How to resolve the algorithm Fast Fourier transform step by step in the PicoLisp programming language

Published on 12 May 2024 09:40 PM
#Picolisp

How to resolve the algorithm Fast Fourier transform step by step in the PicoLisp programming language

Table of Contents

Problem Statement

Calculate the   FFT   (Fast Fourier Transform)   of an input sequence. The most general case allows for complex numbers at the input and results in a sequence of equal length, again of complex numbers. If you need to restrict yourself to real numbers, the output should be the magnitude   (i.e.:   sqrt(re2 + im2))   of the complex result. The classic version is the recursive Cooley–Tukey FFT. Wikipedia has pseudo-code for that. Further optimizations are possible but not required.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Fast Fourier transform step by step in the PicoLisp programming language

Source code in the picolisp programming language

# apt-get install libfftw3-dev

(scl 4)

(de FFTW_FORWARD . -1)
(de FFTW_ESTIMATE . 64)

(de fft (Lst)
   (let
      (Len (length Lst)
         In (native "libfftw3.so" "fftw_malloc" 'N (* Len 16))
         Out (native "libfftw3.so" "fftw_malloc" 'N (* Len 16))
         P (native "libfftw3.so" "fftw_plan_dft_1d" 'N
            Len In Out FFTW_FORWARD FFTW_ESTIMATE ) )
      (struct In NIL (cons 1.0 (apply append Lst)))
      (native "libfftw3.so" "fftw_execute" NIL P)
      (prog1 (struct Out (make (do Len (link (1.0 . 2)))))
         (native "libfftw3.so" "fftw_destroy_plan" NIL P)
         (native "libfftw3.so" "fftw_free" NIL Out)
         (native "libfftw3.so" "fftw_free" NIL In) ) ) )

(for R (fft '((1.0 0) (1.0 0) (1.0 0) (1.0 0) (0 0) (0 0) (0 0) (0 0)))
   (tab (6 8)
      (round (car R))
      (round (cadr R)) ) )

You may also check:How to resolve the algorithm Sum of a series step by step in the DWScript programming language
You may also check:How to resolve the algorithm 99 bottles of beer step by step in the SenseTalk programming language
You may also check:How to resolve the algorithm Sum digits of an integer step by step in the Sidef programming language
You may also check:How to resolve the algorithm Teacup rim text step by step in the Nim programming language
You may also check:How to resolve the algorithm Assertions step by step in the Objective-C programming language