b05c6ba9-34b3-4574-9ed1-232b75b7ed02 22 6 9 decimal

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Fourier demo apodising wave train

pad 20 :

=> AUTO

L H N xd U 0 : dx H L - N / : i 1 N range U i el L dx - (dx i * + : for U 41 line :

Y n 2 pad * 1 - (: i pad n range Y i el 1 : for i pad 1 + (n range Y i el 0 : for Y 41 line :

Module 'Y' constructs a vector of length 'n', @ center '1'. In words: Fourier padded. The wave train can be shifted, shrinked/expanded.

Options=> Answer(set) => Auto This option take effect after close Smath, open Smath.

Fourier "ifft" from padded created vector [Numeric] v ifft N v length : s 1 N sqrt / : 12 mat n 0 N range I n 1 + el s (v k 1 + el e i 2 π * n * N / (* k * -^* (k 0 N 1 - sum eval * : for I 31 line :

U Y ifft mat2sys sys2mat :

a U Re mat2sys sys2mat :

b U Im mat2sys sys2mat :

ω 2 π N / * : Δx X N el X 1 el - (N 1 - / : u λ u X 1 el - (ω Δx / * : 31 line

N a length : L 0 : H π : 12 mat X L H N xd : 31 line

p 10 : Apodising period ≡ ε 0.01 : increment ≡ shift π (: 31 line

n 2 pad * 1 - (:

B39(u) => adapted from Mathsoft Collab Theodore Bones.
Algo known as "Budapest 39" u B39 a 1 el 2 / a n 1 + el u λ n * cos * b n 1 + el u λ n * sin * + (n 1 p sum + :

fit x 02 π * ε range : i 1 x rows range v i el x i el B39 eval : for scale 1 v Max / : x shift - scale v * augment 41 line :

Fourier polynomial adjustable apodising wave train

0 fit 2 1 sys

Center apodisation, coplanar circles

pad 15 :

Y n 2 pad * 1 - (: i 1 n range Y i el 1 : for i 2 n 1 - range Y i el 0 : for Y 41 line :

U Y ifft mat2sys sys2mat :

A U Re mat2sys sys2mat :

B U Im mat2sys sys2mat :

Y transpose 10000000000000000000000000001129 mat

N 50 : L 0.5 π * - : H 0.5 π * : 12 mat X L H N xd : 31 line

ω 2 π N / * : Δx X N el X 1 el - (N 1 - / : u λ u X 1 el - (ω Δx / * : 31 line

p 7 : Apodising period ≡ ε 0.01 : increment ≡ shift 0 : 31 line

u B39 A 1 el 2 / A n 1 + el u λ n * cos * (n 1 p sum + :

fit x L H L ε + (range : i 1 x rows range v i el x i el B39 eval : for scale 1 v Max / : x shift - scale v * augment 41 line :

data spec pts i 1 data rows range p i el a b c spec : for v p 1 el : Unest 'p' j 2 p rows range v v p j el stack : for data v augment 51 line :

ø 4 :

XY ø A * ø B * augment :

a b c spec . 8 black 13 mat :

pts XY a b c spec pts :

Fourier polynomial adjustable wave train added: ½ coplanar circle

0 fit π x * sin pts 4 1 sys