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