176844ff-e2f9-45aa-a4c1-a7a7254be497 15 6 5 auto

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An application of Fourier padding "0's "

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

V 1.137 1.106 0.228 i * - 1.016 0.439 i * - 0.875 0.617 i * - 0.694 0.748 i * - 0.488 0.823 i * - 0.275 0.839 i * - 0.072 0.796 i * - 0.105 - 0.7 i * - 0.242 - 0.563 i * - 0.328 - 0.397 i * - 0.359 - 0.22 i * - 0.334 - 0.048 i * - 0.257 - 0.102 i * + 0.139 - 0.216 i * + 0.007 0.283 i * + 0.166 0.297 i * + 0.321 0.256 i * + 0.455 0.164 i * + 0.553 0.031 i * + 0.605 0.132 i * - 0.602 0.309 i * - 0.544 0.482 i * - 0.431 0.636 i * - 0.273 0.754 i * - 0.081 0.825 i * - 0.129 - 0.839 i * - 0.341 - 0.793 i * - 0.536 - 0.689 i * - 0.699 - 0.533 i * - 0.816 - 0.337 i * - 0.877 - 0.115 i * - 0.877 - 0.115 i * + 0.816 - 0.337 i * + 0.699 - 0.533 i * + 0.536 - 0.689 i * + 0.341 - 0.793 i * + 0.129 - 0.839 i * + 0.081 0.825 i * + 0.273 0.754 i * + 0.431 0.636 i * + 0.544 0.482 i * + 0.602 0.309 i * + 0.605 0.132 i * + 0.553 0.031 i * - 0.455 0.164 i * - 0.321 0.256 i * - 0.166 0.297 i * - 0.007 0.283 i * - 0.139 - 0.216 i * - 0.257 - 0.102 i * - 0.334 - 0.048 i * + 0.359 - 0.22 i * + 0.328 - 0.397 i * + 0.242 - 0.563 i * + 0.105 - 0.7 i * + 0.072 0.796 i * + 0.275 0.839 i * + 0.488 0.823 i * + 0.694 0.748 i * + 0.875 0.617 i * + 1.016 0.439 i * + 1.106 0.228 i * + 631 mat :

Dirac 1 2.828427 0 5.196152 000000000000000000000000000000000000000000000000000000000000641 mat :

L H N xd U 0 : dx H L - N / : i 1 N range U i el L dx - (dx i * + : for U 21 line 31 line :

Filter 126 - 314 mat transpose :

Both Filter & α are user at will

N 64 :

α 1.5 :

Dirac n 1 N range n Filter rows ≤ Dirac n el Filter n el (α^Re : Dirac n el 0 : if for Dirac 21 line :

Transit: 1. Dirac vector 2. ifft(dirac) => V

N V length :

H 5 :

L 0 :

U L H N xd :

Vectorise 'V' to get Dirac Filter F t U : Ω V mat2sys abs sys2mat : t Ω augment 31 line :

scale 1 F 12 el / :

Scale Ω , span/center 'V' [H,L]

0 scale F * 2 1 sys

scale 0.879507

Our Fourier "ifft" does the project perfect. This application is sanity wrt 0's padding. Excellent for Edu. Not very practical to experiment different Fillter and/or user 'α' because we have to transit each experiment and the vector are not Mathcad table style.

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 :

a b c spec . 10 black 13 mat :

pts scale F * a b c spec pts :

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

0 scale F * pts 3 1 sys

Imagination is the limit to construct discrete filters of user shape to suit specific application.

jmGiraud: 2016-01-10

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

θ 2 el V 2 el arg :

θ 2 el ° 11.64825 -

Phase_mod_π i 2 V rows range φ i el V i el arg : x i el U i el : 21 line for x φ augment 21 line :

Phase_mod_π