can replace the multiplexer 42. The FIFO accumulates these m samples and outputs m samples per clock. The component that outputs m samples per ADC clock cycle is referred to herein as a "data collector." The data collector may include, for example, a multiplexer or a FIFO.

[0032] In another embodiment, a random sample clock scheme may be employed with m ADCs 16 in the array of ADCs 18, where the desired number of samples is some multiple of the number m of ADCs. One or more processors 24 execute a program that provides the sample clock so that each ADC samples repeatedly to achieve the desired number of samples. Each clock for each ADC 16 in each iteration may be out of phase.

[0033] In an interleaved system, the phase is (m-1) The phase delay is delayed in the range [0,2π] in a linear increment of 2π / m until the sample interval is reached. The size of this phase delay step is Δθ=2π / m, but instead of using Δθ=2π / m in the CS system, we use Δθ=2π / (mM), where M=n / m and Δθ=2π / n. Thus, the sample interval is smaller, and the resolvable bandwidth increases by a factor of M, but the total number of samples taken is still m. Therefore, the average sample rate is Mmf s Not mf s It remains as it is.

[0034] To formulate an interleaved system, we use the following definition: The ratio of the target Nyquist sample rate to the hardware Nyquist sample rate is M=n / m. The uniform time-interleaved sample rate f of m ADCs isilv , mf s This means that the period of the uniformly time interleaved samples is T ilv =1 / f ilv The target sample interval is T CS =T ilv / M, the target sample rate is f CS =1 / T CS The average sample interval is T avg =M*T CS =T ilv where T avg is always T ilv is equal to

[0035] To achieve non-constant sample intervals, T[i] is CS where r is an integer random variable with a flat distribution ranging from 0 to M-1. As a result, the sampling time is t[i]=iT avg +T[i]. This sampling time satisfies the measurement matrix Φ with the necessary conditions for CS.

[0036] Figure 3 shows a graphical representation of the phase angle of each ADC. In this example, there are m=7 ADCs, numbered 0 through 6. The ratio of the target Nyquist rate to the hardware sample rate is 3, so the CS system takes 7 samples for every 21 in the Nyquist system. Each ADC has 51 degrees of phase (0, 51, 102, 153, 204, 255, and 306), and each position is represented in the diagram by an ADC number 0 through 6. The 51 degrees between each ADC's phase position is divided into M segments (3 in this example). The phase of each ADC is its phase position plus a random number between 0 and 2, which is generated at each phase position.

[0037] Thus, each ADC assumes a phase angle of (0, 1, or 2)*2π / n degrees, or approximately 51 degrees, as indicated by its numbered position in the diagram. The phase of each ADC is then adjusted by multiplying 0, 1, or 2 by a factor r (each r is 17 degrees). This adjustment results in ADC0's phase = 0 + ((0, 1, or 2) * 17 degrees)), ADC1's phase = 51 + (((0, 1, or 2) * 17 degrees)), ADC2's phase = 102 + ((0, 1, or 2) * 17 degrees), and so on, resulting in ADC6's phase = (51 * 6) + ((0, 1, or 2) * 17 degrees).

[0038] In summary, this process achieves compressive sensing using non-uniform sampling. FIG. 4 shows a flowchart of an embodiment of a method for compressing sensing. The user interface 26 on the test and measurement instrument 10 may provide the user with the option to perform compressed sensing and bypass the higher Nyquist rate. The user can make that decision based on the user's knowledge of the signal. Alternatively, the test and measurement instrument may exist as a compressed sensing instrument rather than being able to select between compressed and conventional sensing. Thus, step 50 of FIG. 4 is optional.

[0039] In step 52, the test and measurement instrument 10 receives a signal from a DUT (e.g., DUT 11 in FIG. 1). The test and measurement instrument 10 then provides a sample clock for the non-constant sample interval. As described above, this may involve an array of ADCs 18, with each ADC having a clock phase position multiplied by 2π / n times the number of ADCs, and then adjusted by some subset of the phase division multiplied by r. The test and measurement instrument 10 then outputs the samples generated from the compressed sensing array of ADCs 18 for further analysis. In some embodiments, the test and measurement instrument 10 may use one or more processors 24 to reconstruct the signal using one of several different options.

[0040] Figure 5 shows the original modulated waveform 60. Circles 62 indicate sample points. In this example, there are 42 times fewer samples than the Nyquist requirement. The waveform 64 at the bottom right is the waveform reconstructed using the simplest matching pursuit algorithm. Figure 6 shows a similar comparison of a four-level pulse amplitude modulation (PAM4) SSPRQ (short stress pattern random quaternary) waveform 70. Samples are taken at the "x" spots 72. In this example, the number of samples is less than half. The reconstructed waveform 74 is shown at the bottom right and is also obtained with the matching pursuit algorithm.

