#### Nonuniform Spectral Resampling

Recall sinc interpolation of a discrete-time signal [270]:*interpolation kernel*that is sampled where needed to satisfy the needs of the inner product operation. In the time domain, our interpolation kernel is a scaled sinc function, while in the frequency domain, it is an asinc function. The interpolation kernel can of course be horizontally

*scaled*to alter bandwidth [270], or more generally

*reshaped*to introduce a more general

*windowing*in the opposite domain:

- Width of interpolation kernel (main-lobe width) 1/width-in-other-domain
- Shape of interpolation kernel gain profile (window) in other domain

*interpolation kernel*for nonuniformly resampling the STFT frequency axis. In other words, an auditory filter bank may be implemented as a non-uniform resampling of the uniformly sampled frequency axis provided by an ordinary FFT, using the auditory filter shape as the interpolation kernel. When the auditory filters vary systematically with frequency, there may be an equivalent

*non-uniform frequency-warping*followed by a

*uniform sampling*of the (warped) frequency axis. Thus, an alternative implementation of an auditory filter bank is to apply an FFT (implementing a uniform filter bank) to a signal having a properly

*prewarped spectrum*, where the warping is designed to approximate whatever auditory frequency axis is desired. This approach is discussed further in Appendix E. (See also §2.5.2.)

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Auditory Filter Shapes

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Excitation Pattern