A Fourier-domain formula for the least-squares projection of a function onto a repetitive basis in N-dimensional space

Author

Oakley, John Peter ; Cunningham, Michael John ; Little, Graham

Author_Institution

Manchester Univ., UK

Volume

38

Issue

1

fYear

1990

fDate

1/1/1990 12:00:00 AM

Firstpage

114

Lastpage

120

Abstract

A theorem concerning the least-squares projection of an arbitrary function onto an infinite basis of translated function is given. The theorem provides an explicit formula for the Fourier transform, of the projected function. The formula has the advantage of being valid for least-squares projections in any N-dimensional space. The expression for the projected function can be approximately inverted, using the discrete Fourier transform, to find the actual basis coefficients

Keywords

fast Fourier transforms; least squares approximations; signal processing; FFT; Fourier-domain formula; LSA; N-dimensional space; basis coefficients; discrete Fourier transform; explicit formula; least-squares projection; projected function; repetitive basis; signal processing; translated function infinite basis; Application software; Books; Computer graphics; Computer vision; Discrete Fourier transforms; Fourier transforms; Image processing; Lattices; Spline; Surface fitting;

fLanguage

English

Journal_Title

Acoustics, Speech and Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

0096-3518

Type

jour

DOI

10.1109/29.45623

Filename

45623