Behavior of Formula for Spectrum of Sampled Signal when Sampling Period Tends to Zero

ABSTRACT: This paper is devoted to consideration of behaviour of two formulas used in the literature to describe the spectra of sampled signals in the case of value of the sampling period going to zero. It is shown here that they do not lead to the same result, as we would expect. Only one of them gives an outcome compatible with reality.

KEYWORDS: Digital Signal Processing (DSP), Signal Sampling, Spectrum of Sampled Signal, Fourier Transform, Weighted Dirac Comb, Step Function Model, Sampling Period Limit, Nyquist Condition

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Citation note:

Borys A.: Behavior of Formula for Spectrum of Sampled Signal when Sampling Period Tends to Zero. TransNav, the International Journal on Marine Navigation and Safety of Sea Transportation, Vol. 19, No. 3, doi:10.12716/1001.19.03.21, pp. 875-877, 2025

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