Accession Number : AD0292733

Title :   THE INDEPENDENT SPECIFICATION OF THE MODULUS OF A FUNCTION AND THE MODULUS OF ITS FOURIER TRANSFORM

Corporate Author : MITRE CORP BEDFORD MASS

Personal Author(s) : FOWLE,EVERT N.

Report Date : 03 AUG 1962

Pagination or Media Count : 1

Abstract : Fourier theory imposes constraints which prevent one from specifying independently and exactly the modulus of a function and the modulus of its Fourier transform. However, as the product of the 'extents' of the two moduli (or the TW product) becomes large, the constraints appear to weaken, and it is possible under certain circumstances to obtain approximate expressions for phase functions which when associated with the two moduli make an approximate Fourier pair. A method for constructing the phase characteristics is given. How large the TW product must be to give good accuracy in the approximate Fourier pair is shown to depend heavily on the shape of the moduli. When both moduli are smooth continuous functions TW products of less than 10 will give good results. When one modulus is limited in extent and the other smooth and continuous, the approximate Fourier pair can be quite accurate for TW products of he order of 10. Finally, when both moduli are required to be limited in extent (a condition which expressly violates a requirement of Fourier theory) TW pro ucts of 100 or larger are required to give good accuracy in the approximate Fourier pair. (Author)

Descriptors :   *COMPLEX VARIABLES, *FOURIER ANALYSIS, CIRCUITS, DIFFERENTIAL EQUATIONS, NUMERICAL INTEGRATION

Distribution Statement : APPROVED FOR PUBLIC RELEASE