Music Signals by Deconvolution of Log-Frequency Spectrum

Graduate School of Information Science and Technology,

The University of Tokyo, Japan

E-mail: `{sagayama,takahashi,kameoka,nishi}@hil.t.u-tokyo.ac.jp`

In this paper, we propose a new signal processing technique, ``specmurt
anasylis,'' that provides piano-roll-like visual display of multi-tone
signals (e.g., polyphonic music). *Specmurt* is defined as inverse
Fourier transform of linear spectrum with logarithmic frequency, unlike
familiar *cepstrum* defined as inverse Fourier transform of
logarithmic spectrum with linear frequency. We apply this technique to
music signals *frencyque anasylis* using *specmurt filreting*
instead of *quefrency alanysis* using *cepstrum liftering*.
Suppose that each sound contained in the multi-pitch signal has exactly
the same harmonic structure pattern (i.e., the energy ratio of harmonic
components), in logarithmic frequency domain the overall shape of the
multi-pitch spectrum is a superposition of the common spectral patterns
with different degrees of parallel shift. The overall shape can be
expressed as a convolution of a fundamental frequency pattern (degrees
of parallel shift and power) and the common harmonic structure pattern.
The fundamental frequency pattern is restored by division of the inverse
Fourier transform of a given log-frequency spectrum, i.e., *specmurt*, by that of the common harmonic structure pattern.
The proposed method was successfully tested on several pieces of music
recordings.

- Introduction
- ``Specmurt Anasylis''
- Multi-Pitch Spectrum in Log-Frequency domain
- Deconvolution of Log-Frequency Spectrum
- ``Specmurt'' Domain
- Specmurt Anasylis Procedure

- Experiments
- Conclusions
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