Cepstrum

About: Cepstrum is a research topic. Over the lifetime, 3346 publications have been published within this topic receiving 55742 citations.

The PDF projection theorem and the class-specific method

Abstract: We present the theoretical foundation for optimal classification using class-specific features and provide examples of its use. A new probability density function (PDF) projection theorem makes it possible to project probability density functions from a low-dimensional feature space back to the raw data space. An M-ary classifier is constructed by estimating the PDFs of class-specific features, then transforming each PDF back to the raw data space where they can be fairly compared. Although statistical sufficiency is not a requirement, the classifier thus constructed becomes equivalent to the optimal Bayes classifier if the features meet sufficiency requirements individually for each class. This classifier is completely modular and avoids the dimensionality curse associated with large complex problems. By recursive application of the projection theorem, it is possible to analyze complex signal processing chains. We apply the method to feature sets, including linear functions of independent random variables, cepstrum, and Mel cepstrum. In addition, we demonstrate how it is possible to automate the feature and model selection process by direct comparison of log-likelihood values on the common raw data domain.

Terahertz material detection from diffuse surface scattering

Abstract: The potential for terahertz (THz) spectroscopy to detect explosives and other materials of interest is complicated by rough surface scattering. Our previous work has demonstrated that by averaging over diffuse observation angles and surfaces, spectral features could be recovered from laboratory measurements and numerical computer simulations. In addition to averaging, a low-pass cepstrum filter was used to reduce noise due to the random rough surface. This paper expands on these concepts by using the cepstrum of both the random rough surface and the material properties of the target material to choose an optimal cutoff frequency for the filter. The utility of these techniques is evaluated using laboratory measurements and Monte Carlo simulations for many sets of random surface realizations. The Kirchhoff Approximation is used to quickly model diffuse scattering from dielectric materials with gradually undulating rough surfaces when the incident and diffuse scattering angles are near the surface normal. Th...

Causal-Anticausal Decomposition of Speech using Complex Cepstrum for Glottal Source Estimation

Abstract: Complex cepstrum is known in the literature for linearly separating causal and anticausal components. Relying on advances achieved by the Zeros of the Z-Transform (ZZT) technique, we here investigate the possibility of using complex cepstrum for glottal flow estimation on a large-scale database. Via a systematic study of the windowing effects on the deconvolution quality, we show that the complex cepstrum causal-anticausal decomposition can be effectively used for glottal flow estimation when specific windowing criteria are met. It is also shown that this complex cepstral decomposition gives similar glottal estimates as obtained with the ZZT method. However, as complex cepstrum uses FFT operations instead of requiring the factoring of high-degree polynomials, the method benefits from a much higher speed. Finally in our tests on a large corpus of real expressive speech, we show that the proposed method has the potential to be used for voice quality analysis.

Cepstrum-based deconvolution for speech dereverberation

Abstract: We present a blind deconvolution-based approach for the restoration of speech degraded by the acoustic environment. The proposed scheme processes the outputs of two microphones using cepstra operations and the theory of signal reconstruction from phase only. Under mild assumptions, it reconstructs the room impulse response associated with each microphone and restores the speech signal.

Mathematical evidence of the acoustic universal structure in speech

Abstract: The paper shows mathematically that there exists an acoustic universal structure in speech, which can be interpreted as a physical implementation of structural phonology. The structure has completely no dimensions of multiplicative and linear transformational distortions, which are inevitably involved in speech communication as differences of vocal tract shape, gender, age, microphone, room, line, hearing characteristics, and so on. A speech event, such as a phone, is probabilistically modeled as a distribution of parameters calculated by a linear transformation of a log spectrum, e.g., cepstrum. A set of events, such as a word, is relatively captured as structure composed of the distributions. An n-point structure is uniquely determined by fixing the lengths of its /sub n/C/sub 2/ diagonal lines, namely, the distance matrix among the n points. The distance between two distributions is calculated as a Bhattacharyya distance. The resulting structure has very interesting characteristics. Multiplicative and linear transformational distortions are geometrically interpreted as shift and rotation of the structure, respectively. This fact implies that there always exists a distortion-free communication channel between a speaker and a listener.