Computation of the one-dimensional unwrapped phase

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (p. 101-102). "Cepstrum bibliography" (p. 67-100).In this thesis, the computation of the unwrapped phase of the discrete-time Fourier transform (DTFT) of a one-dimensional finite-length signal is explored. The phase of the DTFT is not unique, and may contain integer multiple of 27r discontinuities. The unwrapped phase is the instance of the phase function chosen to ensure continuity. This thesis presents existing algorithms for computing the unwrapped phase, discussing their weaknesses and strengths. Then two composite algorithms are proposed that use the existing ones, combining their strengths while avoiding their weaknesses. The core of the proposed methods is based on recent advances in polynomial factoring. The proposed methods are implemented and compared to the existing ones.by Zahi Nadim Karam.S.M

Optophone design: optical-to-auditory vision substitution for the blind

An optophone is a device that turns light into sound for the benefit of blind people. The present project is intended to produce a general-purpose optophone to be worn on the head about the house and in the street, to give the wearer a detailed description in sound of the'scene he is facing. The device will therefore consist'of an'electronic camera, some signal-processing electronics, earphones`, and a battery. The two major problems are the derivation of (a) the most suitable mapping from images to sounds, and (b) an algorithm to perform the mapping in real'time on existing electronic components. This thesis concerns problem (a). Chapter 2 goes into the general scene-to-sound mapping problem in some detail'and presents the work of earlier investigators. Chapter 3 1- discusses the design of tests to evaluate the performance of candidate mappings. A theoretical performance test (TPT) is derived. Chapter 4 applies the TPT to the most obvious mapping, the cartesian piano transform. Chapter 5 applies the TPT to a mapping based on the cosine transform. Chapter 6 attempts to derive a mapping by principal component analysis, using the inaccuracies of human sight and hearing and the statistical properties of real scenes and sounds. Chapter 7 presents a complete scheme, implemented in software, for representing digitised colour scenes by audible digitised stereo sound. Chapter 8 tries to decide how'many numbers are required to specify a steady spectrum with no noticeable degradation. Chapter 9 looks'at a scheme designed to produce more natural-sounding sounds related to more meaningful portions of the scene. This scheme maps windows in the scene to steady spectral patterns of short duration, the location of the window being conveyed by simulated free-field listening. Chapter 10 gives detailed recommendations as to further work

Time-Domain Cepstral Transformations

This paper addresses the realization of homomorphic systems for convolution. The motivation for the work comes from the limitations of the method commonly used in homomorphic (complex cepstral) filtering, which is based on the application of the Fourier transform. The calculation of the unwrapped phase, the effects of regions with low signal-to-noise ratios (and spectral notching), aliasing, windowing, and signal truncation effects are some common limitations of the Fourier transform (FT) method. We introduce a new method, time-domain cepstral transformation (TDCT), that is entirely based on time-domain calculations. It thus avoids or minimizes the problems associated with the FT method. Explicit transformations of an ordinary mixed phase time sequence (belonging to convolution space) into its complex cepstrum time sequence (belonging to additive cepstrum vector space) and vice versa are derived. The TDCT method does not require unwrapped phase calculations and no specific windows are used to precondition the signal in order to produce a more accurate representation of the complex cepstrum. The TDCT\u27s are matrix formulas, and their results match well the theoretical complex cepstrum (calculated for known systems). The TDCT method trades reduced computational efficiency for improved performance. Examples are presented comparing Fourier-based and TD cepstrum transformations. © 1993 IEE