The systematic treatment of speech-spectrum transformation can be obtained in terms of algebraic topology and Morse theory. Some properties of homotopy-equivalence in the transformation of 1- and 2-dimensional speech spectrum are discussed.

We propose a new class of binary nonlinear codes of constant weights derived from a permutation representation of a group that is given by a combinatorial definition such as Cayley graphs of a group. These codes are constructed by the following direct interpretation method from a group: (1) take one discrete group whose elements are defined by generators and their relations, such as those in the form of Cayley graphs; and (2) embedding the group into a binary space using some of their permutation representations by providing the generators with realization of permutations of some terms. The proposed codes are endowed with some good characteristics as follows: (a) we can easily learn information about the distances of the obtained codes, and moreover, (b) we can establish a decoding method for them that can correct random errors whose distances from code words are less than half of the minimum distances achieved using only parity checking procedures.

We propose Optimal Temporal Decomposition (OTD) of speech for voice morphing preserving Δ cepstrum. OTD is an optimal modification of the original Temporal Decomposition (TD) by B. Atal. It is theoretically shown that OTD can achieve minimal spectral distortion for the TD-based approximation of time-varying LPC parameters. Moreover, by applying OTD to preserving Δ cepstrum, it is also theoretically shown that Δ cepstrum of a target speaker can be reflected to that of a source speaker. In frequency domain interpolation, the Laplacian Spectral Distortion (LSD) measure is introduced to improve the Inverse Function of Integrated Spectrum (IFIS) based non-uniform frequency warping. Experimental results indicate that Δ cepstrum of the OTD-based morphing spectra of a source speaker is mostly equal to that of a target speaker except for a piecewise constant factor and subjective listening tests show that the speech intelligibility of the proposed morphing method is superior to the conventional method.

In this paper, we propose a rectangular weighting function that can be used in the method of iteratively reweighted least squares (IRWLS) for designing equiripple all-pass IIR filters. The purpose of introducing this weighting function is to improve the convergence performance in the solution of the IRWLS. The height of each rectangle is designed to be equal to the local maximum of each ripple, and the width of each rectangle is designed so that the area of each rectangle becomes equal to the area of each ripple. Here, the ripple is the absolute value of the phase error. We show experimentally that the convergence performance in the solution of the IRWLS can be improved by using the proposed weighting function.

Let A(n, d, w) denote the maximum possible number of code words in binary (n,d,w) constant weight codes. For smaller instances of (n, d, w)s, many improvements have occurred over the decades. However, unknown instances still remain for larger (n, d, w)s (for example, those of n > 30 and d > 10). In this paper, we propose a new class of binary constant weight codes that fill in the remaining blank instances of (n, d, w)s. Specifically, we establish several new non-trivial lower bounds such as 336 for A(64, 12, 8), etc. (listed in Table 2). To obtain these results, we have developed a new systematic technique for construction by means of groups acting on some sets. The new technique is performed by considering a triad (G, Ω, f) := ("Group G," "Set Ω," "Action f on Ω") simultaneously. Our results described in Sect. 3 are obtained by using permutations of the elements of a set that include ∞ homogeneously like the other elements, which play a role to improve their randomness. Specifically, in our examples, we adopt the following model such as (PGL2(Fq), P1(Fq), "linear fractional action of subgroups of PGL2(Fq) on P1(Fq)") as a typical construction model. Moreover, as an application, the essential examples in [7] constructed by using an alternating group are again reconstructed with our new technique of a triad model, after which they are all systematically understood in the context of finite subgroups that act fractionally on a projective space over a finite field.