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Dear Jun
Thanks for your reply. even if we know the areas where there Fourier series used, it's hard to understand in what sense it helping to solve the problems. for eg.
Jun Du wrote: Computer science: data compression, pattern recognition
how it solves the problems in the quoted domain?
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Firstly, you need to understand the concepts of fourier series. Secondly, you need to then to have a thorough understanding of the domain you are interested in. Only then you will understand how concepts of fourier series can be used to solve problems.
If you are truly interested in fourier etc, then my recommendation will be to download a DSP pdf book from Analog Devices titled "The Scientist & Engineer's Guide to Digital Signal Processing". This is a great book and any DSP engineer will recommend it. Just ask Eric Jaccobson. Here is the URL:
http://www.analog.com/processors/learning/training/dsp_book_index.html
My other recommendation will be to learn matlab to gain an understanding in programming aspects of fourier series. This was the best way I had learnt fourier, laplace transforms etc.
My final recommendation will be to get yourself a engineering mathematics book i.e. Advanced Engineering Mathematics by Peter O'Neil here is a link: http://www.amazon.com/gp/product/0534400779/102-2429887-6445756?v=glance&n=283155 I have used this book and its an excellent reference in learning fourier laplace etc.
I dont want to sound harsh but to learn fourier requires dedication and it wont happen via osmosis nor will it happen overnight.
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thanks for your reply.
actually I'm studying about Fourier series as part of my exams.
so I wanted to get some detailed information on same. yea I heard that image processing, video filters are all based on Fourier series 
but your replies are something more informative.
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ekynox wrote: I dont want to sound harsh but to learn fourier requires dedication and it wont happen via osmosis nor will it happen overnight.
As a side note to his comment, I would recommend learning their mathematical properties prior to learning their applications. If you understand what the series (be it Fourier or Laplace) does for you mathematically, you won't have any problem understanding a specific application of it.
If you decide to become a software engineer, you are signing up to have a 1/2" piece of silicon tell you exactly how stupid you really are for 8 hours a day, 5 days a week
Zac
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Sarath,
Ekynox has posted a great answer. As you know, Fourier is just one of the spectral analytical methods used in science and engineering. Other frequently used ones include Laplace, wavelet, etc. Learning Fourier Analysis is not hard at all, but knowing when, where and how to apply it to certain problems is. This demands proper domain knowledge and experience.
As a trivial example, take pattern recognition (PR). With PR, we often need to compare a 2D data array with the reference so that we can find similarities or differences of the two patterns. Using Fourier analysis, instead of compare the raw data directly, we can change to compare a selected set of wave components. Thus, by reducing the amount of data we need to compare, we can speed up the PR significantly.
Similar applications in data compression (DC). By expanding to Fourier series, we can (approximately) represent the original data set by less amount of data (wave component coefficients).
Best,
Jun
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Hii,
I was wondering if anybody has an algorithm, pseudocode, or implementation of obtaining the eigen values.
Also if anybody has an algorithm for applying the SVD on a matrix.
SVD is short for Singular Value Decomposition.
Thanks in advance.
Cheers,
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I think you can refer to Matlab for some help.
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A free e-book:
Numerical Recipes[^]
Has *extensive* algorithms on all aspects of what you are looking for. The algorithms are written in C, but you should be able to port them if needed.
Singular value decomposition[^]
As for eigenvalues, it depends on the form of your matrix. See Chapter 11 of Numerical Recipes in C for a discussion of tri-diagonal, symmetric, and Hermitian matrices because when you say "obtaining eigenvalues", that is extremely general.
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What's the use of Laplace?
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Laplace is a mathematician[^], and looking at his age, i don't think you'll be able to do anything with him 
what do you mean by "using Laplace" ? which theorem ? which formula ??
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toxy
sometimes your jokes makes me laugh...
but I expect some common sense tooo
-- modified at 8:52 Friday 18th August, 2006
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but actually, the last question was a serious one... no joke in fact... 
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There is the Laplace-Experiment and the Moivre-Laplace Approximation.
The Laplace-Experiment is a combinational model for finite elementary events with the same probability.
The combinational model (Ω, ε, P) consists of:
i) the finite set Ω = {ω1, ..., ωn) (the set of probabilities)
ii) the events ε = Pot(Ω) (the potency set of Ω)
iii) the measure of probabilities P(E) = |E| / |Ω|
The elements ωi of the space of samples Ω are named elementary probabilities.
For example:
The probability that for lottery where are 49 number the number '6' will fall, is the 1/49 (there are 49 numbers, the probability for each number is 1/49).
You have to calculate all positive events by all possible events.
For 6 given numbers out of 49 its 49 above 6 = 49! & (6! · 43!) = 13 983 816 so P(E) = 1/13 983 816.
If you want to know something about Moivre-Laplace approximation, just ask.
Regards,
Ingo
------------------------------
PROST Roleplaying Game
War doesn't determine who's right. War determines who's left.
"Would you like us to drop a bomb on you too? We have 10,000 of them!"
- espeir
"Perhaps we should lend them a nuke or two."
- espeir
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In addition to the other answers, there is also the Laplace transform
So, if you want a clear answer, you need to ask a much more specific question: Laplace, what is it you are looking for ? In which context ? What do you mean by 'use' ?
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Laplace did a lot of things. If you are referring to Laplace Transforms, they are very helpful for solving certain types of differential equations.
If you decide to become a software engineer, you are signing up to have a 1/2" piece of silicon tell you exactly how stupid you really are for 8 hours a day, 5 days a week
Zac
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Some months have 30 days, Some months have 31 days. How many Months have 28 days?
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dan neely wrote:
All 12 of them.
Yeppers
I'd like to help but I don't feel like Googling it for you.
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This is no maths. Post this on the board for "Old and silly jokes" not here. 
------------------------------
PROST Roleplaying Game
War doesn't determine who's right. War determines who's left.
"Would you like us to drop a bomb on you too? We have 10,000 of them!"
- espeir
"Perhaps we should lend them a nuke or two."
- espeir
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...when I travel and meet foreign people, it happens to ask - sometimes - stupid things. They, kindly say:
- That's a good question...
I think that you posted a good question...;P
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Divide 30 by half and add 10, so what will you get?
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Integer or floating point arithmetic? 
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how old are you ? 
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