Python在信号处理中的应用

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"Python for Signal Processing" 是一本由José Unpingco编写的关于使用Python进行信号处理的书籍，特别包含IPython Notebook的应用。在现代科技领域，信号处理是至关重要的一部分，它涉及到对各种形式的信号（如声音、图像、视频、生物信号等）进行分析、转换和操作。Python作为一种强大的编程语言，因其易读性强、丰富的库支持和强大的科学计算工具而被广泛用于信号处理。本书"Python for Signal Processing"深入浅出地介绍了如何利用Python进行高效的信号处理工作。 Python中的几个关键库在信号处理中起着核心作用，例如NumPy提供了高效的数组操作，SciPy包含了众多的科学计算函数，包括傅立叶变换、滤波器设计等。matplotlib和Pandas则用于数据可视化和管理。此外，IPython Notebook是本书的一大亮点，它允许用户在交互式环境中编写和运行代码，结合文本、公式、图表，为学习和分享信号处理概念提供了一个直观的平台。书中可能涵盖了以下主题： 1. **基础概念**：介绍信号处理的基本理论，包括时域和频域分析、傅立叶变换以及滤波器理论。 2. **Python基础知识**：讲解如何使用Python进行数据操作和编程，包括变量、控制流、函数和类。 3. **NumPy和SciPy应用**：演示如何使用这两个库进行数值计算和信号处理任务，如采样、滤波、谱分析等。 4. **IPython Notebook教程**：展示如何利用IPython Notebook创建交互式的信号处理实验和报告。 5. **实例分析**：通过具体的信号处理案例，如音频处理、图像处理或生物信号分析，来实践所学知识。 6. **高级话题**：可能涵盖更复杂的技术，如小波分析、自适应滤波器或非线性信号处理。 7. **软件工具和库**：介绍其他相关的Python库，如scikit-image、scikit-learn在图像处理和机器学习中的应用。通过这本书，读者不仅可以学习到信号处理的基础知识，还能掌握使用Python这一强大工具进行实际问题解决的技能。对于科研人员、工程师以及对信号处理感兴趣的爱好者来说，"Python for Signal Processing"是一本极好的学习资源。

6 1 Introduction

other competing methods for two-dimensional scientiﬁc visualization and today is a

very actively maintained project, even without John Hunter, who sadly passed away

in 2012.

John had a few basic requirements for Matplotlib:

• Plots should look publication quality with beautiful text.

• Plots should output Postscript for inclusion within L

X documents and publi-

cation quality printing.

• Plots should be embeddable in a Graphical User Interface (GUI) for application

development.

• The code should be mostly Python to allow for users to become developers.

• Plots should be easy to make with just a few lines of code for simple graphs.

Each of these requirements has been completely satisﬁed, judging from the

enthusiastic reception of Matplotlib by the scientiﬁc Python community. In the

beginning, to ease the transition from MATLAB to Python, many of the Matplotlib

functions were closely named after the corresponding MATLAB commands. The

community has moved away from this style and, even though you will still ﬁnd the

old MATLAB-esque style used in the Matplotlib documentation. This book uses the

more powerful and explicit Matplotlib interfaces.

Listing 1.19 shows the quickest way to draw a plot using Matplotlib and the

plain Python interpreter. Later, we’ll see how to do this even faster using IPython.

The ﬁrst line imports the requisite module as plt which is the recommended

convention. The next line plots a sequence of numbers generated using Python’s

range function. Note the output list contains a Line2D object. This is an artist

in Matplotlib parlance. Finally, the plt.show() function draws the plot in a GUI

(i.e. ﬁgure window).

If you try this in your own plain Python interpreter (and you should!), you will

see that you cannot type in anything further in the interpreter until the ﬁgure window

is closed. This is because the plt.show() function preoccupies the interpreter with

the controls in the GUI and blocks further interaction. As we discuss below, IPython

provides ways to get around this blocking so you can simultaneously interact with

the interpreter and the ﬁgure window.

The plot function returns a list containing the Line2D object as shown

in Listing 1.19. More complicated plots yield larger lists ﬁlled with artists in

Matplotlib terminology. The suggestion is that artists draw on the canvas contained

in the Matplotlib ﬁgure. The ﬁnal line is the plt.show function that provokes the

embedded artists to render on the Matplotlib canvas. The reason this is a separate

function is that plots may have dozens of complicated artists and rendering may be a

time-consuming task to only be undertaken at the end, when all the artists have been

mustered. Matplotlib supports plotting types such as images, contours, and many

others that we cover in detail in the following chapters.

Even though Listing 1.19 is the quickest way to draw a plot in Matplotlib, it is

not recommended because there are no handles to the intermediate products of the

plot such as the plot’s axis. While this is okay for a simple plot like this, later on

we will see how to construct complicated plots using the recommended style. There

1.5 Alternatives to Matplotlib 7

is a close working relationship between Numpy and Matplotlib and you can load

Matplotlib’s plotting functions and Numpy’s functions simultaneously using pylab

as from matplotlib.pylab import *. Although importing everything this way

as a standard practice is not recommended because of namespace pollution, there

is no danger in this case due to the close working relationship between Numpy and

Matplotlib.

