{"id":14774,"date":"2022-12-24T14:29:07","date_gmt":"2022-12-24T12:29:07","guid":{"rendered":"http:\/\/journals.khnu.km.ua\/vestnik\/?p=14774"},"modified":"2023-02-17T11:54:50","modified_gmt":"2023-02-17T09:54:50","slug":"pobudova-ta-verifikacziya-modeli-czyfrovogo-ekvalajzera","status":"publish","type":"post","link":"https:\/\/journals.khnu.km.ua\/vestnik\/?p=14774","title":{"rendered":"\u041f\u043e\u0431\u0443\u0434\u043e\u0432\u0430 \u0442\u0430 \u0432\u0435\u0440\u0456\u0444\u0456\u043a\u0430\u0446\u0456\u044f \u043c\u043e\u0434\u0435\u043b\u0456 \u0446\u0438\u0444\u0440\u043e\u0432\u043e\u0433\u043e \u0435\u043a\u0432\u0430\u043b\u0430\u0439\u0437\u0435\u0440\u0430"},"content":{"rendered":"


\n\u041f\u041e\u0411\u0423\u0414\u041e\u0412\u0410 \u0422\u0410 \u0412\u0415\u0420\u0406\u0424\u0406\u041a\u0410\u0426\u0406\u042f \u041c\u041e\u0414\u0415\u041b\u0406 \u0426\u0418\u0424\u0420\u041e\u0412\u041e\u0413\u041e \u0415\u041a\u0412\u0410\u041b\u0410\u0419\u0417\u0415\u0420\u0410<\/p>\n

CONSTRUCTION AND VERIFICATION OF A DIGITAL EQUALIZER MODEL<\/p>\n

\u0421\u0442\u043e\u0440\u0456\u043d\u043a\u0438: 178-184. \u041d\u043e\u043c\u0435\u0440: \u21165, 2022 (313)\u00a0\u00a0 <\/strong> \"\"<\/a>
\nDOI:<\/strong> https:\/\/www.doi.org\/10.31891\/2307-5732-2022-313-5-178-184<\/a>
\n\u0410\u0432\u0442\u043e\u0440\u0438: <\/strong>
\n\u041a\u0423\u0414\u041b\u0410\u0419 \u0421\u0432\u044f\u0442\u043e\u0441\u043b\u0430\u0432
\n\u041d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u0442\u0435\u0445\u043d\u0456\u0447\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u0423\u043a\u0440\u0430\u0457\u043d\u0438
\n\u00ab\u041a\u0438\u0457\u0432\u0441\u044c\u043a\u0438\u0439 \u041f\u043e\u043b\u0456\u0442\u0435\u0445\u043d\u0456\u0447\u043d\u0438\u0439 \u0406\u043d\u0441\u0442\u0438\u0442\u0443\u0442 \u0456\u043c\u0435\u043d\u0456 \u0406\u0433\u043e\u0440\u044f \u0421\u0456\u043a\u043e\u0440\u0441\u044c\u043a\u043e\u0433\u043e\u00bb
\nORCID ID: 0000-0003-3972-405\u0425<\/a>
\ne-mail: slava-16@ukr.net
\n\u0411\u041e\u041d\u0414\u0410\u0420\u0415\u041d\u041a\u041e \u041d\u0430\u0442\u0430\u043b\u0456\u044f
\n\u041d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u0442\u0435\u0445\u043d\u0456\u0447\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u0423\u043a\u0440\u0430\u0457\u043d\u0438
\n\u00ab\u041a\u0438\u0457\u0432\u0441\u044c\u043a\u0438\u0439 \u041f\u043e\u043b\u0456\u0442\u0435\u0445\u043d\u0456\u0447\u043d\u0438\u0439 \u0406\u043d\u0441\u0442\u0438\u0442\u0443\u0442 \u0456\u043c\u0435\u043d\u0456 \u0406\u0433\u043e\u0440\u044f \u0421\u0456\u043a\u043e\u0440\u0441\u044c\u043a\u043e\u0433\u043e\u00bb
\nORCID ID: 0000-0002-9237-8187<\/a>
\ne-mail: nalbondarenko@gmail.com
\n\u0411\u041e\u041d\u0414\u0410\u0420\u0415\u041d\u041a\u041e \u0412\u0456\u043a\u0442\u043e\u0440
\n\u041d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u0442\u0435\u0445\u043d\u0456\u0447\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u0423\u043a\u0440\u0430\u0457\u043d\u0438
\n\u00ab\u041a\u0438\u0457\u0432\u0441\u044c\u043a\u0438\u0439 \u041f\u043e\u043b\u0456\u0442\u0435\u0445\u043d\u0456\u0447\u043d\u0438\u0439 \u0406\u043d\u0441\u0442\u0438\u0442\u0443\u0442 \u0456\u043c\u0435\u043d\u0456 \u0406\u0433\u043e\u0440\u044f \u0421\u0456\u043a\u043e\u0440\u0441\u044c\u043a\u043e\u0433\u043e\u00bb
\nORCID: 0000-0003-1663-4799<\/a>
\ne-mail: vicnbondarenko@gmail.com
\nKUDLAI Vladyslav, BONDARENKO Nataliia, BONDARENKO Viktor
\nNational Technical University of Ukraine \u00abIgor Sikorsky Kyiv Polytechnic Institute\u00bb<\/p>\n

