We present a new analysis of the frequency-domain block least-mean-square (FBLMS) algorithm. An earlier analysis uses a mapping of the frequency-domain information to the time-domain before proceeding with the analysis of the algorithm. We present a direct analysis of the FBLMS algorithm in the frequency domain. As compared with the previous analysis, the new analysis is easier to follow. It is also more rigorous than the previous works and gives a better insight to the effect of various processing components in the algorithm structure on its convergence behavior. In particular, we show how the transformation of input samples to the frequency domain, combined with the effect of the involved windowing matrices, and step-normalization affect the convergence behavior of both constrained and unconstrained versions of the FBLMS algorithm. We also report a procedure for derivation of misadjustment equations of various versions of the FBLMS algorithm.
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