Re: integration of a continuous function
- From: Rune Allnor <allnor@xxxxxxxxxxxx>
- Date: Mon, 23 Feb 2009 06:21:36 -0800 (PST)
On 23 Feb, 14:23, "Alex_001" <a.bast...@xxxxxxxx> wrote:
Hi,
it's well known that sampling a continuous function according to the
sampling theorem requirements, you get all the information on the
contunuous function just from the samples.
now, if you have to get an accurate estimate of the integral of the
continous function from samples satisfying the sampling theorem
requirements, how can you get a good estimate of such an integral?
I noticed that if you use a sampling frequency close to the Nyquist rate
and apply the definition of integration in the time domain ( sum(Xi*
delta(x))) the value you get for the integral is totally inaccurate...
Numerically integrating continuous functions and sampling
are two different cups of tea. If you have an analytical
expression for the function, you can use integration
schemes with different inherent accuracies, as well as
adaptive integration schemes.
Besides, sampling close to the Nyquist limit is a bad idea
anyway; it would do you no favours with integration eiter.
Rune
.
- References:
- integration of a continuous function
- From: Alex_001
- integration of a continuous function
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