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A method for accurate and efficient parameter estimation and decomposition of sinusoidally frequency modulated signals is presented. These kinds of signals are of special interest in radars and communications. The proposed method is based on the inverse Radon transform property to transform a two-dimensional sinusoidal pattern into a single point in a two-dimensional plane. Since the signal is well concentrated (sparse) in the inverse Radon transform domain, its reconstruction can be performed from a reduced set of observations (back-projections). Theory is illustrated on signals with one and more components, including noise and disturbances, as well as time-frequency patterns that deviate from sinusoidal form.

The method for detection of complex sinusoids in additive white Gaussian noise and estimation of their frequencies is proposed. It contains two stages: 1) sinusoid detection (model order estimation) and coarse frequency estimation, and 2) fine frequency estimation. The proposed method operates in the frequency domain, i.e., it uses the discrete Fourier transform (DFT) as the main tool. Sinusoid detection is performed so that a fixed probability of false alarm is provided (Neymann-Pearson criterion). For both coarse and fine frequency estimations, the three-point periodogram maximization approach is used. Simulations are carried out for variable signal-to-noise ratio, variable frequency displacement between the sinusoids and variable offset from the frequency grid. The proposed method meets the Cramér-Rao lower bound in frequency estimation and practically does not depend on the frequency displacement except for very small displacement values. In terms of model order estimation accuracy, it outperforms the state-of-the-art approaches. The most expensive operation in the method is the calculation of the DFT. Therefore, in terms of calculation complexity, the proposed method is on par with the most efficient algorithms for multiple frequency estimations. INDEX TERMS Cramér-Rao lower bound, discrete Fourier transform, model order estimation, multiple frequency estimation, Neymann-Pearson criterion.

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