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README
GPL-2.0

信号实验箱

starfork

本软件为一个基于表达式的信号计算、绘图软件, 主要功能为对输入的信号进行采样, 然后对采样序列进行各种运算, 并将运算结果绘制为波形, 支持使用动态库扩充软件内可调用的函数

For native English speaker, please check out English Version Readme

That Document have the same content as this one, but write in English.

本软件支持跨平台部署, 这主要得益于QT的跨平台API以及CMake的跨平台构建能力, 你可以在一个宿主机上编译出不同平台的目标, 目前已测试过Ubuntu 22.04(基于Win11 WSL2)、Win7/Win10/Win11、Android x86/Android armeabi-v7a(基于Win11 WSA和Realme X2 pro)

本软件支持国际化, 使用QT的国际化机制实现, 目前拥有简体中文翻译数据(软件内默认使用英文作为原始语言, 然后再添加其他语言的翻译文件实现国际化, 这也是QT翻译机制的推荐做法), 软件在启动时会获取操作系统使用的语言设置, 因此会自动适配语言, 如果操作系统的语言是中文简体和英文之外的语言, 会默认使用英文

由于本软件的支持库是以git submodule形式引入的, 所以请在克隆仓库时, 使用git clone --recursive命令递归将子模块一起克隆下来, 如果克隆时忘记, 也可以在克隆完成之后在源码路径下执行git submodule initgit submodule update两条指令来补救

如果你使用Download ZIP功能而不是git clone, 那么请将z-fft一同下载, 并解压到external_libs路径下, 最终应该形成这样的文件目录结构

子模块

本文档由多个文件构成, 在此文档内提及的任意其他文件均为超链接形式(蓝色字体), 只需点击即可跳转到对应的文档

如果你在使用、阅读源码、构建等方面有任何疑问, 均可在仓库内提交Issues, 我看到会处理

1. 简单示例

在信号列表框内右键单击(安卓平台为长按), 在弹出的菜单内选择新增信号, 然后输入信号表达式, 设置采样率和采样点数后点击计算当前信号即可看到波形, 显示波形的图表可以放大缩小(鼠标滚轮操作), 也可以平移(按住鼠标左键拖动)
信号0
信号1

信号可以嵌套使用, 方便拿两个信号做运算, 最大可嵌套32层
信号2

除正余弦以外, 内置还有一些其他的函数可供使用, 例如软件随机rand和硬件随机hrand
信号3
信号4

傅立叶变换, 对变换结果调用length是因为fft函数输出为复数, 而length函数为向量求模函数, 因此可求出幅度谱
输入信号
幅度谱

软件自带的filters库内带有几个滤波函数, 其中lpfhpf为IIR滤波器, 分别为低通滤波器与高通滤波器, 接收采样序列和截止频率作为参数, fir为FIR滤波器, 接收采样序列、滤波器阶数和滤波器系数(可使用matlab导出)作为参数

这里给出1阶IIR低通滤波器、3阶IIR低通滤波器和32阶FIR低通滤波器的示例效果, 关于滤波器的更多信息, 请阅读10. 滤波器指南

OrigSig
IIR_filter1
IIR_filter2
FIR_filter

查看滤波之后的频谱图可以发现, 高阶数的滤波器可达到较好的滤波效果

IIR_freq1
IIR_freq2
FIR_freq

2. 工作原理

  1. 一个信号可用一个表达式 f 进行描述, 在任意的 t 时刻, 信号的强度为 f(t)
  2. 若给定某时刻 t , 则表达式 f(t) 的运算结果即为信号 ft 时刻的信号强度采样值
  3. t 可根据软件内设置的采样频率计算得出, 然后重复采样 N 次, N 为软件内设置的采样点数
  4. 软件在计算前会将要计算的信号的表达式编译为语法树
  5. 语法树内每个节点在计算自身的值之前, 会先将子节点的值计算出来, 因此根节点的计算值即为表达式整体的值
  6. 若自定义信号之间存在相互引用, 则内层信号将会先运算得到运算值, 然后再进行外层信号的运算
  7. 信号存在最大嵌套层数限制, 防止某信号引用自身或者多个信号交叉引用造成无限递归的情况

3. 信号定义

在软件内所有的信号定义均为表达式形式, 例如sin(t)便是代表了经过数字采样的 sin 信号, sin(100*t) + sin(200*t)便是将两个频率不同的信号叠加

