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#### Overview of this book

Data analysis enables you to generate value from small and big data by discovering new patterns and trends, and Python is one of the most popular tools for analyzing a wide variety of data. With this book, you’ll get up and running using Python for data analysis by exploring the different phases and methodologies used in data analysis and learning how to use modern libraries from the Python ecosystem to create efficient data pipelines. Starting with the essential statistical and data analysis fundamentals using Python, you’ll perform complex data analysis and modeling, data manipulation, data cleaning, and data visualization using easy-to-follow examples. You’ll then understand how to conduct time series analysis and signal processing using ARMA models. As you advance, you’ll get to grips with smart processing and data analytics using machine learning algorithms such as regression, classification, Principal Component Analysis (PCA), and clustering. In the concluding chapters, you’ll work on real-world examples to analyze textual and image data using natural language processing (NLP) and image analytics techniques, respectively. Finally, the book will demonstrate parallel computing using Dask. By the end of this data analysis book, you’ll be equipped with the skills you need to prepare data for analysis and create meaningful data visualizations for forecasting values from data.
Preface
Section 1: Foundation for Data Analysis
Free Chapter
Getting Started with Python Libraries
Section 2: Exploratory Data Analysis and Data Cleaning
Data Visualization
Cleaning Messy Data
Signal Processing and Time Series
Section 3: Deep Dive into Machine Learning
Supervised Learning - Regression Analysis
Supervised Learning - Classification Techniques
Unsupervised Learning - PCA and Clustering
Section 4: NLP, Image Analytics, and Parallel Computing
Analyzing Textual Data
Analyzing Image Data
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# Fourier analysis

Fourier analysis uses the Fourier series concept thought up by the mathematician Joseph Fourier. The Fourier series is a mathematical method used to represent functions as an infinite series of sine and cosine terms. The functions in question can be real- or complex-valued:

For Fourier analysis, the most competent algorithm is Fast Fourier Transform (FFT). FFT decomposes a signal into different frequency signals. This means it produces a frequency spectrum of a given signal. The SciPy and NumPy libraries provide functions for FFT.

The rfft() function performs FFT on real-valued data. We could also have used the fft() function, but it gives a warning on this Sunspot dataset. The fftshift() function moves the zero-frequency component to the middle of the spectrum.

Let's see the following example to understand FFT:

1. Import the libraries and read the dataset:
`# Import required libraryimport numpy...`