Dec 282017

Source to perform Fast Fourier Transforms in Fortran. | |||
---|---|---|---|

File Name | File Size | Zip Size | Zip Type |

DFT.FOR | 1336 | 363 | deflated |

FFT.DOC | 1818 | 915 | deflated |

FFT1.FOR | 3012 | 711 | deflated |

FFT2.FOR | 1596 | 515 | deflated |

NFFT.FOR | 3721 | 1244 | deflated |

# Download File FFT_FOR.ZIP Here

## Contents of the FFT.DOC file

These 4 programs are FORTRAN subroutines which do

Fourier Transforms by various methods.

DFT does a straight forward Discrete Fourier Transform -

The long way. You could call it a "Slow Fourier Transform".

It is useful to see the basis for some of the short cut

routines more commonly used.

FFT1 and FFT2 are typical Fast Fourier Transform

routines. They have the classical limitation of only working

on 2 to the nth power (2**n) points. You can add zeros to

the end of your data to get enough points. This has a minor

effect on the accuracy - see a reference book for more

details.

NFFT is a unique routine, and can be very useful,

especially if you don't know how many data points you will

have ahead of time. There is a classic misconception that

FFT algorithms only work for 2**n points. Not True! Any

number of points that can be factored into more than one

prime factor can be sped up considerably - 2**n is just the

fastest possible number. NFFT does this for you

automatically. It factors the number of data points and does

the FFT the fastest possible way - from a 2**n all the way

down to DFT speed. It is instructive to try different

numbers of data points and time them - for example, using

the same data, try 512 points, 500 points, and 499 points.

If you have comments or questions, let me know. A good

book on FFT's (and just the Fourier Transform) is the one by

E. Oran Brigham, "The Fast Fourier Transform", Prentice

Hall, 1974.

Bill Wittig

11215 Birmingham Ct.

St. Louis, MO 63138

SLHUG Fido 100/512

Fourier Transforms by various methods.

DFT does a straight forward Discrete Fourier Transform -

The long way. You could call it a "Slow Fourier Transform".

It is useful to see the basis for some of the short cut

routines more commonly used.

FFT1 and FFT2 are typical Fast Fourier Transform

routines. They have the classical limitation of only working

on 2 to the nth power (2**n) points. You can add zeros to

the end of your data to get enough points. This has a minor

effect on the accuracy - see a reference book for more

details.

NFFT is a unique routine, and can be very useful,

especially if you don't know how many data points you will

have ahead of time. There is a classic misconception that

FFT algorithms only work for 2**n points. Not True! Any

number of points that can be factored into more than one

prime factor can be sped up considerably - 2**n is just the

fastest possible number. NFFT does this for you

automatically. It factors the number of data points and does

the FFT the fastest possible way - from a 2**n all the way

down to DFT speed. It is instructive to try different

numbers of data points and time them - for example, using

the same data, try 512 points, 500 points, and 499 points.

If you have comments or questions, let me know. A good

book on FFT's (and just the Fourier Transform) is the one by

E. Oran Brigham, "The Fast Fourier Transform", Prentice

Hall, 1974.

Bill Wittig

11215 Birmingham Ct.

St. Louis, MO 63138

SLHUG Fido 100/512

December 28, 2017
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