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.
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