<content> POINTS PER DECADE SNIPPET </content>

3941c9d2-8aef-475c-acb3-c743f29c41c0 49 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.

NPD 30 :

Power of Starting Point

NFS 11 - :

Power of End Point

NFF 4 - :

t NFS NFF NPD PPD eval :

t length 210

t max 9.9 105 -^*

t min 1.297 1011 -^*

k 1 t length range :

Nt t length :

Nt 2.1 102^*

E.o 5105^* :

α 4106^* :

β 480106^* :

t.o β α / ln β α - / :

t.o 1.0058 108 -^*

Norm α t.o * - exp β t.o * - exp - :

Norm 0.9526

t k el 1.297 1011 -^* 1.593 1011 -^* 1.890 1011 -^* 2.187 1011 -^* 2.483 1011 -^* 51 mat

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 5.489 10167 -^*

tplot t EE augment eval :

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tplot <content> FREQUENCY DOMAIN FUNCTION </content>

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

NPD 100 :

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 1200

f max 9.9 109^*

f min 0.01

n 1 f length range :

Nf f length :

Nf 1.2 103^*

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

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

a 0 :

b 1015^:

a f Re 1.301 101 -^*

b f Re 2.499 1016 -^* -

Nf 1.200 103^*

a f Im 0.000

b f Im 1.209 1022 -^*

FREQUENCY SPACING = h

INITIAL GUESS = \[REGION[2211a3d9332b43af8f759101eed4b94b]]\

h ω Nf el ω 1 el - : 6.220 1010^*

NOW REDUCE h BY FACTORS OF 2 UNTIL A GOOD TRANSFORM IS ACHIEVED. THIS MAY REQUIRE A LARGE FACTOR OF 2 TO ACHIEVE A GOOD TRANSFORM .IF YOU CONTINUE TO REDUCE h BEYOND THE OPTIMUM VALUE, THE TRANSFORM WILL BEGIN TO DEGRADE.

m 14 :

h h 2 m^/ : 3.797 106^*

t min 1.297 1011 -^*

t max 9.900 105 -^*

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.

Nt 2.100 102^*

Nf 1.200 103^*

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

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

EvenF k el FilonPlus k el FilonMinus k el + 2 / :

OddF k el FilonPlus k el FilonMinus k el - 2 / :

TOTALFILON k el EvenF k el OddF k el + :

TOTALFILON 2.862 104^* - 2.899 105^* i * - 2.246 104^* - 2.354 105^* i * - 1.811 104^* - 1.979 105^* i * - 1.484 104^* - 1.706 105^* i * - 1.225 104^* - 1.498 105^* i * - 1.013 104^* - 1.334 105^* i * - 8.342 103^* - 1.201 105^* i * - 71 mat

EvenF 8.653 102^* 1.833 103^* i * + 8.835 102^* 1.833 103^* i * + 9.055 102^* 1.832 103^* i * + 9.312 102^* 1.831 103^* i * + 9.606 102^* 1.830 103^* i * + 9.938 102^* 1.829 103^* i * + 61 mat

OddF 2.948 104^* - 2.917 105^* i * - 2.334 104^* - 2.372 105^* i * - 1.902 104^* - 1.997 105^* i * - 1.577 104^* - 1.724 105^* i * - 1.322 104^* - 1.516 105^* i * - 1.113 104^* - 1.352 105^* i * - 61 mat

Feven k el EvenF k el abs :

Fodd k el OddF k el abs :

Filon k el TOTALFILON k el abs :

EvenPlot t Feven augment eval :

OddPlot t Fodd augment eval :

Fplot t Filon augment eval :

Eplot t EE augment eval :

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EvenPlot OddPlot Fplot Eplot 4 1 sys

Frequency Points Per Decade: \[REGION[58986ac99a584d74b389b165803452f6]]\

NPD 1.000 102^*

Frequency Spacing: \[REGION[fdbdc71efc8f43b89869c7d558bc1350]]\

h 3.797 106^*

1 time TSTART - 258.56 s *