<p> pts(data,spec)</p>

7c56edb6-6d84-4361-a4c9-e4044cfbb79a 11 6 9 decimal

&[DATE] &[TIME] - &[FILENAME]

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 :

Fourier padding app's

=> AUTO

Fourier OFF center padding 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 :

U Y ifft mat2sys sys2mat :

pad 9 :

a U Re mat2sys sys2mat : b U Im mat2sys sys2mat : 21 line

Y rows 17

Y transpose 00000000100000000117 mat

a b augment

pad 2 triangle ≡ 3 penta star ≡ 4 epta star ≡ # 9 bulleye star ≡ 51 mat ≡

Fourier CENTER padding 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 :

pad 4 :

U # :

U Y ifft mat2sys sys2mat :

a U Re mat2sys sys2mat : b U Im mat2sys sys2mat : 21 line

Y rows 7

Draw odd polygon

a b augment

Y transpose 100000117 mat

=============================================

Y 10000116 mat transpose :

U # :

U Y ifft mat2sys sys2mat :

a U Re mat2sys sys2mat : b U Im mat2sys sys2mat : 21 line

Draw the hexagon

a b augment <p> pts(data,spec)</p>

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 :

vx vy a b c plotG a char ≡ b size ≡ c color ≡ 13 mat n vx length : plot vx 1 el vy 1 el a b c augment : i 2 n range plot plot vx i el vy i el a b c augment stack : for plot 51 line :

An application of Fourier padding "0's "

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

'N' pts in range [L, H] 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 :

120414 mat

Filter 120414 mat transpose :

1010115 mat

Both Filter & α are user at will

110214 mat

N 65 :

10 # # # 116 mat n arch ≡

N sets the span of the Dirac ≡

Dirac n 1 N range n Filter rows ≤ Dirac n el Filter n el : Dirac n el 0 : if for Dirac 21 line :

V Dirac ifft :

NN V length : L 0 : H π : U L H NN xd : 41 line

Vectorise on length 'V' F t U : Ω V mat2sys abs sys2mat : t Ω augment 31 line :

V length 65

a b c spec . 8 black 13 mat :

scale 1 F 12 el / : 1.142857

pts scale F * a b c spec pts :

Publish your project, Smath style [Fourier-Dirac Discrete Filter]

pts scale F * 2 1 sys

arg("complexNumber") Returns the angle from the real axis to the given complex number

Phasemod_π i 1 V rows range φ i el V i el arg eval : x i el U i el : 21 line for x φ augment 21 line :

Conjugate v conj v abs (2^v / :

a b c spec . 8 red 13 mat :

Φmod_π Phasemod_π a b c spec pts :

Plot clean Phasemod_π

1.594962 5 1.594962 2 - 1.594962 0 2.126617 0 2.126617 5 2.126617 2 - 6 2 mat Φmod_π 2 1 sys

Phase-unwrap θ t U : n 1 V rows range n 1 ≡ θ 1 el V 1 el arg : θ n el V n 1 - el arg V n el V n 1 - el conj * arg + : if for t θ augment 31 line :

Phasemod_π 00 0.048332 0 0.096664 3.141593 0.144997 3.141593 0.193329 3.141593 0.241661 3.141593 0.289993 3.141593 0.338325 3.141593 0.386658 3.141593 0.43499 3.141593 0.483322 3.141593 0.531654 3.141593 0.579986 3.141593 0.628319 0 0.676651 0 0.724983 0 0.773315 0 0.821647 0 0.86998 0 0.918312 0 0.966644 3.141593 1.014976 3.141593 1.063308 3.141593 1.11164 3.141593 1.159973 3.141593 1.208305 3.141593 1.256637 3.141593 1.304969 3.141593 1.353301 3.141593 1.401634 3.141593 1.449966 3.141593 1.498298 3.141593 1.54663 3.141593 1.594962 0 1.643295 0 1.691627 0 1.739959 0 1.788291 0 1.836623 0 1.884956 0 1.933288 0 1.98162 0 2.029952 0 2.078284 0 2.126617 0 2.174949 3.141593 2.223281 3.141593 2.271613 3.141593 2.319945 3.141593 2.368278 3.141593 2.41661 3.141593 2.464942 3.141593 2.513274 0 2.561606 0 2.609939 0 2.658271 0 2.706603 0 2.754935 0 2.803267 0 2.851599 0 2.899932 0 2.948264 0 2.996596 0 3.044928 0 3.09326 0652 mat

CWD C:\SmathFile CurrentDirectory :

θ CWD Dirac wfile 1

θ CWD Dirac rfile :

n 21 :

θangle n el V n el arg : local angle ≡

The plot 'pts' does not recognise θ from the program module. Spool to file.

a b c spec . 8 black 13 mat :

Angle θ a b c spec pts :

θ n 1 el θ n 2 el + 15 red 1 5 mat Angle π π - 4 1 sys