  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 Schr\"odinger equation.
Thanks to the dispersive smoothing property of the Schr\"odinger evolution,
ODAT spectrum is 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.
