Wikipedia:Reference desk/Archives/Mathematics/2006 September 17

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September 17

Multidimensional stochastic processes

I am studying stochastic processes in applications to biology. I need to find textbook/publications/other sources regarding multidimensional random walks and multidimensional diffusion. When I say multidimensional I mean that it is really multi: dimension is in thousands. The most popular textbooks, like Cramer-Leadbetter, Feller, Gardiner, Van Kampen, etc. usually after pronouncing word "multidimensional" immediately reduce the problem to dimesion 2, sometimes 3, cite the Polya result regardting recurrence and they are done. So far I failed to find a good treatment of even such simple problem as computation of diffusion coefficient in Fokker Plank equation in N dimensions, Can anybody help? Thank you

How about searching for things like "multidimensional random walk protein"? Does this help? Fokker-Planck equation might have something, but I suspect this is not what you need. --HappyCamper 02:52, 18 September 2006 (UTC)

(Edit conflict) Are you asking about a multidimensional generalization of $u_{t}=u_{xx}+u+x\,u_{x}$? This is called the Fokker-Planck equation in Bluman and Kumei and bears an obvious relation to the diffusion equation. This doesn't answer your question, but have you seen this book?:

• Berg, Howard C. (1983). Random Walks in Biology. Princeton University Press. ISBN 0-691- 00064-6. (1993 reprint)

---CH 03:00, 18 September 2006 (UTC)

(I added a header to the question so that it shows up in the contents. Feel free to improve the title if you can. – b_jonas 18:36, 18 September 2006 (UTC))

Currency matters

Hello sir/mam

what is yen? and how it is converted in rupees ? can u please explain me.

Yours faithfully,

ASHOK.

For yen, see our article Yen. To convert yen to rupees, go to a large bank with a bag of yen and have them convert to rupees. Or if you just want to know the equivalent value, use any of several currency converters on the Internet. --Lambiam^Talk 19:21, 17 September 2006 (UTC)

The easiest one is simply by using google. Type in "100 Japanese yen in Indian rupees" and you'll get a good result. See [1]. Oskar 01:14, 18 September 2006 (UTC)

Google can do that now? Neat. --HappyCamper 02:19, 18 September 2006 (UTC)

That's amazing. I wish I had known about that last week, when I was in Canada, and I could have easily done things like this. Chuck 16:15, 21 September 2006 (UTC)

Sinc Filter?

Could someone please explain to me the concepts behind a Sinc Filter especally how they relate to Anti-Aliasing and the function sin(x)/(x). Any input is appreciated, thanks. HP 50g 23:56, 17 September 2006 (UTC)

The sinc function in the time domain is a windowing function in the frequency domain. Browse around Fourier transform for some goodies - Continuous Fourier transform might be of use too. To prevent aliasing, you want to fit the frequency content of your signal of interest inside the entire window. --HappyCamper 02:19, 18 September 2006 (UTC)

A sinc filter is a lowpass filter (with a really, really sharp cutoff). If you are resampling something below a certain frequency (i.e. scaling an image down), applying a sinc convolution filter beforehand to the original would prevent aliasing of frequencies greater than the new nyquist frequency. - Rainwarrior 07:11, 18 September 2006 (UTC)

It's hard to answer briefly, since this topic is part of a much broader discussion. In digital signal processing, a core theorem is that the frequency response of a (time-invariant, linear) filter is the Fourier transform of the filter impulse response. That is, if we feed the filter a Dirac delta function, essentially an instantaneous unit spike, and record the output for all time, then the Fourier transform of that output describes the effect of the function across frequencies. (To get a sense impression of an impulse response, stand in a large empty room with eyes closed, sharply and loudly clap your hands once, and listen.) Another core fact is that such a filter can only scale or phase shift a sinusoidal input, but not change its frequency.

When a continuous signal is digitally sampled at periodic intervals, the frequency spectrum of the input is replicated periodically as well, with period inversely proportional to the sampling period. This can produce the phenomenon called "aliasing", where high frequencies masquerade as low ones. When this occurs, we can no longer reliably reproduce the continuous signal from the sampled one. To avoid this, we need to select a single period in the frequency domain, to filter the input before we sample. The ideal filter has a simple frequency response, one that looks like a square box.

So now the question is, what filter has a frequency response that looks like a box? Yep, you guessed it. And what is its impulse response? Right again. --KSmrq^T 11:17, 18 September 2006 (UTC)

Thanks for the responses. I be sure to read about the topics you told me about. Thanks. HP 50g 14:52, 18 September 2006 (UTC)

I award KSmrq with this mathematical equation for his comprehensive contributions to the Mathematics Reference Desk. :-) --HappyCamper 15:41, 18 September 2006 (UTC)

$f\left(t\right)={\frac {1}{\sqrt {2\pi }}}\int \limits _{-\infty }^{\infty }F\left(\omega \right)e^{i\omega t}\,d\omega .$