The line spectrum pair (LSP) decomposition is a widely used method in speech coding. In this article, we will show that the LSP polynomials, whose trivial zeros have been removed, are equivalent to two optimal (in the mean square sense) predictors in which a sample is predicted from linear combinations of its previous averaged and differentiated values.

Frequency warping using all pass structures or Laguerre filters has increasingly found applications in audio signal processing due to having a good match with auditory frequency resolution. Kautz filters are an extension where the frequency warping and related resolution can have more freedom. We discuss the properties of Kautz filters and how they meet typical requirements found in modeling and equalization of audio systems. Case studies include transfer function modeling of the guitar body and loudspeaker response equalization.

In this paper we discuss various digital filter principles as models for synthetic speech generation. Warped linear prediction (WLP) and frequency-warped filters have been introduced earlier as a method to reduce the filter order in high-quality wideband speech synthesis. In addition to analyzing WLP and frequency-warped filters we introduce new related structures and techniques for arbitrary frequency resolution allocation. Kautz filters can be considered as generalized structures for pole-zero modeling. This study focuses on residual-excited synthesis and diphone-oriented reconstruction of speech signals. Control strategies for text-to-speech synthesis are discussed briefly.