Stochastic Digital Measurement Method and Its Application in Signal Processing

Classical measurement approach is often described as a process of discretizing an analogue signal in order to easily process it in some type of digital signal processor. Although this approach has been considered to be universally applicable, practical experience has shown that some signals (e.g. fast and/or noisy signals) cannot be always precisely measured. To overcome this problem, in the late 1990s, a new measurement approach called stochastic digital measurement method (SDMM) was presented. At the beginning, this method was intended for high-precision measurements of the integral (the mean value) of a product of two signals. However, in the late 2000s, it was shown that SDMM can be used to compute the Discrete Fourier Transform (DFT). Compared to the classical DFT/FFT processors, SDMM-based ones have two important advantages: first, they are much simpler and cheaper to implement, and second, they allow us to compute individual DFT components either in isolation or in parallel. This chapter is a review of the evolution of SDMM with a special emphasis on a two-bit SDMM. Topics covered include: theoretical foundations of SDMM, the architecture of SDMM-DFT processor and an example of prototype instrument used in power grid networks.This is the peer-reviewed version of the chapter: Radonjić, A., Sovilj, P., Đorđević Kozarov, J., Vujičić, V., 2019. Stochastic Digital Measurement Method and Its Application in Signal Processing, in: Advances in Engineering Research. Volume 27. Nova Science Publishers, Hauppauge, pp. 169–190. ISBN 978-1-5361-4803-

Measurement in Fourier domain – a Natural Method of Big Data Volume Reduction

The paper presents an idea of a measurement in a Fourier domain by a means stochastic digital measurement method (SDMM) as a natural and logical way to reduce the amount of big data in for processing in real time. The measurement method is explained and its application to the power and energy measurements in the power grid is briefly described

Stochastic measurement of noise true RMS using two-bit flash A/D converters

U ovom radu je predstavljena primjena pristupa stohastičkog mjerenja u mjerenju efektivne vrijednosti i snage šuma. Struktura instrumenta je zasnovana na dva dvo-bitna flash analogno-digitalna (A/D) konvertora, na čije ulaze se dovodi diterovani šum, i na akumulaciji proizvoda konvertorskih izlaza. Izvedeni su novi teorijski izrazi za predviđanje rezultata mjerenja i mjerne nesigurnosti, koji uključuju stohastičku prirodu ulaznih signala. Ekstenzivne simulacije i eksperimenti dokazuju validnost predložene metode i njenu nisku mjernu nesigurnost, čak i pri relativno niskoj frekvenciji uzorkovanja. Ovo ukazuje da je prikazani instrument, osim za opću primjenu u mjerenju šuma, pogodan i za detekciju kemijskih i bioloških tvari, zasnovanu na upotrebi grafenskih senzora.The paper presents an application of the stochastic measurement approach for true RMS and power of noise. The instrument structure is based on two 2-bit flash analog-to-digital (A/D) converters whose inputs are the dithered noise, and on accumulation of the product of the converters’ outputs. New theoretical expressions for predicting measurement result and measurement uncertainty, with inclusion of input signal’s stochastic nature, are derived. Extensive simulations and experiments prove the validity of the proposed method and its low measurement uncertainty, even at a relatively low sampling rate. These indicate that, beside general applications for noise measurements, the instrument is suitable for chemical and biological substances detection that utilizes graphene sensors

REDUCTION OF GIBBS PHENOMENON IN EOG SIGNAL MEASUREMENT USING THE MODIFIED DIGITAL STOCHASTIC MEASUREMENT METHOD

The method of digital stochastic measurement is based on stochastic analog-to-digital conversion, with a low-resolution A/D converters and accumulation. This method has been mainly tested and used for the measurement of stationary signals. This paper presents, analyses and discusses a simulation model development for an example of electrooculography (EOG) signal measurement in the time domain. Tests were carried out without adding a noise, and with adding a noise with various level of signal-to-noise ratio. For these values of signal-to-noise ratio, the mean and maximal relative errors are calculated and the significant influence of Gibbs phenomenon is noticed. In order to eliminate Gibbs phenomenon and decrease measurement error, a modified stochastic digital measurement method with overlapping measurement intervals has been developed and applied. On the basis of obtained results, the possibility of design and realization of an instrument with sufficient accuracy benefiting from the hardware simplicity of the method has been formulated. Also, the idea for the future research for developing a simulation model with a lower sampling frequency and implementing the proposed method is outlined

Optimal resolution of stochastic embedid systems

U radu se elabolira primena stohastičke digitalne merne metode (SDMM) u embedid sistemima. U literaturi je dokazano da je optimalna rezolucija SDMM trobitna i da je optimalni brojni sistem za primenu u obradi takođe trobitni. Ove činjenice su motivisale autore da analiziraju optimalne rezolucije stohastičke A/D konverzije, stohastičke obrade i stohastičke D/A konverzije.The paper elaborates the application of stochastic digital measurement method (SDMM) in embedded systems. It has been proven in the literature that the optimal SDMM resolution is three-bit and that the optimal number system for application in signal processing is also three-bit. These facts motivated the authors to analyze the optimal resolutions of stochastic A/D conversion, stochastic processing, and stochastic D/A conversion

