A.V. Bogoslovsky − Honored Scientist of the Russian Federation, Dr.Sc. (Eng.), Professor, 

Department «Radioelectronic», MESC AF «N.E. Zhukovsky and Y.A. Gagarin Air Force Academy» (Voronezh) E-mail: p-digim@mail.ru

I.V. Zhigulina − Ph.D. (Eng.), Associate Professor, Professor of the Department «Mathematics»,  MESC AF «N.E. Zhukovsky and Y.A. Gagarin Air Force Academy» (Voronezh) E-mail: ira_zhigulina@mail.ru

Compared to the amplitude-frequency spectrum, the phase-frequency spectrum receives much less attention while processing signals. The appearance of the phase-frequency spectrum is different in numerous publications, which makes it difficult to apply. The purpose of this article is to refine the algorithm for constructing the phase-frequency spectrum taking into account the properties of its defining functions.

The changes in the phase-frequency spectrum as an arctangent function for the series, integral, and coordinate-discretized Fourier transform have been analyzed.

In the Fourier series, to find the phase-frequency spectrum, it is necessary to analyze the signs of the series coefficients, and the coefficient at the sine must be considered with the opposite sign. Analytical expressions for finding the phase-frequency spectrum are refined and examples of finding it for several sequences of video pulses are given.

It is shown that to find phase-frequency spectrum discretized by the coordinate of the Fourier transform, the signs of the real and imaginary components of the spectrum need to be analyzed.

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