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The hybrid filterbank architecture permits implementing accurate, high speed analog-to-digital converters. However, its design requires an accurate knowledge of the analog filterbank parameters, which is difficult to have due to the nonstationary nature of these parameters. This paper proposes a blind estimation method for the analog filterbank parameters, which is able to cope with nonstationary input signals. This is achieved by using the notion of averaged input spectrum. The estimated parameters are used to reconstruct the samples in a least mean squares (LMS) sense. The proposed LMS design generalizes existing approaches by dropping the bandlimited assumption on the input signal. Instead, it assumes that the input has an arbitrary power spectrum which is adaptively estimated. Numerical experiments are presented showing the good performance of the blind estimation stage and the clear advantage of the proposed LMS design.