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At any angular frequency , the Fourier transform of a discrete,
regular function of time is given by the following summation:

| |
(1) |

where *N* is the number of time samples, is the time sampling
rate, and *f*_{n} is the discrete signal. We notice that
equation (1) relates a discrete signal to its continuous
Fourier transform. This expression can also be interpreted as a dot
product between the discrete time function and a vector of powers
of exponentials that depend on the particular frequency .Then, for a set of frequencies , the estimates of the
Fourier transform result from a matrix multiplication with the discrete
time function.
The implementation of this method is straightforward. The calculation
of the matrix of exponentials is coded in parallel, for all frequencies
. A built-in function of Fortran 90 performs an efficient
vector-matrix multiplication directly yielding the remapped frequency
domain.

** Next:** NON-PARALLEL FEATURES OF INTERPOLATION
** Up:** Blondel & Muir: Parallel
** Previous:** INTRODUCTION
Stanford Exploration Project

11/16/1997