/sci/ - Science & Math

[Anonymous No.4973773]

Hi fellow /sci/entists,

I'm doing some research on the modeling of piezo electric sensors. When such a sensor gets an impulse, a decaying sinusoidal pulse is generated as <span class="math">\sin(x)e^{-x}[/spoiler].

I'd like to express a pulse train in an equation, with a pulse taking place every 4 minutes. The easiest way for this is convolution of the signal with a dirac pulse train: <div class="math">f(x)= \delta(kx) * sin(x)e^{-t}</div> However, this leaves me with a discrete function which is hard to use in future processing. The only alternative I can think of is a Fourrier series, but that's even more cumbersome...

Does anyone happen to know how to express the function shape of the lower graph in the drawing, as a continuous function? Thanks for the input guys!

[Anonymous No.4973807]

bump for science

[Anonymous No.4973862]

>dirac pulse
>discrete

The dirac delta is a continuous function, Kronecker delta is the discrete.

Why not be lazy and write the answer out in terms of the Heaviside step function...
<span class="math">f(t)= ∑_k u(kt) sin(t-k)e^{-t+k}[/spoiler]

http://en.wikipedia.org/wiki/Heaviside_step_function

[Anonymous No.4973864]

>>4973862
>dirac delta
>continuous function
It's not even a function, so where do you get the idea that it's a continuous one?

[Anonymous No.4973866]

bumping for science. I have no idea what any of this means.

[Anonymous No.4973876]

>>4973864
continuous <span class="math"> \bf TIME[/spoiler] function i.e. 'defined' for all t∈ℝ. Stop being a fucking aspie

[Anonymous No.4974004]

>>4973876
Defined for all t does not imply it's continuous. Stop being so wrong.

[Anonymous No.4974013]

>>4974004
Nor that it's a function for that matter.

Lol engineers.

[Anonymous No.4974014]

>>4973866
You'll have some idea after you start university.

[Anonymous No.4974024]

pro tip: convolution with inpulse train (saw function)

[Anonymous No.4974031]

The Dirac delta is not a function. Deal with it.

[Anonymous No.4974036]

>>4974031
approximation with bounded integral over its frequency components not good enough mang?

no on will notice ;)

[Anonymous No.4974041]

>>4974004
δ(t)=Lim n↦∞ sin(t/n)/t=sinc(t/n)/n

pick n big enough and you have your continuous delta function.

[Anonymous No.4974044]

>>4974041
This is not how limits work, EK.

[Anonymous No.4974046]

>>4974041
Oh engineers. You should just stick to what you do best (insert gay joke), and let mathematicians and physicists handle the math. Learn to distinguish between pointwise and uniform convergence.

[Anonymous No.4974047]

>>4974041
you mean a->0 and a small enough

[Anonymous No.4974050]

>>4974046
This wasn't the only mistake she made. Read again and shit bricks.

[Anonymous No.4974053]

>>4974050
I had already noticed. But it was obvious from the context that they meant to write lim sinc(t/n)/n. It's just a fuck up in notation, not very interesting. I used to make this mistake all the time, and always ended up writing really small lims after the = sign.

Also, I doubt it's EK, because she probably doesn't know about sinc. Hell, she probably doesn't even know what a dirac delta is.

[Anonymous No.4974056]

>>4974041 hurr durr
Why are there people on a science board who have yet to take analysis?

[Anonymous No.4975200]

>>4973862

OP here, thanks for the input Anon. I also thought of a similar solution as described in signal processing theory, but later on in my study I'd like to integrate the function... hence why I want a continuous <span class="math">f(x)[/spoiler] and try to avoid <span class="math">\sum[/spoiler].

[Anonymous No.4975208]

>>4973864

The Dirac Delta function is uniquely defined in every point, doesn't that make it a continuous function?

[Anonymous No.4975216]

>>4975208
0/10

[Anonymous No.4975218]

>>4974036

OP here, could you please elaborate what you mean with this? Aren't you referring to the function's Fourier series?

[Anonymous No.4975225]

>>4975208
The function <span class="math">f(x) = x^{-1}[/spoiler] is also defined in every point (with <span class="math">f(0) = \infty[/spoiler]) but that doesn't make it continuous I thought...

[Anonymous No.4975236]

>>4974041

A sinc function is decaying linearly, while the impulse in this example decays exponentially. Learn reading the question, EK.

[Anonymous No.4975250]

>>4974013

OP here and engineer indeed... sorry for sacrificing your math, I'm just looking for an easily integratable function to express the piezo electric pulses. Hence it doesn't have to be exact, as long as it more or less looks like the physical phenomenon I'm happy.

[Anonymous No.4975681]

< pic related

[Anonymous No.4975720]

>>4975250
you know what your thing reminds me of, OP? diffraction figures cut in half.

[Anonymous No.4975730]

>>4975720
>>4975720
I meant interferograms

[Anonymous No.4975741]

i don't know much about the math you guys are doing, but if you want to take a look at peizo electric sensors a good place to start would be an "O2" sensor in a car. it's basicly an emissions control input and and fuel trim input

[Anonymous No.4976347]

Good news! It's not necessary anymore to start a campaign against failbook and plan its destruction. It seems to be doing that on its own.

Word is out that the failbook share dropped to $20, about half of its initial opening value of $38.

It looks like time will erase our eye sore, dear friends.

[Anonymous No.4976354]

>>4975741

OP here, thanks for the input Anon. I don't see how piezo electric sensors can be used to control emission and fuel injection. Piezo electric sensors must be activated with a mechanical impulse, e.g. a physical deformation in the crystal structure.

I'm interested in your thoughts, could you please elaborate?

[Anonymous No.4976381]

>the Dirac delta is not a function they said
>use it as it if were one anyway