RECONSTRUCTION OF SIGNALS FROM PHASE: EFFICIENT ALGORITHMS, SEGMENTATION, AND GENERALIZATIONS
MERCHANT, GULAMABBAS ABDULHUSEIN
Doctor of Philosophy
It is well known that the phase of the Fourier transform of a signal contains a significant amount of information about the signal. Under certain circumstances the knowledge of phase is sufficient to recover the original signal. This idea can be used to perform blind deconvolution of a signal which has been distorted by a linear phase filter. However this requires the knowledge of the entire output of the filter. Here several new formulations of phase-only blind deconvolution have been developed. Each of these formulations lead to a system of simultaneous equations whose of coefficient matrix is representable by a sum of a Toeplitz and a Hankel matrix. It is shown that this system of equations can be solved efficiently by a block-Levinson type algorithm. To handle long duration filter output a procedure for approximately reconstructing the original signal from short segments is developed. Some application of the techniques above are presented. It is seen that the signal recovery is excellent. Phase-only blind deconvolution for linear phase filters relies on the reciprocal symmetry of the zeros of the transfer function H(z) of the filter. This is generalized to include the filters whose zeros have other kind of symmetries.
Electronics; Electrical engineering