An orthogonal discrete auditory transform (ODAT) from sound signal to
spectrum is constructed by combining the auditory spreading matrix of
Schroeder et. al. and the time one map of a discrete nonlocal
Schrodinger equation. Thanks to the dispersive smoothing property of
the Schrodinger evolution, ODAT spectrum is a smoother than that of
the discrete Fourier transform (DFT) consistent with human audition.
ODAT and DFT are compared in signal denoising tests with spectral
thresholding method. The signals are noisy speech segments. ODAT
outperforms DFT in signal to noise ratio (SNR) when the noise level
is relatively high.