Low-Complexity Three-Channel Variable Filter-Bank Using Coefficient-Symmetries

Our previous work has shown that a three-channel (3-channel) variable filter-bank (VFB) can be successfully applied for compensating various hearing loss patterns (audiograms) with high-accuracy. The 3-channel VFB consists of variable lowpass, variable bandpass, and variable highpass digital filters that are transformed from a normalized analog prototype Chebyshev type-I lowpass filter. Since both the magnitudes (gains) and band edge frequencies of the three variable digital filters are independently adjustable, the 3-channel VFB is considerably flexible for achieving high-accuracy audiogram fitting. The objective of this paper is to reveal and theoretically prove the numerator coefficient-symmetries of the three variable filters, and show that each variable filter requires only one multiplication for its numerator filtering operations, so the total number of multiplications can be significantly reduced, which facilitates high-speed audiogram fitting and low-power implementation.