One of the best ways to get started with Matplotlib is to browse the extensive

on-line “gallery” of plots on the main Matplotlib site. Each of the plots comes with

corresponding source code that you can use as a starting point for your own plots.

In Sect. 1.6, we discuss special “magic” commands that make this particularly easy.

1.5 Alternatives to Matplotlib

Even though Matplotlib is unbeatable for script-based plotting, there are some

alternatives for specialized scientiﬁc graphics that may be of interest. PyQwt is a

set of bindings for the Qwt library, which contains useful GUI components and

widgets for technical plotting. Matplotlib has some widgets for interactive plots,

but they are pretty limited. The downside of PyQwt is that it relies on the Qwt

documentation, which might be hard to read if you are not comfortable with C++

codes. Furthermore, the package does not seem to be currently maintained. The

upside is that these libraries have been around for at least a decade, so they are

well-tested and lighter-weight than Matplotlib.

Chaco is part of the Enthought Tool-Suite (ETS) and implements many real-

time data visualization concepts and corresponding widgets. It is available on

all of the major platforms and is also actively maintained and well-documented.

Chaco is geared towards GUI application development, rather than script-based data

visualization. It depends on the Traits package, which is also available in ETS and

in the Enthought Python Distribution (EPD). If you don’t want to use EPD, then

you have to build Chaco and its dependencies separately. On Linux, this should

be straight-forward, but potentially a nightmare on Windows if not for Christoph

Gohlke’s one-click installers.

If you require real-time data display and tools for volumetric data rendering and

complicated 3D meshes with isosurfaces, then PyQtGraph is an option. PyQtGraph

is a pure-Python graphics and GUI library that depends on Python bindings for the

Qt GUI library (i.e. PySide or PyQt4) and Numpy. This means that the PyQtGraph

relies on these other libraries (i.e. Qt’s GraphicsView framework) for the heavy-

duty numbercrunching and rendering. This package is actively maintained, but is

still pretty new, with good (but not comprehensive) documentation. You also need

to grasp a few Qt-GUI development concepts to use this effectively. Mayavi is

another Enthought-supported 3D visualization package that sits on VTK (open-

source C++ library for 3D visualization). Like Chaco, it is a toolkit for scientiﬁc

GUI development as opposed to script-based plotting. To use it effectively, you need

1.6 IPython 9

and IPython provides the built-in help documentation. Note that you can also get this

documentation with help(x.center) which works in the plain Python interpreter

as well.

The combination of dynamic tab-based introspection and quick interactive help

accelerates development because you can keep your eyes and ﬁngers in one place as

you work. This was the original IPython experience, but IPython has since grown

into a complete framework for delivering a rich scientiﬁc computing workﬂow that

retains and enhances these fundamental features.

1.6.1 IPython Notebook

As you may have noticed investigating Python on the web, most Python users are

web-developers, not scientiﬁc programmers, meaning that the Python toolchain

is very well developed for web technologies. The genius move of the IPython

development team was to leverage these technologies for scientiﬁc computing by

embedding IPython in modern web-browsers. You can start the IPython Notebook,

with all the Matplotlib and Numpy functions set up with the following command-

line: ipython notebook --pylab=inline.Theinline ﬂag embeds Matplotlib

graphics created in the IPython Notebook into the browser itself instead of popping

open a separate GUI. After starting the notebook, you should see something like the

following in the terminal,

[NotebookApp] Using existing profile dir: u’C:\\.ipython\\profile_default’

[NotebookApp] Serving notebooks from local directory: D:\

[NotebookApp] The IPython Notebook is running at: http://127.0.0.1:8888/

[NotebookApp] Use Control-C to stop this server and shut down all kernels.

The ﬁrst line reveals where IPython looks for default settings. The next line

shows where it looks for documents in the IPython Notebook format. The third

line shows that the IPython Notebook started a web-server on the local machine

(i.e. 127.0.0.1) on port number 8888. This is the address your browser needs to

connect to the IPython session although your default browser should have opened

automatically to this address. The port number and other conﬁguration options are

available either on the commandline or in the profile_default shown in the ﬁrst

line. If you are on a Windows platform and you do not get this far, then the Window’s

ﬁrewall is probably blocking the port. For additional conﬁguration help, see the

main IPython site (ipython.org) or e-mail the very responsive IPython mailing

list (ipython-dev@scipy.org).

When IPython starts, it initiates many small Python processes that use the

blazing-fast ZeroMQ message passing framework for interprocess-communication,

along with the web-sockets protocol for back-and-forth communication with the

browser. As of yet, because neither Internet Explorer nor Safari support web-

sockets, you will have to use Firefox or Google Chrome to use the IPython

Notebook. To start IPython and get around your default browser, you can use the

additional –-no-browser ﬂag and then manually type in the local host address

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