Time-Frequency Uncertainty

The Uncertainty Principle is first proposed by Heisenberg to describe that you can’t precisely measure the position and momentum of a particle at the same time. This principle is well known in quantum physics. It then became a very “general” idea, and can also be used in the field of signal processing. In this article, I will describe the time-frequency uncertainty principle theorem and then show the proof.

直观理解 Wavelets

刚开始接触小波变换的时候完全搞不清楚其基本原理,对“多分辨率分析”、“时频分辨率”这些术语更是云里雾里。网络上好的教程极度稀缺。这时候就必须强烈推荐 The Wavelet Tutorial:http://users.rowan.edu/~polikar/WTtutorial.html ,真正做到了深入浅出,通读下来让人感觉受益匪浅。

Time Resolution

DTCWT Lowpass Shape

双树复小波变换 (Dual-Tree Complex Wavelet Transform, DTCWT) 低频系数矩阵的尺寸一致很让人困惑,许多文献都重点讨论了高频部分(6 个方向),而对低频部分的介绍较少。对一个单通道,大小为 (N, N) 的二维图像做一次 2D DTCWT 变换,高频部分应该有 6 个,尺寸均为 (N/2, N/2) 其中每个都是复数。那么低频部分呢?


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