<content> POINTS PER DECADE SNIPPET </content>

3941c9d2-8aef-475c-acb3-c743f29c41c0 11 Reg Curry 3 0 true false 0 0 decimal

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

FILON TRAPAZOID TRANSFORM

TSTART 1 time :

POINTS PER DECADE SNIPPET

NUMBER OF POINTS PER DECADE = NPD:

POWER OF START POINT = NFS

POWER OF END POINT = NFF

TOTAL NUMBER OF POINS = Nt

NFS NFF NPD PPD Δ 9.9 1 - NPD / : i 1 NPD range j 1 NFF NFS - (range FF i j el 1 i Δ * + (10 j NFS + 1 - (^* : for for ColF.1 FF 1 col : V ColF.1 : i 2 FF cols ((range V V FF i col stack : for V 61 line :

EXAMPLE: CHANGE THESE TO FIT YOUR NEEDS

NUMBER OF POINTS PER DECADE = NPD: \[REGION[ec6716e9ac63413ca84b0883b5ee9e3a]]\

NPD 20 :

POWER OF START POINT = NFS \[REGION[4b748ee7eedd4ff3aface9322cf8812a]]\

NFS 9 - :

POWER OF END POINT = NFF \[REGION[da59fb5711124a75aca6bb88497c0a1c]]\

NFF 1 - :

t NFS NFF NPD PPD eval :

t length 160

t max 9.9 102 -^*

t min 1.45 109 -^*

k 1 t length range :

Nt t length :

Nt 1.6 102^*

<content> TIME DOMAIN FUNCTION </content>

Define more time points per decade using snippet.

Points/Decade =

NPD 50 :

Power of Starting Point

NFS 11 - :

Power of End Point

NFF 3 - :

t NFS NFF NPD PPD eval :

t length 400

t max 9.9 104 -^*

k 1 t length range :

Nt t length :

Nt 4102^*

E.o 5105^* :

α 4106^* :

β 480106^* :

t min 1.18 1011 -^*

t.o β α / ln β α - / :

t.o 1.0058 108 -^*

Norm α t.o * - exp β t.o * - exp - :

Norm 0.9526

k 1 Nt range EE k el E.o Norm / e α t k el * -^e β t k el * -^- (* : for

EE max 5105^*

EE min 0

tplot t EE augment eval :

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tplot <content> FREQUENCY DOMAIN FUNCTION </content>

POINTS PER DECADE = NPD: \[REGION[ec6716e9ac63413ca84b0883b5ee9e3a]]\

NPD 20 :

POWER OF START POINT = NFS \[REGION[4b748ee7eedd4ff3aface9322cf8812a]]\

NFS 2 - :

POWER OF END POINT = NFF \[REGION[da59fb5711124a75aca6bb88497c0a1c]]\

NFF 10 :

f NFS NFF NPD PPD eval :

f length 240

f max 9.9 109^*

f min 0.01

n 1 f length range :

Nf f length :

Nf 2.4 102^*

ω n el 2 π * f n el * :

Eω n el E.o Norm / 1 α i ω n el (* - / 1 β i ω n el (* - / - (* :

REω n el Eω n el Re abs :

REω max 1.301 101 -^*

REω min 6.457 108 -^*

Rplot f REω augment eval :

IEω n el Eω n el Im abs :

Iplot f IEω augment eval :

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Rplot Iplot 2 1 sys

DEVELOP FILON TRANSFORM

ω f E.o Norm / 1 α i ω * - / 1 β i ω * - / - (* :

Nf 2.400 102^*

a 0 :

b 1030^:

a f Re 1.301 101 -^*

b f Re 2.499 1046 -^* -

a f Im 0.000

b f Im 0.000

Upper Frequency Index NU; Lower Frequency Indes = NL \[REGION[05c247e12ee841c98551df23e7cd039b]]\ \[REGION[8be1b8a521a34388bba236eb1a81b763]]\

NU Nf :

NL 1 :

FREQUENCY SPACING = h

h ω NU el ω NL el - : 6.220 1010^*

t min 1.178 1011 -^*

t max 9.900 104 -^*

k 1 t length range :

t C 1 t 2^h 2^* / 1 e i t * h * -^- i t * h * - (* eval n Nf - ≡ 1 t 2^h 2^* / 1 e i t * h * -^- i t * h * + (* eval n Nf ≡ 1 t 2^h 2^* / 2 e i t * h * -^- e i t * h * +^- (* eval cases :

THIS FORM OF C[T] IS OBTAINED BY THE cases FUNCTION. THE RESULT IS THE SAME IF I USE A STRING OF if..else PROGRAMMING FUNCTIONS.

UNLIKE MATHCAD, EFilon IN SMATH IS COMPLEX. SO SOMETHING IS DIFFERENT IN HOW THE CALCULATIONS ARE DONE IN SMATH VERSUS MATHCAD. THE MATHCAD RESULT IS A REAL VECTOR. ALSO, SMATH IS TERRIBLY SLOW. IF I INCREASE THE NUMBER OF POINTS TO GET A GOOD TRANSFORM, MATHCAD COMPLETES IN 14 SECONDS. SMATH NEVER COMPLETES; THEREFORE, SMATH IS NOT GOOD FOR THESE KINDS OF CALCULATIONS.

EFilon k el h 2 π * / t k el C e i t k el * n * h * -^n h * f * (* n Nf - Nf sum * eval :

RAns EFilon Re :

IAns EFilon Im :

ImAns k el IAns k el abs :

ImAns max 2.759 102 -^*

tplot2 t EE augment eval :

rplot t RAns augment eval :

iplot t ImAns augment eval :

`

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rplot iplot tplot2 3 1 sys

1 time TSTART - 50.52 s *