




Description 
This module implements the Fast Fourier Transformation purely in Haskell.


Synopsis 




FFT



FFT transformation. Input is grouped into overlapping parts of 2^(N+2) reals and mapped to sublists
with 2^(N+1) complex numbers.



Inverse FFT transformation. Complex input is grouped into parts with length 2^(N+1) and mapped to
sublists with 2^(N+2) reals, which are overlapped and mixed.



FFT transformation with overlapping and windowing.
Argument function maps the coefficients. Windowsize: 2^(N+2), i. e. 2^(N+1) coefficients


FFT



FFT transformation for complex input (segments of length 2^n).
No overlapping or windowing.



Inverse FFT transformation for complex input (segments of length 2^n).
No overlapping or windowing.





FFT for complex input with overlapping. Segmentsize: 2^(n+1)





A selfinverse transformation similar to FFT but with a simple butterfly
operation that uses always W=1. Modifying the data between application
and inverse is similar to filtering but the result will be built up from
rectangle waves instead of sinus waves.







The complex value i = (0 :+ 1)



The nth root of 1



the 2nth root with exponents 0, 1, .. n. False=inverse (exponents are negated)


map2 :: (a > a > b) > [a] > [b]  Source 


zip2 :: [a] > [a] > [a]  Source 


evens 

odds 

drop_odds 

appendpair :: ([a], [a]) > [a]  Source 

returns [] if argument has zero or one element.



list is grouped into sublists with length N (must be power of 2) and bitwise reverse order


reorder_init 

reorder_init' :: [a] > [[a]]  Source 










fft_init_overlap 





fft_init 

fft_overlap_loop 

expandComplex 


Creates a fade with length N



Overlaps a sequence of parts of length N (overlaps by N/2).


Produced by Haddock version 2.4.2 