Phase retrieval from Fourier magnitude and several initial time samples using Newton´s formulae

Author

Yagle, Andrew E.

Author_Institution

Dept. of Electr. Eng. & Comput. Sci., Michigan Univ., Ann Arbor, MI, USA

Volume

46

Issue

7

fYear

1998

fDate

7/1/1998 12:00:00 AM

Firstpage

2054

Lastpage

2056

Abstract

The problem of reconstructing a discrete-time one-dimensional (1-D) signal from its discrete Fourier transform magnitude and several initial time samples arises in ARMA system identification problems in which the system is driven by white Gaussian noise and has a known additive MA component. Its solution requires testing all possible zero configurations to find the one yielding the known signal values. We show how Newton´s formulae may be used to reduce the number of configurations that must be tested by transforming the given problem into one with a specified endpoint and with zeros farther away from the unit circle

Keywords

Fourier transforms; Gaussian noise; Newton method; autoregressive moving average processes; discrete time systems; phase estimation; poles and zeros; signal reconstruction; signal sampling; white noise; ARMA system identification problems; Fourier magnitude; Newton´s formulae; additive MA component; discrete Fourier transform magnitude; discrete-time one-dimensional signal; initial time samples; phase retrieval; unit circle; white Gaussian noise; zero configurations; Additive noise; Autocorrelation; Discrete Fourier transforms; Discrete transforms; Gaussian noise; Iterative algorithms; Polynomials; Signal processing; System identification; Testing;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.700982

Filename

700982