An application of the Yang-Mills equations to speech signal processing
by
Yoshinao Shiraki
NTT Communication Science Labs

The object of this note is to generate a spectral sequence between two given speech spectra, Y_A and Y_B, and to show that vector fields of given spectra and a kind of smoothness of connections on the field play an important role in maintaining speech intelligibility.

Let us consider an interpolation function between a pair of given speech spectral sequences. The first difficulty in obtaining a smooth interpolation is that speech characteristics distribute in two (time and frequency) or more higher dimensions. And the second difficulty is that speech has a discrete (or local) structure of phonemes, which limit the distribution regions of the first and the second formant frequencies. In other words, the smooth interpolation considered here needs to satisfy the maintenance of the local-discrete structure as well as the smooth functions over two dimensions or more. Furthermore, such an interpolation function is not uniquely determined by these two conditions. In this note, we propose a method which determines the interpolation function by adding a condition of minimizing an energy of connections. Here, we do not fix the one connection. We list up many of connections and select the connection best suited for the conditions. To do this, we use a functional of connections and investigate the functional by applying the variational scheme. Our focus is on speaker individualities.

We obtained the following results: (1) We can use a moduli space of the Yang-Mills equations to investigate a smooth interpolation of a pair of spectral sequences. In other words, we can adopt the problem of minimizing an energy of connections as the interpolation scheme. (2) A flat connection is one of solutions of the equations. (3) A locally-linear interpolation scheme is derived by the flat connection. (4) A unitary transformation of a dynamic measure is directly derived by the linear interpolation. (5) A Laplacian Spectral Distance (LSD) is also derived by the flat connection. (6) An algorithm for constructing the locally-linear interpolation is introduced. (7) An algorithm for locally-combining LSD and IFIS methods is also introduced. (8) Some experimental results show that the speech produced by the proposed methods is of good speech quality and is superior to the speech produced by the conventional interpolation methods.

http://www.brl.ntt.co.jp/people/shiraki/

Date received: June 25, 1999