Sampling of frequency-modulated signals

Most of the digital signal processing methods is based on the Whittaker-Nyquist-Shannon-Kotelnicov (WNSK) theorem and uniform time samples. But non-uniform samples may be more preferable in some cases. The generalization of the WNSK theorem allows us to process a frequency modulated signal using non-uniform time samples. This paper shows one of the possible generalizations of the sampling theorem by a change of variable. It is shown that it is possible to use non-equidistant samples for efficient processing of frequency modulated signals. Also the relationship between the spectrum of uniform signal samples and the spectrum of non-uniform signal ones is presented. The linear frequency-modulated signal is discussed as an example of using the described approach.