Recommend a wavelet analysis textbook suitable for self-study

I wanted to teach myself about 2 years ago. Wavelet analysis, also read a few of the wavelet analysis of the book. But it is not understood that you see a chapter. No way, who let me level too low. Simply recalled, I have read at least a few books on wavelet analysis:

Tri Jintai "Introduction to Wavelet Analysis"

This book is very famous and many people recommend it. I read the third chapter, learned the integral wavelet transform, the back is not understood, stuck in the second into the small waves.

Xu Chang, "practical Wavelet Method"

After reading the first three chapters, the fourth chapter of multi-resolution analysis to see the half can not understand. This book is too brief, and there is no example, it is difficult to teach yourself.

DaubechiestheTen Lectures on wavelets"

The basic is to see the third chapter will not go down. The difficulty is a bit large, is to do the wavelet analysis of the people read the book, The Mathematical foundation of the people who are slightly worse than the estimate can not understand.

《Fundamentals of Wavelets:theory, algorithms, and Applications"

This book from the perspective of self-study is better than the previous ones, exercises rich, the starting point is also low. I have been learning the first 5 Chapters, the basic understanding of multi-resolution analysis. But the sixth chapter failed to read.

Until this year, from the internet and found a relatively new wavelet analysis of teaching materials, which has aroused my enthusiasm to re-learn the wavelet. This time, I really insisted on reading a book.

Ruch, David K. and Van Fleet, Patrick J.theWavelet theory:An elementary approach with Applications"

This is the book I am recommending today, a Wavelet introductory book that is very suitable for self-study . Starting point very much, having the knowledge of university engineering advanced Mathematics and linear algebra is sufficient.

The first and second chapters of the book are preparatory knowledge, explaining linear space and Fourier transform.

The third chapter and the fourth chapter introduce Haar wavelet and its application. As we all know,Haar wavelet can be said to be the simplest small wave function. Haar wavelet is simple, but the main features of multi-resolution analysis are all possessed. By learning Haar wavelet, the intuitionistic concept of multi-resolution analysis can be established.

The fifth chapter introduces the multi-resolution analysis. The properties of multi-resolution analysis are given. For the sixth chapter constructs the Daubechies wavelet to manufacture many handy tools.

The sixth chapter constructs the Daubechies wavelet. The seventh chapter is The application of Daubechies wavelet.

The eighth chapter explains the biorthogonal scale function and the wavelet, and gives a comparatively detailed introduction of the Riesz base in this chapter. (One of the reasons why the previous books are hard to learn is that the orthogonal scale function and the biorthogonal scale function are mixed together to explain, suddenly the knowledge point is much more, increase the difficulty of learning)

Finally the Nineth chapter explains the wavelet packet.

Overall, the idea of the book is very clear, the formula deduction is very detailed. and gives a lot of very good exercises.

The disadvantage of this book is that it does not introduce continuous wavelet transform (integral wavelets transform).

In fact, in the second chapter after the introduction of Fourier transform, you can add a section to speak of continuous wavelet transform, so the whole book is more complete.

Recently also bought a new wavelet analysis of the book:A Wavelet Tour of signal processing , not carefully read, and so after reading I will write a book review.

Recommend a wavelet analysis textbook suitable for self-study