Book Image

NumPy Essentials

By : Leo (Liang-Huan) Chin, Tanmay Dutta, Shane Holloway
Book Image

NumPy Essentials

By: Leo (Liang-Huan) Chin, Tanmay Dutta, Shane Holloway

Overview of this book

In today’s world of science and technology, it’s all about speed and flexibility. When it comes to scientific computing, NumPy tops the list. NumPy gives you both the speed and high productivity you need. This book will walk you through NumPy using clear, step-by-step examples and just the right amount of theory. We will guide you through wider applications of NumPy in scientific computing and will then focus on the fundamentals of NumPy, including array objects, functions, and matrices, each of them explained with practical examples. You will then learn about different NumPy modules while performing mathematical operations such as calculating the Fourier Transform; solving linear systems of equations, interpolation, extrapolation, regression, and curve fitting; and evaluating integrals and derivatives. We will also introduce you to using Cython with NumPy arrays and writing extension modules for NumPy code using the C API. This book will give you exposure to the vast NumPy library and help you build efficient, high-speed programs using a wide range of mathematical features.
Table of Contents (16 chapters)
NumPy Essentials
Credits
About the Authors
About the Reviewers
www.PacktPub.com
Preface

Chapter 6. Fourier Analysis in NumPy

Fourier analysis is commonly used, among other things, for digital signal processing. This is thanks to it being so powerful in separating its input signals (time domain) into components that contribute at discrete frequencies (frequency domain). Another fast algorithm to compute Discrete Fourier transform (DFT) was developed, which is well known as Fast Fourier transform (FFT), and it provides more possibilities for analysis and its applications. NumPy, as it targets numeric computing, also supports FFT. Let's try to use NumPy to apply some Fourier analysis on applications! Note, no familiarity with signal processing or Fourier methods is assumed in this chapter.

The topics that will be covered in this chapter are:

  • The basics of Fourier analysis
  • One and two-dimensional Fourier transformations
  • Spectral density estimation
  • Time frequency analysis