Recent content by thrillhouse86

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    Limit involving dirac delta distributions

    Sorry I mean to evaulate: \lim_{x\to 0^{+}} \frac{\delta'(x)}{\delta''(x)}
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    Limit involving dirac delta distributions

    Hey All, I am trying to evaluate the limit: \lim_{x\to 0^{+}} \frac{\delta''(x)}{\delta''(x)} Where \delta'(x) is the first derivative of the dirac distribution and \delta''(x) is the second derivative of the dirac distribution. I thought about the fact that this expression...
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    I think this is a dominated convergence theorem question

    Thanks mathman, I think I expressed the question wrong. I don't really care (for the purposes of this post) about when the expression will be zero, I am more interested in understanding what the mathematician was talking about with the theorem of dominated convergence. Lets say the function...
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    I think this is a dominated convergence theorem question

    Hey All, I have the following integral expression: y = lim_{h\to0^{+}} \frac{1}{2\pi} \left\{\int^{\infty}_{-\infty} P(\omega)\left[e^{i\omega h} - 1 \right] \right\} \Bigg/ h And I am trying to understand when this expression will be zero. I was talking to a mathematician who said...
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    Derivation of Vasicek Entropy Estimator

    Hey All - I am trying to solve a problem that should be really easy (at least every paper I read says the step is!) I'm trying to understand where the Vasicek entropy estimator comes from: I can write the differential entropy of a system as: H(f) = -\int^{\infty}_{-\infty} f(x)log(f(x))dx...
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    Is this integral possible to solve

    Thanks for the help guys - can you briefly explain (or point me towards) why real roots are a problem ? is it something to do with branch points in the complex plane ?
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    Is this integral possible to solve

    Hi I was wondering if anyone has seen this integral in a table, or indeed knows if it is possible to solve: \int^{\infty}_{-\infty} \frac{x^{2}}{ax^{4} + bx^{2} + c} every table I look at seems to only go up to the first power of x in the numerator Thanks, Thrillhouse
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    Correlation functions

    In the case of autocorrelation functions - have a look at any material you can on Gauss-markov processes - a book with a little bit on them is "Introduction to Random Signals and Applied Kalman Filtering" by Brown & Hwang
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    Difference between Renewal Process and Poisson Processes

    Hey All, Can someone please explain to me the difference between a Poisson Process and a Renewal Process ? is it just that the Holding times for Poisson processes are exponential and Holding times for Renewal Processes are any kind of probability distribution (as the wiki page seems to imply)...
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    Conceptual Problem with Convolution Theorem

    Thanks AlpehZero - I guess it always helps to go back to the fundamental definitions ...
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    Conceptual Problem with Convolution Theorem

    Hi - I'm trying to work out the following convolution problem: I have the following integral: \int^{\infty}_{-\infty}p(x)U(x)e^{-i \omega x}dx Where p(x) is any real function which is always positive and U(x) is the step function Obviously this can easily be solved using the...
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    Fourier Transform of One-Sided Convolution

    Hey Ray, yeah I've noticed that Laplace transform one, but I really need the Fourier transform of this one sided one. I was hoping that the heaviside function would kill the -ve bounds of my Fourier Transform so that it would look like a Laplace transform, but in order to do that I need to...
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    Fourier Transform of One-Sided Convolution

    Hi, Can anyone tell me if there is a convolution theorem for the fourier transform of: \int^{t}_{0}f(t-\tau)g(\tau)d\tau I know the convolution theorem for the Fourier Transform of: \int^{\infty}_{-\infty}f(t-\tau)g(\tau)d\tau But I can't seem to find (or proove!) anything...
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    Asymptotic Form of an Integral

    Hey: I have an integral of the form: \int^{\infty}_{-\infty}\frac{x(\omega)}{\sigma^{2} + \omega^{2}}d\omega I'm wondering if this integral is a candidate for asymptotic analysis. My rationale is that as omega increases to either positive infinity or negative infinity, the function being...
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