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authorBryan Newbold <bnewbold@robocracy.org>2017-02-20 00:05:28 -0800
committerBryan Newbold <bnewbold@robocracy.org>2017-02-20 00:05:28 -0800
commitbd9733926076885e3417b74de76e4c9c7bc56254 (patch)
tree2c99dced547d48407ad44cb0e45e31bb4d02ce43 /fft.scm
parentfa3f23105ddcf07c5900de47f19af43d1db1b597 (diff)
downloadslib-bd9733926076885e3417b74de76e4c9c7bc56254.tar.gz
slib-bd9733926076885e3417b74de76e4c9c7bc56254.zip
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+;;;"fft.scm" Fast Fourier Transform
+;Copyright (C) 1999 Aubrey Jaffer
+;
+;Permission to copy this software, to redistribute it, and to use it
+;for any purpose is granted, subject to the following restrictions and
+;understandings.
+;
+;1. Any copy made of this software must include this copyright notice
+;in full.
+;
+;2. I have made no warrantee or representation that the operation of
+;this software will be error-free, and I am under no obligation to
+;provide any services, by way of maintenance, update, or otherwise.
+;
+;3. In conjunction with products arising from the use of this
+;material, there shall be no use of my name in any advertising,
+;promotional, or sales literature without prior written consent in
+;each case.
+
+;;;; See:
+;;; Introduction to Algorithms (MIT Electrical
+;;; Engineering and Computer Science Series)
+;;; by Thomas H. Cormen, Charles E. Leiserson (Contributor),
+;;; Ronald L. Rivest (Contributor)
+;;; MIT Press; ISBN: 0-262-03141-8 (July 1990)
+
+;;; http://www.astro.virginia.edu/~eww6n/math/DiscreteFourierTransform.html
+;;; differs in the direction of rotation of the complex unit vectors.
+
+(require 'array)
+
+(define (fft:shuffled&scaled ara n scale)
+ (define lgn (integer-length (+ -1 n)))
+ (define new (apply make-array 0 (array-dimensions ara)))
+ (define bit-reverse (lambda (width in)
+ (if (zero? width) 0
+ (+ (bit-reverse (+ -1 width) (quotient in 2))
+ (ash (modulo in 2) (+ -1 width))))))
+ (if (not (eqv? n (expt 2 lgn)))
+ (slib:error 'fft "array length not power of 2" n))
+ (do ((k 0 (+ 1 k)))
+ ((>= k n) new)
+ (array-set! new (* (array-ref ara k) scale) (bit-reverse lgn k))))
+
+(define (dft! ara n dir)
+ (define lgn (integer-length (+ -1 n)))
+ (define pi2i (* 0+8i (atan 1)))
+ (do ((s 1 (+ 1 s)))
+ ((> s lgn) ara)
+ (let* ((m (expt 2 s))
+ (w_m (exp (* dir (/ pi2i m))))
+ (m/2-1 (+ (quotient m 2) -1)))
+ (do ((j 0 (+ 1 j))
+ (w 1 (* w w_m)))
+ ((> j m/2-1))
+ (do ((k j (+ m k)))
+ ((>= k n))
+ (let* ((k+m/2 (+ k m/2-1 1))
+ (t (* w (array-ref ara k+m/2)))
+ (u (array-ref ara k)))
+ (array-set! ara (+ u t) k)
+ (array-set! ara (- u t) k+m/2)))))))
+
+(define (fft ara)
+ (define n (car (array-dimensions ara)))
+ (dft! (fft:shuffled&scaled ara n 1) n 1))
+
+(define (fft-1 ara)
+ (define n (car (array-dimensions ara)))
+ (dft! (fft:shuffled&scaled ara n (/ n)) n -1))