Abstract
A recursive procedure to reconstruct a given sequence from its group delay or phase derivative is given. The procedure is based on the relationships between minimum, maximum phase sequences and their cepstra, and on the modified least squares (MLS) rational approximation. To avoid unwrapping of the phase, the cepstrum of the sequence is calculated from the group delay function. Using a recursive procedure, we find from the cepstrum values a minimum phase sequence with a phase equal to that of the original sequence. The reconstructed sequence is obtained using the MLS procedure to find recursively a rational approximation of the minimum phase sequence. The constraints under which the phase reconstruction is possible are checked with a root distribution algorithm, and we indicate how to modify the sequence when the constraints are not satisfied. Examples illustrate the efficiency of the proposed procedure.
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