[0041] Many other types of reconstruction algorithms can be used to reconstruct the compressed sensed signal. These may include convex optimization schemes in machine learning (e.g., gradient descent, projected gradient, quasi-Newton, etc.). Other possibilities include interior-point methods using convex conjugate gradients and barrier functions as part of the reconstruction method, which can be used instead of matching pursuit or basis pursuit, and are grouped together in this description as optimal matching nonlinear approximation of the signal. Another option is CUDA®-based parallel processing techniques, which are widely adopted in methods such as those that solve the L1 minimization problem present in compressed sensing.

[0042] Some approaches are sometimes called gradient approaches. An example is gradient with derivatives, which is an approach to convex optimization that first calculates the gradient of a convex function and then uses this derivative to perform convex optimization. Projected gradient methods: This convex optimization approach was originally introduced to solve convex problems with convex objective functions and convex constraints. It has the advantage over gradient with derivatives that if a system of convex constraints cannot be satisfied at the current iteration, it simply projects into the subspace defined by these convex constraints.

[0043] Other approaches may include quasi-Newton methods. These methods are based on approximating the Hessian of the second derivative with a quadratic approximation (any convex function, such as a linear function, can be used). Convex problems with convex constraints can be solved using quasi-Newton methods, resulting in faster convergence. Both the first and second derivatives of the convex objective function are used to iteratively calculate the minimum of the convex function using only function evaluations. This algorithm uses a quadratic approximation around the convex minimization iteration, so only function evaluations are required. An initial point is required to start the convex optimization.

[0044] Further approaches include interior-point methods using convex conjugate gradients and barrier functions. Convex optimization problems can be solved using barrier convex conjugate gradients if the convex function is twice differentiable, as convexity is easy to check. Combining the two methods also makes it easier to avoid getting trapped in local minima, since before each iteration there is a gradient test that checks whether the step approaches a local minimum. Global Convex Minimization: For convex problems, quasi-Newton methods typically provide better convergence results compared to other methods, such as gradient-based methods and barrier convex conjugate gradients. However, this is not always the case; quasi-Newton methods may converge slowly, or non-convergent convex problems may exist. In such cases, an alternative approach is to use global convex minimization methods instead of local convex minimization methods.

[0045] Traditional machine learning approaches can also be used, such as training a model using a data set consisting of the frequency spectrum or other signal shape of the compressed sensed signal and the original waveform, which would train the model to recognize the compressed sensed signal and provide a reconstructed signal.

[0046] In this way, the test and measurement instrument can compressively sense the signal, thereby increasing speed and saving hardware.

[0047] 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.

[0048] 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.

[0049] "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.

[0050] 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

[0051] 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.

[0052] Example 1 is a test and measurement apparatus comprising: one or more ports connected to a device under test (DUT) for receiving signals from the DUT; an array of analog-to-digital converters (ADCs) for receiving signals in parallel; a data collector configured to select each of the ADCs from the array of ADCs so that the ADCs output one sample from each of the ADCs in the array of ADCs during one ADC clock cycle; and one or more processors, the one or more processors configured to execute a program that causes the one or more processors to supply, to each of the ADCs in the array of ADCs, a sample clock that has a clock phase different from that of other ADCs in the array of ADCs and that generates non-uniform sample intervals below the Nyquist frequency, and to cause the ADCs to output samples at non-uniform sample intervals.

[0053] Example 2 is the test and measurement instrument of Example 1, wherein the program that causes the one or more processors to perform a process of supplying sample clocks having different clock phases to each of the ADCs in the ADC array includes a process of causing the one or more processors to perform a process of dividing 2π by m (m is the number of ADCs in the ADC array) to generate an initial clock phase for each of the ADCs, a process of dividing the initial clock phase for each of the ADCs into a number of steps equal to M (M is a ratio of a Nyquist sample rate to a hardware sample rate), and a process of randomly selecting a step r from the plurality of steps for each of the ADCs and adding the step r to the initial clock phase for each of the ADCs to generate a clock phase for each of the ADCs.

[0054] Example 3 is the test and measurement instrument of example 2, wherein the Nyquist sample rate is equal to a ratio M of a Nyquist sample rate to a hardware sample rate multiplied by the number of ADCs in the ADC array.

[0055] Example 4 is the test and measurement instrument of any of Examples 1 to 3, wherein the desired number of samples is a multiple of the number of ADCs in the array of ADCs, and the program that causes the one or more processors to provide the sample clock includes program that causes the one or more processors to provide the sample clock such that each of the ADCs in the array of ADCs samples multiple times to obtain the desired number of samples, and each of the ADC iterations has a different clock phase.

