  A discrete auditory transform (DAT) from sound signal to spectrum is
presented and shown to be invertible in closed form. The transform preserves
energy, and its spectrum is smoother than that of the discrete Fourier
transform (DFT) consistent with human audition. DAT and DFT are compared in
signal denoising tests with spectral thresholding method. The signals are noisy
speech segments. It is found that DAT can gain 5 to 7 decibel (dB) in signal to
noise ratio (SNR) over DFT except when the noise level is relatively low.
