Python实践：Think DSP——探索数字信号处理

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"Think DSP: Digital Signal Processing in Python" 是一本由 Allen B. Downey 所著的教程，专为那些希望理解和实践数字信号处理(DSP)概念的人设计。这本书将复杂的 DSP 知识与Python编程语言相结合，版本为1.0.9，旨在提供一个易于理解且实践性强的学习路径。作者认为，尽管DSP在科学和工程领域有着广泛应用，但传统的教学方法往往过于理论化，忽视了实际应用和对现实世界现象的解释。该书的特点在于采用“自顶向下”的教学方式，而非通常的数学抽象概念起始，如phasors（复数形式的交流电表示法）。它注重将理论知识与实际案例相结合，通过实例帮助读者建立直观的理解，使DSP不再仅仅是数学公式，而是可以解决实际问题的工具。书中涵盖了基础的数字信号处理原理，如滤波、傅里叶变换、频谱分析等，这些都是音频处理、通信系统、图像和视频处理等领域必不可少的基础。《Think DSP》适合电子工程、计算机科学或对信号处理感兴趣但没有接触过相关专业背景的读者。书中不仅提供了理论知识，还配以Python代码示例，让读者能够在实践中学习和掌握DSP技术。此外，根据Creative Commons Attribution-NonCommercial 3.0 Unported License，读者可以在非商业用途下自由复制、分发和修改文档，这使得本书成为了一种开放教育资源，有利于更多人接触并学习数字信号处理。《Think DSP》是一本既富有深度又易于上手的数字信号处理指南，通过Python这一现代编程语言，引导读者跨越理论与实践的鸿沟，深入了解并运用这一关键的工程技术技能。无论是专业人士还是希望扩展技能的业余爱好者，都能从中获益匪浅。

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 fun-

damental:

• 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

1.3. Signals 5

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

by adding up sinusoids. Next we’ll see how.

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 repos-

itory 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

, from negative inﬁnity to inﬁnity.

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

uate” means taking a sequence of points in time,

, and computing the

corresponding values of the signal,

. I represent

and

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.

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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