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A Generalized Method for Fractional-Octave Smoothing of Transfer Functions that Preserves Log-Frequency Symmetry

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Spectral smoothing is a standard operation in many fields of audio. It reduces the often overwhelming detail of high-resolution spectra to the relevant information. A method is presented for fractional-octave smoothing that preserves symmetry after smoothing for spectra that were originally symmetric in log-frequency. While existing methods require interpolation of the FFT spectra to a log-frequency scale, the proposed method uses an analytically-derived smoothing window and operates directly in the FFT domain. This approach retains compatibility with the well-established spectral smoothing techniques such as complex smoothing. The proposed method is compared with two existing methods. The first uses a symmetric (on a linear scale) smoothing window, which exhibits the correct bandwidths but does not span the correct fractional-octave frequency ranges. The second interpolates the spectrum to logarithmically-spaced frequencies and then uses a symmetric fixed-width smoothing window. Results show that the proposed method achieves nearly identical smoothed spectra to the second method, but without the need for interpolation, and that the first method indeed skews the log-symmetry of the original spectra.

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JAES Volume 65 Issue 3 pp. 239-245; March 2017
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AES - Audio Engineering Society