理解小波理论的先决条件
我拥有计算机科学学位，并且修读了以下数学课程。
- 微积分 I
- 微积分 II
- 离散数学和数论
- 线性代数
- 概率逻辑
- 自动
- 机理论
为了准备学习小波（重点是实现小波变换），我还应该学习哪些其他课程？
编辑：
看起来这因与“编程相关”无关而被关闭。那是错误的！
小波变换是一种非常常见的图像处理技术，在H.264和JPEG2000中都有使用。图像处理超出了 StackOverflow 的范围吗？
I have a degree in computer science and I have taken the following math courses.
- Calculus I
- Calculus II
- Discrete Mathematics and Number Theory
- Linear Algebra
- Probability
- Logic
- Automata Theory
What other courses should I take in order to prepare for studying wavelets, with a focus of implementing wavelet transforms?
EDIT:
Looks like this was closed for not being "programming related". That is wrong!
Wavelet transform is a very common image processing technique, it's used in H.264 and JPEG2000. Is image processing beyond the scope of StackOverflow?
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除了您已经掌握的知识之外，我还会推荐信号处理或一些涵盖傅里叶变换等的类似课程。除了可用作小波的基础之外，傅里叶理论还将为您提供一种查看数据的新方法，这种方法通常很有用。小波可能会成为更高级信号处理课程的一部分。
On top of what you've got there already, I would recommend signal processing or some similar course that covers Fourier transforms and the like. Besides being useful as a foundation for wavelets, Fourier theory will give you a new way of looking at data that is often useful. Wavelets will probably be part of the curriculum for more advanced signal processing courses.
线性代数和微积分可能对你有帮助，但除此之外就没有什么帮助了。您还需要了解复分析和微分方程。
Linear algebra and calculus may help you there, but not much else. You'll also want to look at complex analysis and differential equations.
在我看来，你应该开始学习小波变换，然后找出其中的差距。他们并没有那么参与。傅里叶变换等只是正交基的一个例子，它是线性代数的一部分。
It sounds to me like you should just start learning about wavelet transforms and then figure out gaps along the way. They're not that involved. Fourier transforms etc are just an example of an orthogonal basis that is part of linear algebra.
取决于您是想学习离散小波变换还是连续小波变换。如果是离散的，那么您将需要基本的傅立叶理论、线性代数和复数论。如果连续，那么您将需要先进的傅立叶理论和固定相近似。
如果您想进行研究，那么我建议学习离散和连续。大多数人只详细了解其中之一，这严重阻碍了研究。这里有很多异花授粉的机会。
Depends whether you want to learn about discrete or continuous wavelet transforms. If discrete then you'll need basic Fourier theory, linear algebra and complex number theory. If continuous then you'll need advanced Fourier theory and stationary phase approximations.
If you want to do research then I'd recommend learning both discrete and continuous. Most people only know one or the other in detail and it is seriously stifling research. There is a lot of opportunity for cross pollination here.