When it comes to wavelet analysis, I have to say that I browsed the web for a whole week and still had no clue, but I knew the reason, it was just laziness. I got a headache when I saw the integral transformation, and then I pretended to understand and continued to look down. It turned out that basically all the content of the web page is similar (as it is), I have not made any progress at all, just know, oh, wavelet analysis and Fourier transform is related, what is the relationship? complex relationships.
In short, it is a very headache, that is, I know that I should study it, but I just can't watch it. In the end, I had no choice. I was in a hurry to hand in the task. I started to worry. I wanted to find some videos to start watching. However, all the videos, including blogs, start from Fourier transform, but in fact , I don't even know what the Fourier transform is.
So, at the beginning, I started with the exercises. There is an analyzer about wavelet analysis in matlab, and Zhang Defeng's matlab wavelet analysis tutorial is recommended on the Internet. I think it is good, and then I try it as a tutorial. It should be noted that the wavelet analysis matlab is packaged, so it is good to use it directly. Therefore, it is only a thin chapter in Zhang Defeng's book. I just found a time series and tried it out. Doorway.
The wavelet analysis is mainly divided into two parts. Assuming that I already have all the code for the wavelet analysis implementation, then I need to do two important things with the wavelet analysis:
(1) Find a suitable wavelet function for analysis
(2) Explanation of the obtained result is to explain what effect the result has
In fact, my above conclusion is based on the fact that I want to find some data laws based on wavelet analysis, so I draw such a conclusion. But in fact, wavelet analysis can achieve some more purposeful applications, such as signal enhancement, signal compression, signal denoising and other applications, they pay more attention to the internal mechanism of the wavelet function.
Back to the topic, let's talk about wavelet analysis
I can't get out of the cliché. When I talk about wavelet analysis, I still start with Fourier, but I will try my best to make everyone understand. However, all of this is related to the related concepts of vectors and series. It does not need to be very proficient, but cannot be questioned with the concepts of vectors and series.
Knock on the blackboard! Start now.
First of all, let's take a look at the conditions that the wavelet function must meet - there is a square integrable function space .
The square integrable function space is specifically:
specific understanding process
We all know the formula for the distance between two points:
That is, the modulo length of the two points A and B.
The vertical distance between the two functions when X is equal is:
The modular length between those two functions is:
where X and Y are both functions of t.
That is to say, we regard the square integrable space as such a space that can realize the modular length of two functions.
The first time I use it, the format and typesetting are not very good, so let's write these first! I will do my best.
Bibliography:
Wavelet Analysis Theory and Implementation in MATLAB R2007 Ge Philosophy, Javert O241.86 25
MATLAB Wavelet Analysis (Second Edition) Zhang Defeng 0241.86 32=2
Ten Lectures on Practical Wavelet Analysis Yu Fengqin O241.86 39
Hydrological wavelet analysis Wang Wensheng Ding Jing Li Yueqing P333 2