[0056] Example 5 is the test and measurement instrument of any of Examples 1 to 4, wherein the one or more processors are further configured to execute a program for reconstructing the signal from samples at non-uniform sample intervals below the Nyquist frequency.

[0057] Example 6 is the test and measurement instrument of Example 5, wherein the program that causes the one or more processors to perform a process to reconstruct the signal includes a program that causes the one or more processors to perform a process to calculate an optimal matching nonlinear approximation for the signal.

[0058] Example 7 is the test and measurement instrument of Example 5, wherein the program that causes the one or more processors to perform a process of reconstructing the signal includes a program that causes the one or more processors to perform a process of reconstructing the signal using a trained machine learning system based on the waveform shape of the signal.

[0059] Example 8 is the test and measurement instrument of Example 5, wherein the program that causes the one or more processors to perform the process of reconstructing the signal includes a program that causes the one or more processors to perform the process of performing any one of a gradient descent method, a projected gradient method, a quasi-Newton method, or an interior point method.

[0060] Example 9 is a test and measurement device of any of Examples 1 to 8, wherein the one or more processors are further configured to execute a program that causes the one or more processors to present compressed sensing options to a user on a user interface of the test and measurement device.

[0061] Example 10 is a method for compressive sensing of a signal from a device under test (DUT), comprising: receiving a signal from the DUT; providing a sample clock to each ADC in an array of ADCs having a clock phase different from the clock phases provided to other ADCs in the array of ADCs, the sample clock having a non-uniform sample interval that is less than the Nyquist frequency; sampling the signal with the non-uniform sample clock; and outputting the samples at the non-uniform sample interval for further analysis.

[0062] Example 11 is the method of example 10, in which the process of providing sample clocks having different clock phases to each of the ADCs includes a process of dividing 2π by m (m is the number of the ADCs in the ADC array) to generate an initial clock phase for each of the ADCs; a process of dividing the initial clock phase for each of the ADCs into a number of steps equal to M (M is a ratio of a Nyquist sample rate to a hardware sample rate); and a process of randomly selecting a step r from the plurality of steps for each of the ADCs and adding the step r to the initial clock phase for each of the ADCs to generate a clock phase for each of the ADCs.

[0063] Example 12 is the method of any of Examples 10 or 11, wherein the ratio M of the Nyquist sample rate to the hardware sample rate multiplied by the number of ADCs in the array of ADCs equals the Nyquist sample rate.

[0064] Example 13 is the method of example 12, wherein the step of providing the sample clock to each of the ADCs in the array of ADCs includes a step of defining a desired number of samples equal to a multiple of the number of ADCs in the array of ADCs, and a step of obtaining the desired number of samples by sampling each of the ADCs in the array of ADCs multiple times, using a different clock phase for each iteration of each ADC.

[0065] Example 14 is the method of any of examples 11 to 13, further comprising reconstructing the signal from samples having a non-constant sample spacing below the Nyquist frequency.

[0066] Example 15 is the method of example 14, wherein reconstructing the signal includes calculating a best matching nonlinear approximation to the signal.

[0067] Example 16 is the method of example 14, wherein reconstructing the signal includes reconstructing the signal using a trained machine learning system based on a frequency domain version of the signal.

[0068] Example 17 is the method of example 14, in which the signal reconstructing process includes performing any one of gradient descent, projected gradient, quasi-Newton, or interior point methods.

[0069] Example 18 is the method of any of Examples 11 to 17, further comprising presenting a compressed sensing option to a user on a user interface of the device.

[0070] Example 19 is an array of analog-to-digital converters (ADCs) for randomly sampling a signal, comprising: an array of analog-to-digital converters (ADCs) arranged to receive the signal in parallel; a data collector that selects each ADC from the array of ADCs and operates the array of ADCs so that each ADC outputs one sample per clock cycle; and a sample clock connected to each ADC in the array of ADCs, each ADC having a clock phase different from the other ADCs in the array of ADCs that results in non-constant sample intervals below the Nyquist frequency.

[0071] Example 20 is the array of analog-to-digital converters of example 19, wherein the data collector includes either a multiplexer or a FIFO buffer.

[0072] 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.

[0073] 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.

[0074] 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.