Preliminary design of analog discrete uniform noise generator

U radu ce predlaže ideja generatora analognog diskretnog uniformnog šuma (GADUŠ) za primenu u stohastičkoj digitalnoj mernoj metodi. Predloženim rešenjem, za razliku od standardnog, koje koristi generator slučajnih brojeva i precizni i tačni digitalno-analogni konvertor (DAK), se prevazilazi problem ograničene rezolucije DAK-a i njegov uzak propusni opseg.The paper proposes the idea of an analog discrete uniform noise generator for application in the stochastic digital measurement method. The proposed solution, unlike the standard one, which uses a random number generator and a precise and accurate digital-to-analog converter (DAK), overcomes the problem of limited DAK resolution and its narrow bandwidth

Stochastic two-bit on-line temperature measurement with RTD Pt-100 sensor operating in a nonlinear mode

The paper proposes a method and device for on-line temperature measurement with Pt-100 sensor operating in a nonlinear mode. The sensor measures the temperature in range of 00C to 2000C, whereas the measured data are processed by applying a two-bit stochastic digital measurement method. The proposal is theoretically analyzed and tested experimentally. It is shown that the accuracy of the method depends on the accuracy of the sensor. At a sampling frequency of 1 MHz, the maximum accuracy is reached in 17.5 sec. and is equal to 0.015% of full scale (FS). On the other hand, when the measurement time interval is 0.1 sec. (the shortest measurement interval), the accuracy is equal to 0.1% of FS. Therefore, the proposed device can be used for both calibration and measurement purposes

A BRIEF OVERVIEW OF STOCHASTIC INSTRUMENTS FOR MEASURING FLOWS OF ELECTRICAL POWER AND ENERGY

This paper gives a brief overview of three instruments suitable for measuring the flow of electrical power and energy. The first instrument is a single-phase power analyzer, while the other two instruments are double and quadruple three-phase power analyzers. In addition to overviewing these instruments, the paper presents a possible improvement of a quadruple three-phase power analyzer. The implementation of this improvement would make it possible to use a quadruple three-phase power analyzer as support for the phasor measurement unit

Null detection using low resolution A/D converter

U tezi je rešavan centralni problem – detekcija nule dvobitnom stohastičkom digitalnom mernom metodom (SDMM). Formulisane su dve metode detekcije nule primenom dvobitne SDMM. Po prvoj metodi dinamička rezerva je oko 100 dB a po drugoj ne manje od 160 dB. Obe metode su proverene teorijski, simulaciono i eksperimentalno. Pored rešenja centralnog problema, dato je i nekoliko rešenja problema koji su sa njim vezani. Hipoteza ove teze – „dvobitna SDMM je u opsegu 0 % - 10% FS bolja od standardne sempling metode (SSM)“ – je potpuno potvrđena u svim razmatranim slučajevima.The main goal of this thesis was null-detection using a two-bit stochastic digital measurement method (SDMM). Two methods of null-detection, using two-bit SDMM, were formulated. Using the first method around 100 dB of dynamic reserve was achieved and using the second one no less than 160 dB. Both methods were theoretically, using simulation and experimentally confirmed. In addition to the solution of the main problem, several other related problems were also solved. The hypothesis of this thesis – “two-bit SDMM in range from 0 % - 10 % FS is better than the standard sampling method (SSM)” has been fully confirmed in all considered cases

Theory of the Real Integrated Harmonic Instrument

Jedan od najvažnijih parametara kvaliteta električne energije u distributivnoj mreži je harmonijski sastav naponskih i strujnih signala. U disertaciji je razmatrano integrisano merilo harmonika, na principu stohastičke rezonance. Uopštenje postojećeg teorijskog modela rada merila, ostvareno je ukidanjem pojedinih pretpostavki o idealizovanim uslovima rada: idealni intervali merenja, poznata i nepromenljiva osnovna učestanost, idelane diterske sekvence. Na osnovu teorijske analize, simulacija i praktičnih merenja, date su procene reda veličine za svaku od navedenih grešaka. Na kraju je dato šest preporuka za modifikaciju hardvera i načine obrade rezultata merenja, koje mogu značajno poboljšati metrološke performanse budućih generacija ovih merila.One of the most important power quality indicators in power grids is the harmonic composition of voltage and current signals. In this thesis an integrated harmonic instrument has been considered, which operates on the principle of the stochastic resonance. Generalization of the existing theoretical model of the instrument was realized by terminating several idealistic assumptions: perfect measurement intervals, known and stable fundamental frequency, ideal dithering sequences. Based on the performed theoretical analysis, simulations and practical measurements, estimates have been given for each of the measurement error sources. Finally, six recommendations were given for the modification of the hardware and the results processing in order to achieve significantly better metrological performances in future generations of this instrument