\u0410\u043d\u043e\u0442\u0430\u0446\u0456\u044f \u043c\u043e\u0432\u043e\u044e \u043e\u0440\u0438\u0433\u0456\u043d\u0430\u043b\u0443<\/strong><\/p>\n

\u0417\u0430\u043f\u0440\u043e\u043f\u043e\u043d\u043e\u0432\u0430\u043d\u043e \u043f\u0456\u0434\u0445\u0456\u0434 \u0434\u043e \u0440\u043e\u0437\u0440\u043e\u0431\u043a\u0438 \u0435\u043a\u0432\u0430\u043b\u0430\u0439\u0437\u0435\u0440\u0430 \u0448\u043b\u044f\u0445\u043e\u043c \u043f\u043e\u0431\u0443\u0434\u043e\u0432\u0438 \u0439\u043e\u0433\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u043d\u043e\u0457 \u043c\u043e\u0434\u0435\u043b\u0456, \u0437\u0430\u0432\u0434\u044f\u043a\u0438 \u044f\u043a\u0456\u0439 \u0432\u0441\u0456 \u043e\u043f\u0435\u0440\u0430\u0446\u0456\u0457, \u0432 \u0442\u043e\u043c\u0443 \u0447\u0438\u0441\u043b\u0456 \u0440\u043e\u0437\u0440\u0430\u0445\u0443\u043d\u043e\u043a \u044f\u0434\u0440\u0430 \u0435\u043a\u0432\u0430\u043b\u0430\u0439\u0437\u0435\u0440\u0430 \u0442\u0430 \u043e\u0431\u0440\u043e\u0431\u043a\u0430 \u0441\u0438\u0433\u043d\u0430\u043b\u0443, \u0437\u0434\u0456\u0439\u0441\u043d\u044e\u044e\u0442\u044c\u0441\u044f \u0454\u0434\u0438\u043d\u0438\u043c \u043c\u0456\u043a\u0440\u043e\u043a\u043e\u043d\u0442\u0440\u043e\u043b\u0435\u0440\u043e\u043c. \u0420\u043e\u0437\u0440\u0430\u0445\u0443\u043d\u043e\u043a \u044f\u0434\u0440\u0430 \u0437\u0432\u043e\u0434\u0438\u0442\u044c\u0441\u044f \u0434\u043e \u0431\u0430\u0433\u0430\u0442\u043e\u0440\u0430\u0437\u043e\u0432\u043e\u0433\u043e \u0432\u0438\u043a\u043e\u043d\u0430\u043d\u043d\u044f \u0432\u0456\u0434\u043d\u043e\u0441\u043d\u043e \u043f\u0440\u043e\u0441\u0442\u0438\u0445 \u043e\u043f\u0435\u0440\u0430\u0446\u0456\u0439, \u0449\u043e \u0434\u043e\u0437\u0432\u043e\u043b\u044f\u0454 \u0437\u0435\u043a\u043e\u043d\u043e\u043c\u0438\u0442\u0438 \u0447\u0430\u0441 \u0442\u0430 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043d\u0443 \u043f\u0430\u043c\u2019\u044f\u0442\u044c. \u0415\u043a\u0432\u0430\u043b\u0430\u0439\u0437\u0435\u0440 \u0437\u0430\u0431\u0435\u0437\u043f\u0435\u0447\u0443\u0454 \u0437\u0430\u0434\u043e\u0432\u0456\u043b\u044c\u043d\u0443 \u044f\u043a\u0456\u0441\u0442\u044c \u043e\u0431\u0440\u043e\u0431\u043a\u0438 \u043f\u0440\u0438 \u043d\u0435\u0432\u0435\u043b\u0438\u043a\u043e\u043c\u0443 \u043f\u043e\u0440\u044f\u0434\u043a\u0443 \u0444\u0456\u043b\u044c\u0442\u0440\u0430, \u0432 \u044f\u043a\u043e\u0441\u0442\u0456 \u044f\u043a\u043e\u0433\u043e \u043e\u0431\u0440\u0430\u043d\u043e \u0446\u0438\u0444\u0440\u043e\u0432\u0438\u0439 \u0444\u0456\u043b\u044c\u0442\u0440 \u0437 \u043a\u0456\u043d\u0446\u0435\u0432\u043e\u044e \u0456\u043c\u043f\u0443\u043b\u044c\u0441\u043d\u043e\u044e \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043a\u043e\u044e \u0447\u0435\u0440\u0435\u0437 \u0439\u043e\u0433\u043e \u043b\u0456\u043d\u0456\u0439\u043d\u0443 \u0424\u0427\u0425, \u0433\u0430\u0440\u0430\u043d\u0442\u0456\u044e \u0441\u0442\u0430\u0431\u0456\u043b\u044c\u043d\u043e\u0441\u0442\u0456 \u043f\u0440\u0438 \u0441\u043a\u043b\u0430\u0434\u043d\u0456\u0439 \u0410\u0427\u0425, \u0430 \u0442\u0430\u043a\u043e\u0436 \u0432\u043b\u0430\u0441\u0442\u0438\u0432\u0456 \u0439\u043e\u043c\u0443 \u0430\u0441\u043e\u0446\u0456\u0430\u0442\u0438\u0432\u043d\u0456\u0441\u0442\u044c \u0442\u0430 \u043b\u0456\u043d\u0456\u0439\u043d\u0456\u0441\u0442\u044c, \u0449\u043e \u0434\u043e\u0437\u0432\u043e\u043b\u044f\u0454 \u043b\u0435\u0433\u043a\u043e \u0432\u0456\u0434\u0442\u0432\u043e\u0440\u0438\u0442\u0438 \u0441\u043a\u043b\u0430\u0434\u043d\u0443 \u0410\u0427\u0425. \u0421\u0445\u0435\u043c\u043e \u0442\u0435\u0445\u043d\u0456\u0447\u043d\u0430 \u0440\u0435\u0430\u043b\u0456\u0437\u0430\u0446\u0456\u044f \u0431\u0430\u0437\u0443\u0454\u0442\u044c\u0441\u044f \u043d\u0430 \u043f\u0430\u0440\u0430\u043b\u0435\u043b\u044c\u043d\u0438\u0445 \u0441\u043c\u0443\u0433\u043e\u0432\u0438\u0445 \u0444\u0456\u043b\u044c\u0442\u0440\u0430\u0445 \u0442\u0430 \u0444\u0456\u043b\u044c\u0442\u0440\u0456 \u043d\u0438\u0437\u044c\u043a\u0438\u0445 \u0447\u0430\u0441\u0442\u043e\u0442 \u0437 \u043d\u0430\u0441\u0442\u0443\u043f\u043d\u0438\u043c \u0441\u043a\u043b\u0430\u0434\u0430\u043d\u043d\u044f\u043c \u0432\u0456\u0434\u0444\u0456\u043b\u044c\u0442\u0440\u043e\u0432\u0430\u043d\u0438\u0445 \u0442\u0430 \u043f\u0456\u0434\u0441\u0438\u043b\u0435\u043d\u0438\u0445 \u0441\u0438\u0433\u043d\u0430\u043b\u0456\u0432. \u041c\u043e\u0434\u0435\u043b\u044c \u0435\u043a\u0432\u0430\u043b\u0430\u0439\u0437\u0435\u0440\u0430 \u0456 \u044f\u0434\u0440\u043e \u0444\u0456\u043b\u044c\u0442\u0440\u0430 \u043d\u0438\u0437\u044c\u043a\u0438\u0445 \u0447\u0430\u0441\u0442\u043e\u0442 \u0432\u0435\u0440\u0438\u0444\u0456\u043a\u043e\u0432\u0430\u043d\u0456 \u0432 \u0441\u0435\u0440\u0435\u0434\u043e\u0432\u0438\u0449\u0456 GNU Octave. \u0417\u043c\u043e\u0434\u0435\u043b\u044c\u043e\u0432\u0430\u043d\u0435 \u044f\u0434\u0440\u043e \u0435\u043a\u0432\u0430\u043b\u0430\u0439\u0437\u0435\u0440\u0430 \u043f\u043e\u0432\u043d\u0456\u0441\u0442\u044e \u0432\u0456\u0434\u043f\u043e\u0432\u0456\u0434\u0430\u0454 \u0437\u0430\u0434\u0430\u043d\u0456\u0439 \u0410\u0427\u0425, \u0449\u043e \u043f\u0456\u0434\u0442\u0432\u0435\u0440\u0434\u0436\u0443\u0454 \u043f\u0440\u0430\u0446\u0435\u0437\u0434\u0430\u0442\u043d\u0456\u0441\u0442\u044c \u043c\u043e\u0434\u0435\u043b\u0456.
\n\u041a\u043b\u044e\u0447\u043e\u0432\u0456 \u0441\u043b\u043e\u0432\u0430:<\/strong> \u0435\u043a\u0432\u0430\u043b\u0430\u0439\u0437\u0435\u0440, \u0426\u041e\u0421, \u041a\u0406\u0425-\u0444\u0456\u043b\u044c\u0442\u0440, \u0437\u0433\u043e\u0440\u0442\u043a\u0430, \u0424\u0443\u0440\u2019\u0454-\u043e\u0431\u0440\u0430\u0437, \u043c\u043e\u0434\u0435\u043b\u044c, GNU Octave<\/p>\n

