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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))