# LOWPASS Forumla

*LOWPASS Forumla*was created by

*BigJohnT*

`( 1-e^(-2*pi*70*.001) )`

However no explanation of what e^ is so I can't complete the formula and match the example so I know if I'm correct or not.

Also on the man page it shows up like this:

`( 1-e**(-2*pi*70*.001) )`

Thanks to who added the examples but I wonder why the examples were not added to the 2.7 documents?

JT

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*PCW*on topic

*LOWPASS Forumla*

so e**n and e^n mean the same thing

( the constant e (2.71828...) raised to the power n )

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*BigJohnT*on topic

*LOWPASS Forumla*

https://en.wikipedia.org/wiki/E_(mathematical_constant)

And now with that bit of information I'm able to complete the equation and it matches Deweys examples.

Thanks Peter

JT

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*rodw*on topic

*LOWPASS Forumla*

PCW wrote: Rod:

0.355849556024592

( 1-e^(-2*pi*70*.001) )

(assuming 1 KHz sampling)

In my case, I had correctly assumed e = 2.718 but was let down by a crappy calculator on my Chromebook. Once I moved to Google Sheets, it was perfect! Thanks for the tip on spreadsheets John!

It would be good if the docs were updated to state:

where:

e = the mathematical constant 2.71828 https://en.wikipedia.org/wiki/E_(mathematical_constant)

and the more normal ^ symbol was used for y

^{n}instead of ** (which I've never seen in use)

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*andypugh*on topic

*LOWPASS Forumla*

softwareengineering.stackexchange.com/qu...ad-of-exponentiation

I think that it was ** in Sinclair basic because the Sinclair character set didn't have ^

If I was in charge I think I might commonise on ** (super-multiplication).

Though that wouldn't work with C, it would have no way to know if a ** b meant "a to the power of b" or "a • the contents of b"

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*andypugh*on topic

*LOWPASS Forumla*

e has an infinite number of non-repeating decimal places.

i is an imaginary number.

Yet e^i.pi = -1

Which is remarkable.

en.wikipedia.org/wiki/Euler's_identity

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*BigJohnT*on topic

*LOWPASS Forumla*

JT

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*BigJohnT*on topic

*LOWPASS Forumla*

rodw wrote: Funny, we were both struggling with this at the same time. On another thread, Peter said for a 70 Hz filter the gain was:

PCW wrote: Rod:

0.355849556024592

( 1-e^(-2*pi*70*.001) )

(assuming 1 KHz sampling)

In my case, I had correctly assumed e = 2.718 but was let down by a crappy calculator on my Chromebook. Once I moved to Google Sheets, it was perfect! Thanks for the tip on spreadsheets John!

It would be good if the docs were updated to state:

where:

e = the mathematical constant 2.71828 https://en.wikipedia.org/wiki/E_(mathematical_constant)

and the more normal ^ symbol was used for y^{n}instead of ** (which I've never seen in use)

That is my plan when I return from holiday.

JT

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*rodw*on topic

*LOWPASS Forumla*

Either way, in my day it was normal to add a definition clause for maths equations as follows:

*Where:*

a ** b means "a to the power of b eg. same as the pow() function in C or Python";

e = the mathematical constant 2.71828 See https://en.wikipedia.org/wiki/E_(mathematical_constant)a ** b means "a to the power of b eg. same as the pow() function in C or Python";

e = the mathematical constant 2.71828 See https://en.wikipedia.org/wiki/E_(mathematical_constant)

And yes I know these natural ratios often have an infinite number of decimal places.

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*PCW*on topic

*LOWPASS Forumla*

For example, SpeedCrunch likes this:

1 - exp(-2*pi*70*.001)

I guess its arguable that the lowpass filter should have done this internally so you just specify the corner frequency

(as long as it doesn't waste time recalculating the 'gain' unless the corner frequency changes)

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