RosettaCodeData/Task/Fast-Fourier-transform/Scheme/fast-fourier-transform.scm

34 lines
1.4 KiB
Scheme

; Compute and return the FFT of the given input vector using the Cooley-Tukey Radix-2
; Decimation-in-Time (DIT) algorithm. The input is assumed to be a vector of complex
; numbers that is a power of two in length greater than zero.
(define fft-r2dit
(lambda (in-vec)
; The constant ( -2 * pi * i ).
(define -2*pi*i (* -2.0i (atan 0 -1)))
; The Cooley-Tukey Radix-2 Decimation-in-Time (DIT) procedure.
(define fft-r2dit-aux
(lambda (vec start leng stride)
(if (= leng 1)
(vector (vector-ref vec start))
(let* ((leng/2 (truncate (/ leng 2)))
(evns (fft-r2dit-aux vec 0 leng/2 (* stride 2)))
(odds (fft-r2dit-aux vec stride leng/2 (* stride 2)))
(dft (make-vector leng)))
(do ((inx 0 (1+ inx)))
((>= inx leng/2) dft)
(let ((e (vector-ref evns inx))
(o (* (vector-ref odds inx) (exp (* inx (/ -2*pi*i leng))))))
(vector-set! dft inx (+ e o))
(vector-set! dft (+ inx leng/2) (- e o))))))))
; Call the Cooley-Tukey Radix-2 Decimation-in-Time (DIT) procedure w/ appropriate
; arguments as derived from the argument to the fft-r2dit procedure.
(fft-r2dit-aux in-vec 0 (vector-length in-vec) 1)))
; Test using a simple pulse.
(let* ((inp (vector 1.0 1.0 1.0 1.0 0.0 0.0 0.0 0.0))
(dft (fft-r2dit inp)))
(printf "In: ~a~%" inp)
(printf "DFT: ~a~%" dft))