Two longitudinal waves, called fast and slow waves, can be observed in ultrasound signals propagating through in vitro cancellous bone. From the propagation properties of both the fast and slow waves, an estimation of the bone status can be made. However, in in vivo measurements, a wide overlap of the fast and slow waves in the time domain is generally observed. In this study, a derivation of the characteristics of the fast and slow waves was attempted using a generalized harmonic analysis. From the results of this analysis, the times of the leading edges, frequencies, and amplitudes of the fast and slow waves were derived. These derived characteristics were scarcely influenced by the noise when the noise level was low. When the noise level was high, the derived frequencies and amplitudes were influenced by the noise, but the times of leading edges generally were not.

This paper presents a feedback framework that can improve chord recognition for music audio signals by performing approximate note transcription with Bayesian non-negative matrix factorization (NMF) using prior knowledge on chords. Although the names and note compositions of chords are intrinsically linked with each other (e.g., C major chords are highly likely to include C, E, and G notes, and those notes are highly likely to be in C major chords), chord recognition and note transcription (multipitch analysis) have been studied independently. To solve this chicken-and-egg problem, our framework iterates chord recognition and approximate note transcription using each other's results. More specifically, we first perform approximate note transcription based on Bayesian NMF that forces basis spectra to respectively correspond to different semitonelevel pitches covering the whole range. We then execute chord recognition based on Bayesian hidden Markov models (HMMs) that use chroma features obtained from the activation patterns of those pitches. To improve note transcription, we again perform Bayesian NMF that encourages certain kinds of pitches in each chord region to be activated. Experimental results showed that our feedback framework gradually improved the accuracy of chord recognition.