  Many audio applications rely on filter banks (FBs) to analyze, process, and
re-synthesize sounds. To approximate the auditory frequency resolution in the
signal chain, some applications rely on perceptually motivated FBs, the
gammatone FB being a popular example. However, most perceptually motivated FBs
only allow partial signal reconstruction at high redundancies and/or do not
have good resistance to sub-channel processing. This paper introduces an
oversampled perceptually motivated FB enabling perfect reconstruction,
efficient FB design, and adaptable redundancy. The filters are directly
constructed in the frequency domain and linearly distributed on a perceptual
frequency scale (e.g. ERB, Bark, or Mel scale). The proposed design allows for
various filter shapes, uniform or non-uniform FB setting, and large
down-sampling factors. For redundancies $\geq$ 3 perfect reconstruction is
achieved by computing the canonical dual FB analytically. For lower
redundancies perfect reconstruction is achieved using an iterative method.
Experiments show performance improvements of the proposed approach when
compared to the gammatone FB in terms of reconstruction error and resistance to
sub-channel processing, especially at low redundancies.
