On the connection between matrix notch filter and maximum likelihood estimation of sinusoidal parameters

In this paper we consider the problem of notch filtering of short data records to remove interference. We show that the recently proposed cascaded matrix notch filtering method of Tseng and Lee is, for real-valued data, approximately the same as subtracting the maximum likelihood estimate of the interfering sinusoid; in the case of complex data, the equivalence is exact. Furthermore, we show that the well-known technique of forward-backward filtering can be used for effective interference suppression, whose computational burden does not increase with data length (unlike in conventional matrix filter methods).