vocoder_chung free experimental vocoder in freebasic

vocoder chung is a small educational vocoder using discrete fourier transform FFT spectrum written in easy fast compiled freebasic .
(24/12/2019) uses fast and accurate FFTdll.dll
(28/03/2020) algorythmic voice cloning / change / morphing experiment added
(20/04/2020) auto sliders update scan added

=>  https://sourceforge.net/projects/vocoder-chung/  

radio_vocoder a vocoder version of radio_chung

radio_vocoder_FFT is a vocoder + equalizer(s) + FFT effect(s) version of radio chung free internet web radio stream url and audio file player using bass.dll , gui_chung , FFTdll.dll fft fast fourier transform and freebasic .

=>  https://sourceforge.net/projects/radio-vocoder/  

the bidimensional complex numbers nature of world

Wondered why modern physics uses bidimensional complex numbers fourier transforms and waves probability bidimensional complex density functions.( why not one dimension, or 3,4 ?).
In fact it is due to the mathematical property that any function f(t) f(x) or f(x,y,z,t) can be decomposed as a sum of cos cosinus and sin sinus , which can be described as a sum of harmonics : cosinus with amplitude and phase (2 dimensions) for each frequency ,  amplitude*cos(twopi*frequency*t +phase)  which is fourier sum.
And so the nature of world is due to maths.