The authors propose a rapidly converging adaptive spectral analyzer that uses different algorithms for the weight and frequency updates. There is a modest increase in computational complexity, due to the greater complexity of the RLS (recursive-least-square) algorithm compared to the LMS (least-mean-square) adaptive algorithm. In cascaded adaptive algorithms, the first adaptive algorithm should converge faster to guarantee convergence of the second adaptive algorithm. However, using slower converging LMS-type algorithms for both does not guarantee this. The concept of cascading two adaptive algorithms has also been used in other adaptive algorithms for spectral estimation based on recursive-prediction error-parameter-estimation algorithms, but they are more computationally expensive and are modeled differently.
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