Comparative analysis of interpolation methods in evaluation of the frequency of a discretized harmonic signal

DOI: 10.34759/trd-2023-130-15

Аuthors

Alrubei M. A.

State University named after Alexander and Nikolay Stoletovs, 87, Gorky str. Vladimir, 600000, Russia

e-mail: inj.moh3@atu.edu.iq

Abstract

Accurate and efficient signal frequency measurement is an important signal processing task in many technical applications, such as radio electronics and communication systems, modern information transmission systems, research and medical, radio navigation and radar systems, monitoring of electronic equipment. Stand-alone frequency counters use discrete counting and interpolation methods, while embedded control systems employ spectral analysis methods using fast Fourier transform (FFT) with the largest spectral component determination and interpolation along two or three spectral lines.

The article considers the effect of additive stationary noise on the estimate of a periodic signal frequency from the spectrum obtained by the direct Fourier transform application to an array of discrete samples, that is, during transition from the time domain to the frequency domain. Frequency estimation methods may be divided into the groups of signal representation in both time and frequency domains. Discrete counting and interpolation methods are most widely used in the time domain, as well as in the frequency spectral analysis using FFT algorithms for maximum spectral component determining and successive maximum coordinate correcting using mathematical transformations, such as interpolation. To reduce the effect of spectral leakage or spectrum deviation, time sequence smoothing is used through multiplying all signal samples by window function weights. The interpolation algorithms being used were modeled, and a modified formula that allows accuracy increasing of the frequency estimate by several fold was proposed.

The interpolation method is the most widely used, in-depth and most wide-spread correction method in the analysis of a discrete spectrum with error estimates depending on the number of samples and the number of spectral lines accounted for. In practical engineering applications, the most important indicators for the quality assessing of an algorithm are the ability to work in noise, speed, and low frequency estimation error.

Based on a brief review of the state of theoretical research and development of interpolation methods for correcting the maximum sample position, the principles and characteristics of the interpolation algorithms currently used are presented. Characteristics of each algorithm are examined by simulation and interpolation errors are analyzed.

Keywords:

frequency measurement methods, interpolation method, fast Fourier transform, algorithm, frequency estimation, window function

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