Fast and recursive algorithms for magnitude retrieval from DTFT phase at irregular frequencies

A.E. Yagle
1999 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258)  
We derive t wo new algorithms for reconstructing a discretetime 1-D signal from the phase of its discrete-time Fourier transform DTFT at irregular frequencies. Previous algorithms for this problem have either required the computation of a matrix nullspace, requiring ON 3 computations, or have been iterative in nature; for the latter, the irregularity of the frequency samples precludes use of the fast Fourier transform. Our rst algorithm requires only ON 2 computations ON log 3 N asymptotically.
more » ... In the special case of equally-spaced frequency samples, it is related to a previous algorithm. The second algorithm is recursive at each recursion a meaningful magnitude retrieval problem is solved. This is useful for updating a solution; it also allows checking of the result at each recursion, avoiding any errors due to computational roundo error and ill-conditioning of the problem.
doi:10.1109/icassp.1999.756280 dblp:conf/icassp/Yagle99 fatcat:p7sugi4xsvb2ddrop7bzapvxge