A classical problem in engineering is to estimate frequencies and amplitudes of sinusoids in data corrupted by noise. This problem arises in different fields like economics, medicine, seismology, energy conversion, and control systems. Fast Fourier Transform (FFT), a deterministic method, is the most commonly used method to obtain frequency contents of data. However, in the presence of noise FFT does not yield reliable estimates of the amplitudes and frequencies of sinusoids. This book presents stochastic methods to solve the sinusoid estimation problem. The main advantage of the methods presented here is the convergence of the estimated spectrum to the point spectrum of the sinusoids. The convergence property is especially useful at the analysis stage because the artifacts due to noise process disappear with convergence of the spectrum. This helps interpreting the spectrum of a process corrupted by noise with unknown properties. The uses of the methods presented are illustrated on examples from structural vibration analysis.

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