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NAME
wnfft -- discrete Fourier transform package
SYNOPSIS
#include "wnfft.h"
wn_fft_vect(vector,len_i)
wn_cplx vector[];
int len_i;
wn_inverse_fft_vect(vector,len_i)
wn_cplx vector[];
int len_i;
wn_sft_vect(vector,len_i)
wn_cplx vector[];
int len_i;
wn_inverse_sft_vect(vector,len_i)
wn_cplx vector[];
int len_i;
DESCRIPTION
This package implements the discrete Fourier transform and its
inverse. "vector" is the data to be transformed; "len_i" is
its length. The resulting transformed data is also placed in
"vector".
wn_fft_vect and wn_sft_vect implement the following DFT:
out[f] =
(len_i^(-1/2))*sum_over(0<=t<len_i){in[t]*exp(-j*2*PI*f*t/len_i)}
wn_inverse_fft_vect and wn_inverse_sft_vect implement
the following inverse DFT:
out[t] =
(len_i^(-1/2))*sum_over(0<=f<len_i){in[f]*exp(j*2*PI*f*t/len_i)}
where j == (-1)^(1/2).
"sft" stands for "slow Fourier transform" while "fft" stands
for "fast Fourier transform". The fft routines are much faster,
but they require that "len_i" be a power of 2. The sft routines
are much slower, but place no restriction on "len_i".
Applying fft and then inverse_fft to a vector yields the original
vector.
RESOURCES
"wn_fft_vect" and "wn_inverse_fft_vect" require
WORST and AVERAGE CASE:
time = len_i*log(len_i)
stack memory = log(len_i)
dynamic memory = len_i
"wn_sft_vect" and "wn_inverse_sft_vect" require
WORST and AVERAGE CASE:
time = len_i^2
stack memory = 1
dynamic memory = len_i
DIAGNOSTICS
BUGS
This code is new and has not been tested in large industrial
applications.
SEE ALSO
acc/complex/examples.c
AUTHOR
Will Naylor
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