Introduction to the Special Issue on the 20th IMEKO TC4 International Symposium and the 18th TC4 Workshop on ADC and DAC Modelling and Testing

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The analysis of exponential signals by maximum likelihood estimation

Peer Reviewe

DYNAMIC DAC TESTING BY REGISTRATION OF THE INPUT CODE WORDIN EQUALITY WHEN THE DAC OUTPUT MATCHES A REFERENCE SIGNAL

ABSTRAC

Full Information from Measured ADC Test Data using Maximum Likelihood Estimation

Abstract ADC testing is often done using sine wave excitation (see e.g. IEEE standard 1241). A sine wave is fitted to the measured data in least squares sense, and the residuals are analyzed further. In recent papers, it has been recognized that even more (and more precise) information can be extracted by the solution of the maximum likelihood equations. This is an improvement to the usual three-parameter and four-parameter fits. In this paper practical implementation of this algorithm is suggested. Then, theoretical background is overviewed. Further investigations lead to the statement that the same principle can be extended to any measurement which uses an excitation signal which can be described with a few parameters. A candidate for this is an exponential signal, with 3 parameters: e.g. start value, end (steady-state) value, and time constant. The maximum likelihood (ML) equations yield a solution for these too, more accurate than least squares (LS) fitting. Reasonable approximations make the ML problem solvable in practice

Analog-to-Information Conversion with Random Interval Integration

A novel method of analog-to-information conversion—the random interval integration—is proposed and studied in this paper. This method is intended primarily for compressed sensing of aperiodic or quasiperiodic signals acquired by commonly used sensors such as ECG, environmental, and other sensors, the output of which can be modeled by multi-harmonic signals. The main idea of the method is based on input signal integration by a randomly resettable integrator before the AD conversion. The integrator’s reset is controlled by a random sequence generator. The signal reconstruction employs a commonly used algorithm based on the minimalization of a distance norm between the original measurement vector and vector calculated from the reconstructed signal. The signal reconstruction is performed by solving an overdetermined problem, which is considered a state-of-the-art approach. The notable advantage of random interval integration is simple hardware implementation with commonly used components. The performance of the proposed method was evaluated using ECG signals from the MIT-BIH database, multi-sine, and own database of environmental test signals. The proposed method performance is compared to commonly used analog-to-information conversion methods: random sampling, random demodulation, and random modulation pre-integration. A comparison of the mentioned methods is performed by simulation in LabVIEW software. The achieved results suggest that the random interval integration outperforms other single-channel architectures. In certain situations, it can reach the performance of a much-more complex, but commonly used random modulation pre-integrator

ECG Sparsity Evaluation on a Multiwavelet Basis

In this paper, an evaluation of the multiwavelet basis’ capability to represent the ECG signal sparsely was performed. The paper includes the mathematical formulation of sparsity, a brief introduction to the multiwavelet transform, as well as details about the simulation setup used for evaluation. Throughout the paper, various multiwavelets were investigated. The reported results show that the BAT and DB multiwavelets performed well, thus they could be used in the ECG signal sparsification. The investigation also focused on the ECG signals displaying deformations associated with illnesses. Preliminary results suggest that multiwavelets may prove beneficial for diverse processing of ECG signals

Optimization Paradigm in the Signal Recovery after Compressive Sensing

Compressive sensing is a processing approach aiming to reduce the data stream from the observed object with the inherent sparsity using the optimal signal models. The compression of the sparse input signal in time or in the transform domain is performed in the transmitter by the Analog to Information Converter (AIC). The recovery of the compressed signal using optimization based on the differential evolution algorithm is presented in the article as an alternative to the faster pseudoinverse algorithm. Pseudoinverse algorithm results in an unambiguous solution associated with lower compression efficiency. The selection of the mathematically appropriate signal model affects significantly the compression efficiency. On the other hand, the signal model influences the complexity of the algorithm in the receiving block. The suitability of both recovery methods is studied on examples of the signal compression from the passive infrared (PIR) motion sensors or the ECG bioelectric signals