Two stages of bandwidth scaling drives efficient neural coding of natural sounds
Fig 2
Comparing Fourier and cochlear model filterbanks.
(A) Cochlear filter transfer functions are shown for model filters with best frequency between 0.1–10 kHz (color designates gain in dB). The cochlear filters are logarithmically spaced and have bandwidths that scale with frequency (proportional resolution). They exhibit a sharp high-frequency transition and gradual low frequency transition as observed physiologically for auditory nerve fibers. A subset of the transfer functions is line plotted above. Three selected filters (103.5, 830.0, 6653.5Hz) are shown in different colors and their corresponding time domain impulse responses are shown below. (B) The Fourier filterbank, by comparison, has constant resolution filters (30 Hz bandwidth shown here) that are ordered on a linear scale (shown up to 2kHz for clarity, and part of them are line plotted above, three examples are: 250, 750, 1500Hz). In the time domain, the cochlear filter impulse responses (C) have frequency dependent peak amplitudes and delays and the impulse response durations scale inversely with frequency. For visualization purposes and to allow for ease of comparison the impulse response line plots for the three examples are normalized to a constant peak amplitude (C, top). The Fourier filterbank filters, by comparison, have constant duration and are designed for zero delay (D). (E) shows the time (Δt) and frequency (Δf) resolution of the cochlear (colored circles) and three distinct Fourier filterbanks (+ symbols show Δf = 30 Hz, 120 Hz, and 480 Hz). The dotted line represents the uncertainty principle boundary. Although the Fourier filterbanks are represented by a single point and fall on the uncertainty principle boundary, the time-frequency resolution of the cochlear filters is frequency dependent (colored circles).