信号间可以相互引用, 例如sig0 = sin(100*t) sig1 = sin(200*t) sig2 = sig0+sig1

信号自身引用自身或交叉引用均会触发最大嵌套限制

4. 频谱模式

在使用fft函数计算信号的傅里叶变换后, 如果只使用length函数求出幅度谱的话, 图表的X轴坐标为点数, 例如下图

iir_freq_index

可以看到十字光标所在位置X坐标为10, 这表示的是此数据在采样序列里的下标, 如果想要知道此点对应的频率值是多少就需要自己计算, 上图中X=10, 采样率5KHz, 采样点数为256点, 因此此处的频率为5000/256*10=195.3Hz, 也就是原信号里的200Hz频率成分. 进行这样的计算虽然简单, 但是却很麻烦, 而且计算所需的所有参数在软件内都有, 所以, 可以通过勾选右下角的频谱模式复选框来让软件去计算

勾选频谱模式之后, 横坐标的含义将变为实际的频率值, 例如下图中, 这里还是用的一样的信号去绘图, 只是打开了频谱模式而已, 可以看到十字光标所在位置的X值为195.313, 与我们的计算结果一致

IIR_freq1

需要注意的是, 频谱模式实际上只会显示一半的实际计算数据, 即采样点数为1024点时, 图表内实际上只会显示前512个数据点, 这是由于频谱具有对称性, 因此只需要前一半的频谱就足够分析了

5. 内置编译器

软件内置一个简单的编译器, 支持常用的数学表达式文法、双斜杠单行注释文法、数组文法和 if 条件文法

5.1. 表达式文法

数学表达式文法即最常用最简单的数学表达式, 例如(sin(t)+cos(t+3))*6

绝大部分的运算符都是支持的, 包括加减乘除和除余, 二进制与, 二进制或, 二进制异或, 逻辑与, 逻辑或

一些特殊的数学运算使用函数的形式提供, 例如卷积和傅立叶变换

5.2. 注释文法

双斜杠单行注释与C语言的单行注释相同, 例如sin(t)//sin of t, 双斜杠后的所有字符均被忽略

5.3. 数组文法

数组的文法与Python的List类似, 使用方括号作为边界, 使用逗号作为分隔符, 例如[1, 2, 3]

但是由于本软件的基础工作原理为采样, 因此每个数组的实际大小均为采样点数的大小, 所以就存在数据填充问题

5.3.1. 数组数据填充规则

如果一个数组仅包含一个数字, 则使用这个数字填充至采样点数大小, 例如采样点数为128时, 数组[1]代表包含了128个1的数组, 这种情况下也等价于只写数字1, 单个数字也会被扩充至128长度

如果一个数组的大小大于1, 且不足采样点数, 则在数组后补0填充至采样点数的长度

如果一个数组的长度刚好等于采样点数, 则直接使用数组内的数据

如果一个数组的长度大于采样点数, 则截断数组, 只使用数组的前N个数据

5.4. if 条件文法

if条件文法的执行逻辑与C语言的三目运算符相同, 但是并不使用?:符号而是使用ifelse关键字, 并且语法顺序也略有不同, 实际上这里的语法和python的设计一致, 语法规则为数学表达式+if关键字+比较表达式[+else+数学表达式], 方括号内的部分是可省略的, 例如:

  1. 5 if index > 15 else 3//等价于C语言 index > 15 ? 5 : 3
  2. 5 if index > 15//省略else子语句的写法, 等价于 index > 15 ? 5 : 0

if条件语法搭配 index 变量可非常方便的产生阶跃信号和冲激信号, 例如:

  1. 1 if index >= 0//单位阶跃信号
  2. 1 if index == 0//幅值为1的冲激信号
  3. 1 if index >= 5//向右移动5的单位阶跃信号
  4. 1 if index == 5//向右移动5的单位冲激信号
  5. 5 if index >= 0//幅值为5的阶跃信号
  6. 5 if index == 0//幅值为5的冲激信号

5.5. 关键字、特殊变量与常量

编译器识别如下两个关键字

  1. if: 标记if语句的开始, 后跟判断条件
  2. else: 标记else子句的开始, 后跟表达式

编译器支持如下特殊变量:

  1. t: 代表当前的时间, 也就是第 n 次采样除以采样频率 fs, t = n/fs
  2. index: 代表当前是第几次采样, 也就是所谓的 n, 例如采样点数1024, 那么 index 就是[0-1023]的序列
  3. N: 代表总的采样点数, 与软件内设置的采样点数相同, 注意: 这里是大写的N, 与小写的n含义不同, 编译器并不支持小写的n, 而是使用index作为等价的变量
  4. fs: 代表当前的采样率, 单位为Hz

编译器支持如下常量:

