Inverse eigenvalue problem for sinusoidal frequency estimation

The estimation of the frequencies of sinusoids in noise is a very common problem. This paper addresses the estimation of sinusoids in a low SNR environment. This sinusoidal frequency estimation problem can be used to find the carrier frequencies and baud rates of communication waveforms after some appropriate nonlinearity. If the underlying signal model is sinusoids in white Gaussian noise and we use the forward/backward prediction framework, then the forward/backward prediction equations force a Toeplitz/Hankel structure on the data matrix. If there are M distinct sinusoids in the data and no noise, then the data matrix has rank M. Cadzow and Wilkes (1991) enhance a noisy data matrix by enforcing both the structure and the rank of the data matrix, before solving for the coefficient vector of the prediction problem. Besides the Toeplitz/Hankel structure, the estimated singular values of the data matrix are also enforced. Using more information extracted from the original data matrix extends the threshold to lower SNR values.