Recursive Least Squares Spectrum Estimation

This paper presents a unifying basis of Fourier analysis/spectrum estimation and adaptive filters. It begins with the derivation of state-space recursive least squares with rectangular windowing (SSRLSRW). The topics covered are batch processing, recursive algorithm and initialization etc. This is followed by a discussion to track a single tone which is finally extended to the derivation of recursive discrete Fourier transform. The relation between SSRLS and SSRLSRW also provides a mathematical rationale to use resonator banks for spectrum estimation