The problem of the test signal recovery is urgent during the monitoring of the current state of a dynamical system. Such a signal is usually wideband with respect to frequency, has steep leading and trailing edges, and a short duration in the time domain. Under actual conditions, it should be recovered from a small sample of readouts (measurements) at the system output. In this paper, we propose a method of the signal recovery by the generalized Kotel'nikov series for the subsequent estimation of its parameters in the time and frequency domains. The method is more efficient than the existing signal-recovery methods. Its efficiency is confirmed by the quantitative-analysis results.At present, recovery of a signal whose frequency spectrum is in the interval from −α to α is usually performed using the basis of Kotel'nikov functions. For this, the signal in the time intervalHere, f (kπ/α) are the values of the function f (t) measured at the points kπ/α, where k = 0, ±1, ±2, . . . , ±N . The exact representation of the signal is written asHowever, such a series has the following disadvantages: (i) slow convergence to the approximated function;(ii) the interval between the discrete readout times should not exceed π/α; (iii) for the finite number of the series terms (−N ≤ k ≤ N ), the high-frequency harmonics are predominant in the spectrum of the function f (t) if the values of f (kπ/α) near the boundary points of the interval [−T = −Nπ/α, Nπ/α = T ] significantly exceed the values of f (kπ/α) near the interval center. As a result, the Kotel'nikov-series spectrum becomes strongly oscillatory and, therefore, an analog-digital device and an algorithm for recovery of the function f (t) become more complicated.If the readouts can be performed only with the period ∆ = π/α for α < β, where β is the boundary frequency of the recovered-signal spectrum, then the conditions of the Kotel'nikov-Shannon sampling theorem are not satisfied and use of the Kotel'nikov series becomes unjustified.
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