Extended Principal Components Analysis Matching with spectral Weighting for Wavetable synthesis

Wavetable matching of musical instrument tones using principal components analysis (PCA) takes advantage of spectral correlation information to find the basis spectra. Although PCA matching is efficient, it usually poorly matches the low-amplitude parts of a tone due to its inherent statistical bias. This paper describes weighted PCA methods that normalize the tone before PCA to fairly weight its different parts. Matching results for a range of instruments show that PCA of a frame-weighted spectrum with a roughly constant loudness throughout the tone improves on unweighted PCA by about 4% on average. The method gives the most dramatic improvements, up to 20%, for plucked string instruments. Moreover, the frame-weighted PCA results are almost as good as previously reported near-optimal results, especially when the number of wavetables is large.