\u0420\u043e\u0437\u0448\u0438\u0440\u0435\u043d\u0430 \u0430\u043d\u043e\u0442\u0430\u0446\u0456\u044f \u0430\u043d\u0433\u043b\u0456\u0439\u0441\u044c\u043a\u043e\u044e \u00a0\u043c\u043e\u0432\u043e\u044e<\/strong><\/p>\n

An approach to the development of an equalizer by building its mathematical model based on a microcontroller is proposed.\u00a0 All operations, including signal processing and equalizer kernel calculation, are performed by a single microcontroller. Thanks to the created mathematical model of the equalizer, the calculation of the kernel is reduced to multiple uses of relatively simple operations, which saves time and memory of the program. The equalizer provides satisfactory processing quality at a small filter order which is selected as a digital filter with final impulse response (FIR) because of its linear phase-frequency response, a guarantee of stability at the complex amplitude-frequency response, and also its associativity and linearity allowing it easily reproduce a complex amplitude-frequency response. Schematic implementation is based on parallel bandpass filters and a low-pass filter followed by adding filtered and amplified signals. It is the distributive property of the FIR filter that makes it possible to obtain a new kernel that includes all the amplified ranges by the sum of the corresponding kernel elements, instead of adding amplified ranges. The associativity and linearity of the FIR filter gives the opportunity to easily implement different types of filters on the basis of a low-pass filter, for the calculation of which the cardinal sine function is used together with the window function, which in combination gives qualitative frequency characteristics. The low-pass filter kernel and equalizer model are verified in the GNU Octave environment, which is an open-source analogue of Matlab. The model is checked by setting the frequency response of the test equalizer, and for individual filters the allowable width of the transition band and the maximum value of pulsation in the suppression band are set. \u00a0The low-pass filter kernel is created with an arbitrary cutoff frequency, and the filter consists of 129 elements, which were multiplied by the Kaiser window with a value of parameter equal to 4.5. As a result of verification of the mathematical model in the GNU Octave environment, the width of the transition band and the maximum value of pulsation in the suppression band meet the specified conditions. The simulated equalizer kernel fully corresponds to the specified frequency response. Verification of the mathematical model confirmed its efficiency and compliance of the obtained characteristics of the equalizer with the specified requirements.
\nKeywords<\/strong>: equalizer; DSP; FIR filter; convolution; Fourier image; model; GNU Octave.<\/p>\n

