A multitone pseudocascade, filtered-X LMS adaptive notch filter

A filtered-X version of the LMS notch filter (FXLMS) is useful for narrowband applications where the cancelling signal cannot be directly applied to the primary signal. However, cancellation path delay limits the bandwidth performance of the filter. A cascade of FXLMS notch filters using multiple reference tones is examined for alleviating this problem. An analysis of a single-stage notch filter characterizes the response by the cancellation bandwidth and out-of-band overshoot. The results are used to synthesize a multistage cascade with offset reference tones. A pseudocascade configuration that only requires one entry point to the primary disturbance plant is also formulated. Numerical results for a three-stage FXLMS notch filter are given. Results are also presented for the cascade transient response, overshoot compensation, and extension to the multichannel case