diff options
Diffstat (limited to 'fft.scm')
| -rw-r--r-- | fft.scm | 44 |
1 files changed, 34 insertions, 10 deletions
@@ -1,5 +1,5 @@ ;;;"fft.scm" Fast Fourier Transform -;Copyright (C) 1999 Aubrey Jaffer +;Copyright (C) 1999, 2003 Aubrey Jaffer ; ;Permission to copy this software, to modify it, to redistribute it, ;to distribute modified versions, and to use it for any purpose is @@ -8,7 +8,7 @@ ;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 +;2. I have made no warranty 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. ; @@ -28,14 +28,13 @@ ;;; differs in the direction of rotation of the complex unit vectors. (require 'array) +(require 'logical) -(define (fft:shuffled&scaled ara n scale) +;;@code{(require 'fft)} +;;@ftindex fft + +(define (fft:shuffle&scale new 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))) @@ -61,10 +60,35 @@ (array-set! ara (+ u t) k) (array-set! ara (- u t) k+m/2))))))) +;;@args array +;;@var{array} is an array of @code{(expt 2 n)} numbers. @code{fft} +;;returns an array of complex numbers comprising the +;;@dfn{Discrete Fourier Transform} of @var{array}. (define (fft ara) (define n (car (array-dimensions ara))) - (dft! (fft:shuffled&scaled ara n 1) n 1)) + (define new (apply create-array ara (array-dimensions ara))) + (dft! (fft:shuffle&scale new ara n 1) n 1)) +;;@args array +;;@code{fft-1} returns an array of complex numbers comprising the +;;inverse Discrete Fourier Transform of @var{array}. (define (fft-1 ara) (define n (car (array-dimensions ara))) - (dft! (fft:shuffled&scaled ara n (/ n)) n -1)) + (define new (apply create-array ara (array-dimensions ara))) + (dft! (fft:shuffle&scale new ara n (/ n)) n -1)) + +;;@noindent +;;@code{(fft-1 (fft @var{array}))} will return an array of values close to +;;@var{array}. +;; +;;@example +;;(fft '#(1 0+i -1 0-i 1 0+i -1 0-i)) @result{} +;; +;;#(0.0 0.0 0.0+628.0783185208527e-18i 0.0 +;; 0.0 0.0 8.0-628.0783185208527e-18i 0.0) +;; +;;(fft-1 '#(0 0 0 0 0 0 8 0)) @result{} +;; +;;#(1.0 -61.23031769111886e-18+1.0i -1.0 61.23031769111886e-18-1.0i +;; 1.0 -61.23031769111886e-18+1.0i -1.0 61.23031769111886e-18-1.0i) +;;@end example |