Practical Python Wavelet Transforms (II): 1D DWT

Real-World Projects with PyWavelets, Jupyter notebook, Numpy, Pandas, Matplotlib and Many More

The 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 forecasting

• 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.  Practical 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): Fundamentals

• Part (II): 1D 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 second part of this course series. In this course, you will learn the concepts and processes of single-level and multi-level 1D Discrete Wavelet Transforms through simple easy understand diagrams and examples and two concrete world-real cases and exercises. After this course, you will be able to decompose a 1D time series signal into approximation and details coefficients, reconstruct and partial reconstruct the signal, make noise reduction from the data signal, and visualize the results using beautiful figures.