Beating the nyquist limit by utilizing samples of filtered sinisoids

Estimating the frequencies of a number of sinusoids in a signal is considered. It is shown that by passing the signal x(t) through a continuous-time filter f(s) to obtain the filtered signal xit), we can obtain the required frequencies fi-om the eigenvalues of the matrix product my', where X and X, are formed from samples of x and x) respectivel., The result of this paper is a generalization of previous work by the author where xf was the derivative (or integration) of x, i.e. the filter was a differentiator (or integrator). There are two positive points for using a continuous filter instead of a differentiator/integrator: 1relaxing the practical concerns of designing the differentiator/integrator, and 2having some freedom in designing the filter so that attenuation of the noise in the signal is possible especially if the noise spectrum is outside the band of frequencies of interest.