Book Image

Python Data Analysis Cookbook

By : Ivan Idris
Book Image

Python Data Analysis Cookbook

By: Ivan Idris

Overview of this book

Data analysis is a rapidly evolving field and Python is a multi-paradigm programming language suitable for object-oriented application development and functional design patterns. As Python offers a range of tools and libraries for all purposes, it has slowly evolved as the primary language for data science, including topics on: data analysis, visualization, and machine learning. Python Data Analysis Cookbook focuses on reproducibility and creating production-ready systems. You will start with recipes that set the foundation for data analysis with libraries such as matplotlib, NumPy, and pandas. You will learn to create visualizations by choosing color maps and palettes then dive into statistical data analysis using distribution algorithms and correlations. You’ll then help you find your way around different data and numerical problems, get to grips with Spark and HDFS, and then set up migration scripts for web mining. In this book, you will dive deeper into recipes on spectral analysis, smoothing, and bootstrapping methods. Moving on, you will learn to rank stocks and check market efficiency, then work with metrics and clusters. You will achieve parallelism to improve system performance by using multiple threads and speeding up your code. By the end of the book, you will be capable of handling various data analysis techniques in Python and devising solutions for problem scenarios.
Table of Contents (23 chapters)
Python Data Analysis Cookbook
Credits
About the Author
About the Reviewers
www.PacktPub.com
Preface
Glossary
Index

Applying the discrete wavelet transform


The discrete wavelet transform (DWT) captures information in both the time and frequency domains. The mathematician Alfred Haar created the first wavelet. We will use this Haar wavelet in this recipe too. The transform returns approximation and detail coefficients, which we need to use together to get the original signal back. The approximation coefficients are the result of a low-pass filter. A high-pass filter produces the detail coefficients. The Haar wavelet algorithm is of order O(n) and, similar to the STFT algorithm (refer to the Analyzing the frequency spectrum of audio recipe), combines frequency and time information.

The difference with the Fourier transform is that we express the signal as a sum of sine and cosine terms, while the wavelet is represented by a single wave (wavelet function). Just as in the STFT, we split the signal in the time domain and then apply the wavelet function to each segment. The DWT can have multiple levels in this...