bb5ac288-5b28-4c89-896a-d49ed0c4abbc 33 6 9 decimal

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Fourier Window Filter Demo

t0 1 time :

1. Normalise Smath

Absolute of complex vector v Vabs v Abs v Re (2^v Im (2^+ sqrt : j 1 v rows range a j el v j el Abs eval : for a 21 line 21 line :

Smath/User redefinition v n cfft v n al_fftc1d :

v n icfft v n al_fftc1dinv (:

2. Construct a noisy vector

x f x sin (12^1 + 0.1 x * + :

v mwabs v Vabs ≡

m 99 :

n 1 m range t n el n 100 / 3 * π * : for

n 1 m range u n el n : for

α 0.5 : noise magnitude ≡

Generate the demo noisy vector n 1 m range d n el n 100 / 3 * π * f α 1 Random * + eval : 11 line for vx d 1 el : j 2 d rows range vx vx d j el stack : for d vx : 41 line

3. Fourier window

r t d Slope eval :

r 0.086926

dd d t r * - :

D dd m cfft :

Low 10 : High 10 : 13 mat

Create the Fourier window j 1 m range j Low ≤ (m High - j ≤ (¤ DW j el D j el : 0 if for DW 21 line

raw u d augment :

4. Conclude the filter

dw DW m icfft t r * + eval :

dw dw mwabs :

Filter u dw augment :

windowLow 0003 Low 3 Low 042 mat :

windowHigh m High - 0 m High - 3 m 3 m 042 mat :

1 time t0 - 2 sec *

Fourier window padding data smoothing. Works as well if the data set has no trend ...

raw Filter windowLow windowHigh 4 1 sys

How it works ? 1. The entire signal is 'fft' 2. The 'Low & High' parts of 'D' is conserved => DW. The inner 'DW' is padded '0'... DW is 'icfft'. The 'Low & High' are respectively adjustable.