Digitalization of Spectral Measurements in the Fourier Basis – Development Trends and Problems

At the present stage of development of digital information technologies intensive digitalization (computerization) of both direct and indirect measurement methods is taking place. The direct consequence of the computerization of measurements was, firstly, the emergence of a new class of measuring instruments – Processor measuring instruments (PRIS), secondly, increasing the level of formalization of measuring procedures, thirdly, the creation of a new, revolutionary technology –Virtual Instrument (VI). The purpose of the article is to analyze the development of digital technologies for measuring spectra, identifying the problems that arise in this case and formulating priority scientific and applied problems for their resolution.

Theoretical and applied research has established that digital spectrum measurement technologies, in addition to significant advantages, have certain disadvantages. It has been shown that the disadvantages of digital technologies for measuring spectra arise both from the nature of digital methods and from the analytical and stochastic properties of the bases of the applied transformations in measuring the spectra. An analysis of digital methods for measuring spectra showed that methods based on Discrete Fourier Transform (DFT) retain their leading role and are effective in almost all subject areas. However, there are also problems of digitalization of measurements of the spectra of signals based on the DFT, which are associated, first of all, with the manifestation of a number of negative effects that are absent with analog methods for measuring spectra based on the Fourier transform. This is the periodization effect of the measuring signal and its spectrum, the stockade effect, as well as the aliasing effect. As the analysis showed, existing methods of dealing with the negative effects of digitalization of spectrum measurements solve the problems of introducing digital technologies only partially. To combat the negative effects of digitalization of spectral measurements, a generalization of the DFT in the form of a parametric DFT (DFT-P) (Parametric Discrete Fourier Transform – DFT-P) is proposed.

The main scientific and applied problems of computerization of signal spectrum measurements are formulated: the development of the theory of digital methods for measuring signal spectra, the creation of new and improvement of existing digital methods for measuring signal spectra, the development of algorithmic, software and metrological software for PRIS and VI for the implementation of DFT-P.

1. Cooley J., Tukey J. An Algorithm for the Machine Calculation of Complex Fourier Series. Math. Comput., 1965, vol. 19, no. 90, pp. 297–301. DOI: 10.2307/2003354

2. Oppenheim A.V., Schafer R.W. Discrete-Time Signal Processing. Prentice-Hall, Englewood Cliffs, New Jersey, 2009, p. 1120.

3. Sumathi S., Surekha P. LabVIEW based Advanced Instrumentation Systems. Springer, 2007, 728 p.

4. Bress T. Effective Labview Programming. New York: NTC Press, 2013, 720 p.

5. Folea S. LabVIEW - Practical Applications and Solutions. InTech, 2011, 472 p.

6. Richard G. Lyons. Understanding Digital Signal Processing (3rd Edition) 3rd Edition. Prentice-Hall, 2010, 210 p.

7. Finkelstajn L. [The science of measurements: analysis of the state and directions of development]. Datchiki i sistemy [Sensors and systems], 2010, no. 2, pp. 53–57 (in Russian).

8. Yaroslavsky L.P. Compression, restoration, resampling, ‘compressive sensing’ fast transforms in digital imaging. Journal of Optics, 2015, vol. 17, no. 7, p. 073001.

9. Favorskaya M.N., Jain L.C. Development of mathematical theory in computer vision. Intelligent Systems Reference Library, 2015, vol. 73, pp. 1–8. DOI: 10.1007/978-3-319-10653-3_1

10. Gonzalez R.C., Woods R.E. Digital Image Processing. 4th Ed. Published by Pearson, 2018, 1168 p.

11. Hanyan G.S. [Analytical research and error estimation in the problem of measuring the parameters of a harmonic signal by the Fourier transform]. Izmeritel'naya tekhnika [Measuring technique], 2003, no. 8, pp. 3–10 (in Russian).

12. Petrovsky N.A., Rybenkov E.V., Petrovsky A.A. Two-dimensional non-separable quaternionic paraunitary filter banks. IEEE Int. conf. on Signal Processing: Algorighms, Architectures, Arrangements, and Applica- tions, Poznan, Poland, 2018, pp. 120–125. DOI: 10.23919/SPA.2018.8563311

13. Cvetkov E.I. Protsessornye izmeritel'nye sred- stva [Processor measuring tools]. Leningrad, Energoato- mizdat Publ., 1989, 224 p.

14. Cvetkov E.I. Osnovy matematicheskoj metrologii [Fundamentals of Mathematical Metrology]. Saint-Peters- burg, Politekhnika Publ., 2005, 510 p.

15. Melent'ev V.S., Batishchev V.I. Аpproksimatsionnye metody i sistemy izmereniya i kontrolya parametrov periodicheskikh signalov [Approximation methods and systems for measuring and controlling the parameters of periodic signals]. Moscow, Fizmatlit Publ., 2011, 240 p.

16. Prokhorov S.A. Orthogonal models of structure functions. Optoelectronics, Instrumentation and Data Processing, 2011, vol. 47, no. 1, pp. 39–46. DOI: 10.3103/S8756699011010067

17. John W. Multidimtnsional signal, image, and video processing and coding. Academic Press is imprint of Elsevier, 2006.

18. Ponomareva O., Ponomarev A., Ponomarev V. Evolution of forward and inverse discrete fourier transform. IEEE East-West Design & Test Symp., 2018, pp. 313–318. DOI: 10.1109/EWDTS.2018.8524820

19. Ponomarev V.A., Ponomareva O.V., Ponomarev A.V. Method for Effective Measurement of a Sliding Parametric Fourier Spectrum. Optoelectronics, Instrumentation and Data Processing, 2014, vol. 50, iss. 2, pp. 132–138. DOI: 10.3103/S8756699014020046

20. Ponomarev V.A., Ponomareva O.V. Invariance of the current energy Fourier spectrum of complex discrete signals at finite intervals. News of higher educational institutions of Russia. Radio electronics, 2014, no. 2, pp. 8–16 (in Russian).

21. Ponomarev V.A., Ponomareva O.V. Trends in the development of discrete indirect measurements of the parameters of electrical signals. Metrology, 2017, no. 1, pp. 20–32 (in Russian).