Practical Python Wavelet Transforms (I): Fundamentals

Wavelet Transforms (WT)  or wavelet analysis is probably the most recent solution to overcome the shortcomings of the Fourier Transform (FT). WT transforms a signal in period (or frequency) without losing time resolution.  In the signal processing context, WT provides a method to decompose an input signal of interest into a set of elementary waveforms, i.e. “wavelets”., and then  analyze the signal by examining the coefficients (or weights) of these wavelets.

Wavelets transform can be used for stationary and nonstationary signals, including but not limited to the following:

• noise removal from the signals
• trend analysis and forecationg
• detection of abrupt discontinuities, change, or abnormal behavior, etc. and
• compression of large amounts of data
  • the new image compression standard called JPEG2000 is fully based on wavelets
• data encryption，i.e. secure the data
• Combine it with machine learning to improve the modelling accuracy

Therefore, it would be great for your future development if you could learn this great tool.  Practiclal Python Wavelet Transforms includes a series of courses, in which one can learn Wavelet Transforms using word-real cases. The topics of  this course series includes the following topics:

• Part (I): Fundmentals
• Discrete Wavelet Transform (DWT)
• Stationary Wavelet Transform (SWT)
• Multiresolutiom Analysis (MRA)
• Wavelet Packet Transform (WPT)
• Maximum Overlap Discrete Wavelet Transform (MODWT)
• Multiresolutiom Analysis based on MODWT (MODWTMRA)

This course is the fundmental part of this course series, in which you will learn the basic concepts concerning Wavelet transofrms, wavelets families and their members, wavelet and scaling functions and their visualization, as well as setting up Python Wavelet Transform Environment. After this course, you will obtain the basic knowledge and skills for the advanced topics in the future courses of this series. This course is the prerequisite for the advanced topics of this series.