Monthly Archives: June 2012

Monotonically increasing intervals

Problem  A real sequence satisfies for all , where . Let be the length of the th interval. Show that there exists a unique such that for all . Remark  This is a problem that arises from nonlinear quantization in … Continue reading

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3D Matrix Multiplication Tricks

Recently, I came across times 3D matrix multiplication in Matlab. It is for frequency domain signal processing, specifically, frequency-dependent multi-channel Wiener filter. Here, 3D matrix multiplication means 2D matrix multiplication at each frequency (or other parameters):  Given and which are … Continue reading

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Dense Circle

Proposition 1. Let be an irrational number and denote the set of fractional parts of for all . Then is dense in . Proof. We shall first prove that is dense at , then proceed to the whole range of … Continue reading

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