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 3 to 5 decibel (dB) in signal to noise ratio (SNR) over DFT except when the noise level is relatively low.
"An Invertible Discrete Auditory Transform." Commun. Math. Sci. 3 (1) 47 - 56, March 2005.