A Kalman filtering approach to short-time Fourier analysis

The problem of estimating time-varying harmonic components of a signal measured in noise is considered. The approach used is via state estimation. Two methods are proposed, one involving pole-placement of a state observer, the other using quadratic optimization techniques. The result is the development of a new class of filters, akin to recursive frequency-sampling filters, for inclusion in a parallel bank to produce sliding harmonic estimates. Kalman filtering theory is applied to effect the good performance in noise, and the class of filters is parameterized by the design tradeoff between noise rejection and convergence rate. These filters can be seen as generalizing the DFT.