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FFT of Real Valued Sequence.


double x[], sine[];
int m;
fftr(x, m, sine);


Computes the (complex valued) discrete Fourier transform of the real valued sequence x[].  The input sequence x[] contains n = 2**m samples.  The program fills array sine[k] with n/4 + 1 values of sin(2 PI k / n).

Data format for complex valued output is real part followed by imaginary part.  The output is developed in the input array x[].

The algorithm takes advantage of the fact that the FFT of an n point real sequence can be obtained from an n/2 point complex FFT.

A radix 2 FFT algorithm is used.

Execution time on an LSI-11/23 with floating point chip is 1.0 sec for n = 256.


E. Oran Brigham, The Fast Fourier Transform; Prentice-Hall, Inc., 1974