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www.earlevel.com | ||
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www.jeremykun.com
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| | | | | In our last primer we saw the Fourier series, which flushed out the notion that a periodic function can be represented as an infinite series of sines and cosines. While this is fine and dandy, and quite a powerful tool, it does not suffice for the real world. In the real world, very little is truly periodic, especially since human measurements can only record a finite period of time. Even things we wish to explore on this blog are hardly periodic (for instance, image analysis). | |
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cyclostationary.blog
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| | | | | Using complex-valued signal representations is convenient but also has complications: You have to consider all possible choices for conjugating different factors in a moment. | |
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digitalfilms.wordpress.com
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| | | | | Tour any classic analog recording studio and two pieces of outboard hardware tend to show up time after time: a Pultec-style equalizer and a tube-based, opto compressor, such as an LA2A or a CL 1B. Modern reproductions of these classic items can be purchased for tidy sums from companies like Tube-Tech, Warm Audio, and Universal... | |
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djalil.chafai.net
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| | | This post is mainly devoted to a probabilistic proof of a famous theorem due to Schoenberg on radial positive definite functions. Let us begin with a general notion: we say that \( {K:\mathbb{R}^d\times\mathbb{R}^d\rightarrow\mathbb{R}} \) is a positive definite kernel when \[ \forall n\geq1, \forall x_1,\ldots,x_n\in\mathbb{R}^d, \forall c\in\mathbb{C}^n, \quad\sum_{i=1}^n\sum_{j=1}^nc_iK(x_i,x_j)\bar{c}_j\geq0. \] When \( {K} \) is symmetric, i.e. \( {K(x,y)=K(y,x)} \) for... | ||
