Adaptive octave filter bank with adaptive magnitude and phase

The theory and performance of an adaptive octave filter bank is examined. This filter structure is derived from the discrete cosine transform filter, which is itself a generalization of the frequency sampling filter that includes phase. In previous work, the bandpass filters were uniformly spaced in frequency. In this paper, the bandpasses are octavely space in frequency. The previous work resulted in a discrete cosine transform filter that is realized as an FIR filter as the cascade of an all-zero FIR filter with a bank of IIR digital resonators. In this paper, a similar result occurs, although the complexity is increased. In both the previous uniform filter bank and the present octave bank, each bandpass filter has an adaptive magnitude and an adaptive phase. The result of such a realization is that each coefficient can be directly identified with an amplitude or a phase of the transfer function at a particular frequency when run as an adaptive filter. The update method examined is the LMS algorithm, with the coefficients being adapted as the magnitudes and phases at a full range of frequencies.