fft_sine


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Computes the discrete Fourier sine transformation of an odd sequence.

Synopsis

#include <imsl.h>

float *imsl_f_fft_sine (int n, float p[], …, 0)

The type double procedure is imsl_d_fft_sine.

Required Arguments

int n (Input)
Length of the sequence to be transformed. It must be greater than 1.

float p[] (Input)
Array of size n containing the sequence to be transformed.

Return Value

A pointer to the transformed sequence. To release this space, use imsl_free. If no solution was computed, then NULL is returned.

Synopsis with Optional Arguments

#include <imsl.h>

float *imsl_f_fft_sine (int n, float p[],
IMSL_RETURN_USER, float q[],
IMSL_PARAMS, float params[],
0)

Optional Arguments

IMSL_RETURN_USER, float q[] (Output)
Store the result in the user-provided space pointed to by q. Therefore, no storage is allocated for the solution, and imsl_f_fft_sine returns q. The array must be of length at least n + 1.

IMSL_PARAMS, float params[] (Input)
Pointer returned by a previous call to imsl_f_fft_sine_init. If imsl_f_fft_sine is used repeatedly with the same value of n, then it is more efficient to compute these parameters only once.
Default: Initializing parameters computed each time imsl_f_fft_sine is entered

Description

The function imsl_f_fft_sine computes the discrete Fourier sine transform of a real vector of size N. It uses the system’s high performance library for the computation, if available. Otherwise, the method used is a variant of the Cooley-Tukey algorithm, which is most efficient when N + 1 is a product of small prime factors. If N satisfies this condition, then the computational effort is proportional to N logN. Specifically, given an N-vector p, imsl_f_fft_sine returns in q

 

Finally, note that the Fourier sine transform is its own (unnormalized) inverse. The Cooley-Tukey algorithm is based on the sine FFT in FFTPACK, which was developed by Paul Swarztrauber at the National Center for Atmospheric Research.

Example

This example inputs a pure sine wave as a data vector and recovers its Fourier sine series, which is a vector with all components zero, except n at the appropriate frequency.

 

#include <imsl.h>

#include <math.h>

#include <stdio.h>

 

int main()

{

int n = 7;

int i;

float p[7];

float *q;

float pi;

 

pi = imsl_f_constant("pi", 0);

 

/* fill p with a pure sine wave */

 

for (i=0; i<n; i++)

p[i] = sin((float)(i+1)*pi/(float)(n+1));

 

q = imsl_f_fft_sine (n, p, 0);

 

printf (" index\t p\t q\n");

for (i=0; i<n; i++)

printf("\t%1d\t%5.2f\t%5.2f\n", i, p[i], q[i]);

}

Output

 

index p q

0 0.38 8.00

1 0.71 0.00

2 0.92 0.00

3 1.00 0.00

4 0.92 0.00

5 0.71 -0.00

6 0.38 0.00