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Python Data Analysis, Second Edition

You're reading from   Python Data Analysis, Second Edition Data manipulation and complex data analysis with Python

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Product type Paperback
Published in Mar 2017
Publisher Packt
ISBN-13 9781787127487
Length 330 pages
Edition 2nd Edition
Languages
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Author (1):
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Ivan Idris Ivan Idris
Author Profile Icon Ivan Idris
Ivan Idris
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Table of Contents (16) Chapters Close

Preface 1. Getting Started with Python Libraries FREE CHAPTER 2. NumPy Arrays 3. The Pandas Primer 4. Statistics and Linear Algebra 5. Retrieving, Processing, and Storing Data 6. Data Visualization 7. Signal Processing and Time Series 8. Working with Databases 9. Analyzing Textual Data and Social Media 10. Predictive Analytics and Machine Learning 11. Environments Outside the Python Ecosystem and Cloud Computing 12. Performance Tuning, Profiling, and Concurrency A. Key Concepts
B. Useful Functions C. Online Resources

Fourier analysis


Fourier analysis is based on the Fourier series named after 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:

The most efficient algorithm for Fourier analysis is the Fast Fourier Transform (FFT). This algorithm is implemented in SciPy and NumPy. When applied to the time series data, the Fourier analysis transforms maps onto the frequency domain, producing a frequency spectrum. The frequency spectrum displays harmonics as distinct spikes at certain frequencies. Music, for example, is composed from different frequencies with the note A at 440 Hz. The note A can be produced by a pitch fork. We can produce this and other notes with musical instruments such as a piano. White noise is a signal consisting of many frequencies, which are represented equally. White light is a mix of all the visible frequencies of light...

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