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 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. 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 function imsl_f_fft_sine is based on the sine FFT in FFTPACK. The package FFTPACK 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>

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

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