A broad-band digital spectrum analyzer based on a random asynchronous sampling strategy

This paper describes a spectrum analyzer based on a random asynchronous sampling strategy, previously introduced by the authors, whose bandwidth limitation is due uniquely to the bandwidth of the Sample/Hold circuit. The properties of the proposed estimate of each spectral component based on the discretization of the Fourier series, are deduced by considering the statistical parameters of the output. In order to obtain a result independent from the generic measurement occasion, the asymptotic expected value is deduced; however this last results null. In order to overcome this cumbersome, each estimate of the spectral components is normalized with respect to the fundamental frequency. In the paper it is shown that the mean value of this new parameter is independent from the measurement occasion if the number of samples is sufficiently great; besides it is characterized by a bias which depends on the approximation of the estimated fundamental frequency of the signal with respect to its true value. At last a procedure to estimate the fundamental frequency is proposed.