Python数字信号处理实践：ThinkDSP解读

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"thinkdsp.pdf" 是一本关于使用Python进行数字信号处理的书籍，作者是Allen B. Downey。这本书提供了丰富的实例，使得原本可能枯燥的理论变得生动有趣。书中涵盖的内容包括但不限于数字信号处理的基本概念、算法和应用。版本号为1.1.4。在数字信号处理（DSP）领域，本书提供了对这一主题的实用介绍，适合那些没有电气或机械工程背景，但希望了解信号处理的读者。传统的信号处理教材通常从底层的数学概念如相位矢量（phasors）开始，强调理论而较少关注实践应用。而《ThinkDSP》则采取了一种更易于理解的自顶向下方式来讲解，使得非专业背景的读者也能轻松进入这个领域。书中会涉及以下几个关键知识点： 1. **Python编程基础**：作为一门广泛应用于科学计算的语言，Python为数字信号处理提供了便捷的工具和库，如NumPy、SciPy和matplotlib等，这些都是进行信号处理的基础。 2. **信号表示与处理**：介绍如何用Python表示和操作离散时间信号，包括采样、滤波、傅立叶变换等基本操作。 3. **傅立叶分析**：详细解释了傅立叶变换，包括离散傅立叶变换（DFT）和快速傅立叶变换（FFT），以及它们在频率域分析中的应用。 4. **滤波器设计**：讨论了各种滤波器（如低通、高通、带通滤波器）的设计原理和实现方法，如巴特沃兹滤波器、切比雪夫滤波器等。 5. **信号的频谱分析**：涵盖功率谱估计、自相关函数、协方差函数等，用于理解和分析信号的频域特性。 6. **信号的时频分析**：如短时傅立叶变换（STFT）、小波变换等，这些方法能够在时间和频率两个维度上同时分析信号。 7. **信号处理的应用**：可能包含音频处理、图像处理、通信系统、生物医学信号分析等多个领域的案例研究。 8. **实用技巧和最佳实践**：作者可能会分享一些在Python中进行信号处理的实用技巧和优化策略，帮助读者提高代码效率。通过阅读这本书，读者不仅可以掌握数字信号处理的基本原理，还能获得实际动手解决问题的能力。此外，由于该书遵循Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License，读者可以自由复制、分发和修改内容，有利于学习和交流。

4 Chapter 1. Sounds and signals

0 2000 4000 6000 8000 10000

Frequency (Hz)

500

1000

1500

2000

2500

3000

3500

4000

Amplitude

Figure 1.3: Spectrum of a segment from the violin recording.

The lowest frequency component is called the fundamental frequency. The

fundamental frequency of this signal is near 440 Hz (actually a little lower, or

“ﬂat”).

In this signal the fundamental frequency has the largest amplitude, so it is

also the dominant frequency. Normally the perceived pitch of a sound is

determined by the fundamental frequency, even if it is not dominant.

The other spikes in the spectrum are at frequencies 880, 1320, 1760, and 2200,

which are integer multiples of the fundamental. These components are called

harmonics because they are musically harmonious with the fundamental:

• 880 is the frequency of A5, one octave higher than the fundamental. An

octave is a doubling in frequency.

• 1320 is approximately E6, which is a perfect ﬁfth above A5. If you

are not familiar with musical intervals like ”perfect ﬁfth”, see https:

//en.wikipedia.org/wiki/Interval_(music).

• 1760 is A6, two octaves above the fundamental.

• 2200 is approximately C]7, which is a major third above A6.

These harmonics make up the notes of an A major chord, although not all in

the same octave. Some of them are only approximate because the notes that

make up Western music have been adjusted for equal temperament (see

http://en.wikipedia.org/wiki/Equal_temperament).

Given the harmonics and their amplitudes, you can reconstruct the signal by

adding up sinusoids. Next we’ll see how.

1.3. Signals 5

1.3 Signals

I wrote a Python module called thinkdsp.py that contains classes and func-

tions for working with signals and spectrums

. You will ﬁnd it in the repository

for this book (see Section 0.2).

To represent signals, thinkdsp provides a class called Signal, which is the

parent class for several signal types, including Sinusoid, which represents

both sine and cosine signals.

thinkdsp provides functions to create sine and cosine signals:

cos_sig = thinkdsp.CosSignal(freq=440, amp=1.0, offset=0)

sin_sig = thinkdsp.SinSignal(freq=880, amp=0.5, offset=0)

freq is frequency in Hz. amp is amplitude in unspeciﬁed units where 1.0 is

deﬁned as the largest amplitude we can record or play back.

offset is a phase oﬀset in radians. Phase oﬀset determines where in the

period the signal starts. For example, a sine signal with offset=0 starts at

sin 0, which is 0. With offset=pi/2 it starts at sin π/2, which is 1.

Signals have an __add__ method, so you can use the + operator to add them:

mix = sin_sig + cos_sig

The result is a SumSignal, which represents the sum of two or more signals.

A Signal is basically a Python representation of a mathematical function. Most

signals are deﬁned for all values of t, from negative inﬁnity to inﬁnity.

You can’t do much with a Signal until you evaluate it. In this context, “evalu-

ate” means taking a sequence of points in time, ts, and computing the corre-

sponding values of the signal, ys. I represent ts and ys using NumPy arrays

and encapsulate them in an object called a Wave.

A Wave represents a signal evaluated at a sequence of points in time. Each

point in time is called a frame (a term borrowed from movies and video).

The measurement itself is called a sample, although “frame” and “sample”

are sometimes used interchangeably.

Signal provides make_wave, which returns a new Wave object:

wave = mix.make_wave(duration=0.5, start=0, framerate=11025)

The plural of “spectrum” is often written “spectra”, but I prefer to use standard English

plurals. If you are familiar with “spectra”, I hope my choice doesn’t sound too strange.

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Python数字信号处理实践：ThinkDSP解读

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