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Algorithm for calculating the normalized time-frequency correlation function
Abstract.The problem of the normalization of frequency-time correlation functions is considered and solved. The aim of the work is to create a methodology for calculating the coefficients for normalizing the time-frequency correlation functions and integrating them into the known computational algorithm. At the same time, the tasks were to ensure the possibility of normalizing each frequency component of the time-frequency correlation function independently and maintaining high performance of the original algorithm. The latter imposed restrictions on the application of the filtering operation in the time domain and the use of additional discrete Fourier transforms in the algorithm. To minimize the computational costs in calculating and rationing the time-frequency correlation functions, a technique was developed for calculating the normalizing coefficients from the samples of the complex signal spectrum. The main result of the work is a new algorithm for calculating the normalized time-frequency correlation function, which differs by an insignificant increase in computational complexity in comparison with the original algorithm. At the same time, the coefficients obtained can be used both for simultaneous normalization of all the frequency components of the time-frequency correlation function, which is necessary to ensure the independence of the result from the scale of the input signals, and for independent normalization of each of its frequency components. The latter is useful in solving problems of detecting weak correlated components in signal mixtures.
Keywords: computational scheme, correlator, normalization, spectral analysis, digital signal processing, correlation functions, time-frequency analysis, fast Fourier transform, signal detection, correlogram
Article was received:25-10-2017
This article written in Russian. You can find full text of article in Russian here .