\u041b\u0456\u0442\u0435\u0440\u0430\u0442\u0443\u0440\u0430<\/strong><\/p>\n

    \n
  1. \u0421\u043e\u043b\u043e\u043d\u0438\u043d\u0430 \u0410.\u0418. \u0426\u0438\u0444\u0440\u043e\u0432\u0430\u044f \u043e\u0431\u0440\u0430\u0431\u043e\u0442\u043a\u0430 \u0441\u0438\u0433\u043d\u0430\u043b\u043e\u0432 \u0432 \u0437\u0435\u0440\u043a\u0430\u043b\u0435 MATLAB : \u0443\u0447\u0435\u0431.\u043f\u043e\u0441\u043e\u0431\u0438\u0435. \u0421\u041f\u0431 : \u0411\u0425\u0412-\u041f\u0435\u0442\u0435\u0440\u0431\u0443\u0440\u0433, 2018. 560 \u0441. ISBN: 978-5-9775-3946-3<\/li>\n
  2. \u041a\u0430\u043f\u0438\u0442\u043e\u043d\u043e\u0432 \u0410. \u041e\u0441\u043d\u043e\u0432\u044b \u0446\u0438\u0444\u0440\u043e\u0432\u043e\u0439 \u043e\u0431\u0440\u0430\u0431\u043e\u0442\u043a\u0438 \u0441\u0438\u0433\u043d\u0430\u043b\u043e\u0432 : \u043a\u0443\u0440\u0441 \u043b\u0435\u043a\u0446\u0438\u0439. \u0425\u0430\u0431\u0440., 2019. https:\/\/habr.com\/ru\/post\/460445\/<\/li>\n
  3. V\u00e4lim\u00e4ki V., Reiss J. All About Audio Equalization: Solutions and Frontiers.\u00a0Applied Sciences<\/em>, 2016; 6(5):129. URL: https:\/\/doi.org\/10.3390\/app6050129<\/li>\n
  4. \u0423\u043c\u043d\u044f\u0448\u043a\u0438\u043d \u0421.\u0412. \u041e\u0441\u043d\u043e\u0432\u044b \u0442\u0435\u043e\u0440\u0438\u0438 \u0446\u0438\u0444\u0440\u043e\u0432\u043e\u0439 \u043e\u0431\u0440\u0430\u0431\u043e\u0442\u043a\u0438 \u0441\u0438\u0433\u043d\u0430\u043b\u043e\u0432. \u0418\u0437\u0434. 5-\u0435. \u041c.: \u0422\u0435\u0445\u043d\u043e\u0441\u0444\u0435\u0440\u0430, 2019. 549 \u0441. ISBN 978-5-94836-557-2<\/li>\n
  5. Emmanuel C. Ifeachor, Barrie W. Jervis. Digital Signal Processing: A Practical Approach, 2nd Edition, 2002. ISBN-13:\u00a0978-0201596199<\/li>\n
  6. Oppenheim A., Schafer R. Discrete-Time Signal Processing, 3rd ed. 2014. ISBN-9781292025728 1292025727<\/li>\n
  7. Lyons R. Streamlining Digital Signal Processing (2nd Edition). Monography, Wiley-IEEE Press, 2012. 496 p. ISBN-13:\u00a0978-1-118-27838-3<\/li>\n
  8. Smith S. Digital Signal Processing: A Practical Guide for Engineers and Scientists, 1st \u0435d. 2013. ISBN: \u200e\u00a00080477321, 9780080477329<\/li>\n
  9. Weisstein E. Modified Bessel Function of the First Kind. 2021. URL: https:\/\/mathworld.wolfram.com\/ModifiedBesselFunctionoftheFirstKind.html<\/li>\n
  10. Zhu Y. Embedded Systems with ARM Cortex-M Microcontrollers in AssemblyLanguage and C, Ed. Orono, Maine. 2017. 722 p.<\/li>\n
  11. John W. Eaton David Bateman S\u00f8ren Hauberg Rik Wehbring GNU Octave version 6.3.0: A high-level interactive language for numerical computations, 6th ed., 2021. 1125 p.<\/li>\n<\/ol>\n

    References<\/strong><\/p>\n

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