[0075] While specific embodiments of the disclosed technology 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 disclosed technology should not be limited, except as by the appended claims. [Explanation of symbols]

[0076] 10 Test and measurement equipment 11 Device Under Test (DUT) 12 ports 14 Sampler Track & Hold Circuit 16 individual analog-to-digital converters 18 Analog-to-Digital Converter Array 20 memory 24 processors 26 User Interface 28 Display section 30 Machine Learning Blocks 40 sample clocks 42 Multiplexer

Claims

1. 1. A test and measurement device comprising: one or more ports for connecting to a device under test (DUT) and receiving signals from the DUT; an array of analog-to-digital converters (ADCs) for receiving signals in parallel; a data collector that selects each of the ADCs from the array of ADCs so that the array of ADCs outputs one sample from each of the ADCs in the array of ADCs during one ADC clock cycle; one or more processors Equipped with the one or more processors are configured to execute a program that causes the one or more processors to provide, to each of the ADCs in the array of ADCs, a sample clock that has a different clock phase from the other ADCs in the array of ADCs and that generates non-uniform sample intervals below the Nyquist frequency, and to cause the ADCs to output samples at non-uniform sample intervals.

2. The program causing the one or more processors to perform a process of providing a sample clock having a different clock phase to each of the ADCs in the array of ADCs comprises: Dividing 2π by m, where m is the number of ADCs in the array of ADCs, to generate an initial clock phase for each of the ADCs; Dividing the initial clock phase of each of the ADCs into a number of steps equal to M, where M is the ratio of the Nyquist sample rate to the hardware sample rate; randomly selecting a step r from among a plurality of steps for each of the ADCs and adding the step r to the initial clock phase for each of the ADCs to generate a clock phase for each of the ADCs; 2. The test and measurement instrument of claim 1, further comprising a program that causes said one or more processors to:

3. 3. The test and measurement instrument of claim 2, wherein the Nyquist sample rate is equal to the ratio M of the Nyquist sample rate to the hardware sample rate multiplied by the number of ADCs in the array of ADCs.

4. the desired number of samples is a multiple of the number of ADCs in the array of ADCs, 2. The test and measurement instrument of claim 1, wherein the program causing the one or more processors to provide the sample clock comprises program causing the one or more processors to provide the sample clock such that each of the ADCs in the array of ADCs samples multiple times to obtain the desired number of samples, each of the ADC iterations having a different clock phase.

5. 10. The test and measurement instrument of claim 1, wherein the one or more processors are further configured to execute a program for reconstructing the signal from samples at non-uniform sample intervals below the Nyquist frequency.

6. 6. The test and measurement instrument of claim 5, wherein the program that causes the one or more processors to perform the process of reconstructing the signal includes a program that causes the one or more processors to perform the process of reconstructing the signal using a trained machine learning system based on the waveform shape of the signal.

7. 1. A method for compressive sensing of a signal from a device under test (DUT), comprising: receiving a signal from the DUT; providing a sample clock to each of the ADCs in the array of ADCs having a clock phase that differs from the clock phase provided to other ADCs in the array of ADCs, resulting in non-constant sample intervals below the Nyquist frequency; sampling said signal with a non-constant sample clock; Processing to output samples at non-uniform sample intervals for further analysis. A method for compressive sensing of a signal from a DUT, comprising:

8. providing sample clocks having different clock phases to each of the ADCs; Dividing 2π by m, where m is the number of ADCs in the array of ADCs, to generate an initial clock phase for each of the ADCs; Dividing the initial clock phase of each of the ADCs into a number of steps equal to M, where M is the ratio of the Nyquist sample rate to the hardware sample rate; randomly selecting a step r from among a plurality of steps for each of the ADCs and adding the step r to the initial clock phase for each of the ADCs to generate a clock phase for each of the ADCs; 8. The method for compressive sensing a signal from a DUT according to claim 7, comprising:

9. 9. The method for compressive sensing a signal from a DUT according to claim 8, wherein the ratio M of the Nyquist sample rate to the hardware sample rate multiplied by the number of ADCs in the ADC array is equal to the Nyquist sample rate.

10. providing the sample clock to each of the ADCs in the array of ADCs; defining a desired number of samples equal to a multiple of the number of ADCs in the array of ADCs; sampling each of the ADCs in the array of ADCs multiple times, using a different clock phase for each iteration of each ADC, to obtain the desired number of samples; 10. The method for compressive sensing a signal from a DUT according to claim 9, comprising:

11. an array of analog-to-digital converters (ADCs) for randomly sampling a signal, an array of analog-to-digital converters (ADCs) arranged to receive the signals in parallel; a data collector for selecting each of the ADCs from the array of ADCs and operating the array of ADCs so that each of the ADCs outputs one sample per clock cycle; a sample clock connected to each of the ADCs in the array of ADCs; Equipped with An array of ADCs, each of the ADCs having a clock phase that is different from other ADCs in the array of ADCs and that results in non-constant sample spacing below the Nyquist frequency.

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