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An orthogonal discrete auditory transform. (English) Zbl 1095.94011

Summary: An orthogonal discrete auditory transform (ODAT) from sound signal to spectrum is constructed by combining the auditory spreading matrix of M. R. Schröder, B. S. Atal and J. L. Hall [Journal Acoust. Soc. America 66, No. 6, 1647–1652 (1979)] and the time one map of a discrete nonlocal Schrödinger equation. Thanks to the dispersive smoothing property of the Schrödinger 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.

MSC:

94A12 Signal theory (characterization, reconstruction, filtering, etc.)
65T99 Numerical methods in Fourier analysis
68P30 Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.) (aspects in computer science)
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