<think>
Okay, the user is asking about vectors in physics and how to solve problems. First, I need to explain what a vector is. In physics, vectors are quantities that have both magnitude and direction. Examples are velocity, force, and displacement.
Next, they want to know how to solve problems. I should break down the steps: identifying components, using coordinate systems, adding or subtracting vectors, and calculating magnitudes or angles. Maybe give examples like adding two vectors at right angles.
Also, common mistakes to watch out for, like confusing scalar and vector quantities, mishandling directions, or miscalculating components. Emphasize the importance of diagrams and proper notation.
I should structure the answer clearly, maybe start with a definition, then move to solving methods, examples, and pitfalls. Keep it easy to follow, use bullet points or sections. Make sure to mention key concepts like vector addition rules (head-to-tail, parallelogram law), and maybe some formulas like the Pythagorean theorem for magnitude.
Check if there's any specific type of problem they might be encountering, but since they didn't specify, keep it general. Offer to help with a particular example if they provide one later. Use simple language and avoid jargon as much as possible.
</think>
**Vektor dalam Fisika**
Sebuah vektor adalah besaran fisika yang memiliki **besar (magnitude)** dan **arah**. Contoh vektor:
- **Kecepatan** (besar 10 m/s arah utara)
- **Gaya** (besar 5 N arah ke atas)
- **Perpindahan** (besar 3 meter arah timur)
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<|channel|>analysis<|message|>We need explain wavelet packet theory, construction, orthogonal complement, subspaces. No citations needed.<|end|>
<|start|>assistant<|channel|>final<|message|>**小波包（Wavelet Packet）概述**
小波包是对传统小波变换的一种推广。
在标准离散小波变换中，先把信号分解为低频子带 \(A_{j-1}\) 与高频子带 \(D_{j-1}\)，随后仅继续细化（下采样）低频子带；而小波包则允许 **对低频和高频两者都进行进一步的分解**。 因此，小波包得到的是一个完整的二叉树结构，每个节点都是一段时间–频率局部化的“基函数”，其总数等于原始信号长度（假设为 \(N=2^{J}\)）。
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给定一个正交小波基 \(\{\psi_{j,k},\,\phi_{0,0}\}\)，其尺度函数和母小波满足：
{\phi(x)=\sum_{k}h_k\,\sqrt{2}\,\phi(2x-k),\qquad\psi(x)=\sum_{k}g_k\,\sqrt{2}\,\phi(2x-k),}其中 \(h_k,g_k\) 为低通/高通滤波器系数，满足正交性条件
\( \sum_k h_k h_{k-2m}= \delta_m,\; \sum_k g_k g_{k-2m}=\delta_m,\;\sum_k h_k g_{k-2m}=0\).