| This work involves the design and theoretical development of a new technique, used for the problem of signal indentification and matching. The present stage of speech signal recognition technology, is characterized by the lack of sufficiently powerful characterization tools--tools which "encode" the given signal into a vocabulary, that enables comparison between signals. Much of current research, is still dependent on the hope that better understanding of human speech, and more importantly, auditory responses, will facilitate development of better speech encoding techniques, which ultimately enable general purpose speech signal recognition.;It is this void (wherein, lack of knowledge of, how the human auditory system and the human brain, are able to breakdown speech and handle different accents), that this work attempts to fill partially. A new generalized signal analysis technique is developed for 1-Dim signals here. The signals that benefit the most from this new technique, are ones with a large amount of spectral energy in the lowest group of harmonics. In addition, the fundamental harmonic must have the highest amplitude, and the spectral envelope must preferably be a decaying hyperbolic.;The individual harmonics making up the transform, on summation (i.e., Fourier Series) give rise to the original input signal. The technique developed here, utilizes the successive sequence of Partial Fourier Sums where, the first partial sum is just the fundamental harmonic. The theory of Convergence of Fourier Series is solid. Using this convergence property of Partial Sums, combined with advantages of a hyperbolic spectral envelope, new, interesting and useful properties are developed. Given a hyperbolic spectral envelope, the fundamental harmonic sets the global trend of the complete signal envelope. The addition of the higher harmonics (which have lower spectral energy) imbue the higher partial sums with more locality, while still maintaining; the "global general trends" determined by the lower harmonics. A technique utilizing this fact is popularly known as a "multi-resolution" technique. Multi-resolution, is used to "encode" signals with ever-increasing detail (as we go towards higher partial sums). Therefore, if a comparison of encoding of two signals for "low-resolution" (lower partial sums) is bad, the signals are guaranteed to be quite different, given their hyperbolic spectral envelope. If the comparison is good, higher partial sums are used to redo comparison in greater detail" (greater resolution).;The first portion of this thesis described the new encoding technique, which uses the zero-slopes and zero-crossings of the individual harmonics, to create partition boundaries for the time-domain envelope. The partitioned time-domain envelope is then shown to be describable using a very simple alphabet, facilitating previously difficult problem of comparing two signals. |
