Time-frequency Analysis Math 211a—spring 2006

Elements of Density Estimation Math 6070 , Spring 2006

An Optimal Example for the Balian-Low Uncertainty Principle

We analyze the time-frequency concentration of the Gabor orthonormal basis G(f, 1, 1) constructed by Høholdt, Jensen, and Justesen. We prove that their window function f has near optimal time and frequency localization with respect to a non-symmetric version of the Balian-Low Theorem. In particular, we show that if (p, q) = (3/2, 3), then R |t| |f(t)|dt < ∞ and R |γ| | b f(γ)|dγ < ∞, for 0 < ≤ ...

Inequalities on time-concentrated or frequency-concentrated functions

We obtain an inequality on a measure of the spread in time of periodic functions that are concentrated in frequency, i.e. all but a fixed finite number of Fourier coefficients vanish with meansquared error up to . We characterize an extremal function and give an asymptotic formula for the measure of spread of this extremal function as approaches 0. We also consider the corresponding problem for...

نقش متغیرهای شخصی در پیشرفت ریاضی با توجه به نظریه شناختی - اجتماعی

This study examined the role of self-efficacy, math attitude math anxiety, and previous math achievement in math achievement by using path analysis. The sample consisted of 366 third grade guidance school students. Fennema&rsquo;s Math Attitudes Scale, Shokrani&rsquo;s Math Anxiety, a combind test of two Scale of Pajares&rsquo;s Math Selfefficacy, math scores of last year, and final math scores...

Empirical Processes , and the Kolmogorov – Smirnov Statistic Math 6070 , Spring 2006

1 Some Basic Theory 1 1.1 Consistency and Unbiasedness at a Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 The Kolmogorov–Smirnov Statistic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Order Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 Proof of the Kolmogorov–Smirnov Theorem . . ....