  1. pi: 代表圆周率

6. 函数库

所有的函数均为外部函数库解析得到, 每个函数库均需要提供pLibFunction_t lib_init(void)函数, 可用于库被载入时执行一些初始化动作, 并且此函数需要返回函数注册表, 用于描述需要加载动态库文件里面的哪些符号, 以及这些函数所需要的参数数量(用于信号编译时的参数检查)

除此之外, 函数库还可以导出void lib_exit(void)函数用于在库被卸载时做一些收尾清理工作, 此函数是可选函数, 如果没有导出则不调用, 不影响库的导入

如果没有初始化动作的需求, 则lib_init函数可被宏register_function_lib替换, 此宏定义相当于定义lib_init函数, 并返回参数指定的函数注册表, 省去使用者编写定义函数库的代码

目前软件内置了5个库, 即basicfiltersiotransformwindow, 分别是基本函数库、数字滤波器库、IO访问库、信号变换库和窗函数库, 具体的库函数说明请参阅lib/readme.md

同样的, 如果你自己构建了动态库, 你可以把他们放置在安装目录的lib子目录下, 然后在信号表达式内调用即可

7. 工作区

软件内所有的信号、当前的采样率和采样点数的设置共同构成了一个工作区, 而软件可以将这个工作区保存为一个json文件, 并且可从json文件恢复一个工作区, 此json文件的结构是简洁明了的, 很容易看懂其结构, 也很方便手写, 所以你也可以手写一个工作区文件然后直接导入到软件内, 目前此仓库的workspace_demo目录下提供了一些用于验证软件功能或验证库功能的demo工作区, 你可以直接导入使用

关于工作区以及工作区文件的详细说明, 请参阅workspace_demo/readme.md

8. 发行版

为了避免使用者自行构建的麻烦, 你可以在仓库右侧, 简介的下方找到发行版一栏, 在这里是编译并打包好的软件, 可直接下载使用. 但是请注意, 只有较大版本更新之后才会发布发行版, 因此你所下载到的发行版的功能可能是不如源码强的, 如果要体验最新版软件请参考9. 构建源码自行构建最新版软件

9. 构建源码

本工程使用CMake作为顶层构建系统, CMake可产生多种下层构建系统所需文件, 例如Makefilebuild.ninja

除此之外, 本工程的内置编译器并非纯手写完成, 词法分析器和语法分析器基于flex/bison构建, 因此在构建时需要用户的开发环境内有可用的flexbison

本项目自从commit hash: cc33da5de23c4434de462cadfa59c189196cbb15之后, 不再使用原先的方式指定工具链和各种路径相关的信息, 目前使用CMakePreset机制进行环境配置

如果你事先编译过Windows平台软件, 然后需要编译Android平台, 请先删除build目录, 反过来也是一样的

关于如何构建Windows exeAndroid APK的详细流程, 请参阅build_project.md

10. 滤波器指南

软件自带的滤波库内的函数, 主要分为两种, 即IIR滤波器和FIR滤波器, 其中lpfhpf属于IIR滤波器, averagefir属于FIR滤波器, 两种滤波器的使用方法是不一样的

关于如何使用各种滤波函数, 如何使用matlab设计FIR滤波器, 如何使用导出的系数, 请参阅coefficient_demo/readme.md

11. 向本仓库提交代码

如果你希望参与到本项目的开发中, 请参照如下流程

  1. 在云端仓库内点击fork, 将本仓库复制到你自己的名下, 如果遇到不能fork的情况, 说明本仓库正在进行一些较大的修改, 为了防止产生半成品分支, 在此期间会禁止fork, 请等待几天之后再次尝试
  2. 将你自己名下的仓库克隆至本地
  3. 在本地提交代码后, 推送到云端(此时是推送到了你名下的云端仓库)
  4. 向本仓库提交pull request, 方向为[你的仓库] -> [本仓库]
  5. 本仓库的成员会审核(代码风格和实现逻辑)并测试(功能是否达到预期)pull request的代码, 测试通过后此代码将被合并进入本仓库
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You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. Also add information on how to contact you by electronic and paper mail. If the program is interactive, make it output a short notice like this when it starts in an interactive mode: Gnomovision version 69, Copyright (C) year name of author Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'. This is free software, and you are welcome to redistribute it under certain conditions; type `show c' for details. The hypothetical commands `show w' and `show c' should show the appropriate parts of the General Public License. Of course, the commands you use may be called something other than `show w' and `show c'; they could even be mouse-clicks or menu items--whatever suits your program. You should also get your employer (if you work as a programmer) or your school, if any, to sign a "copyright disclaimer" for the program, if necessary. Here is a sample; alter the names: Yoyodyne, Inc., hereby disclaims all copyright interest in the program `Gnomovision' (which makes passes at compilers) written by James Hacker. <signature of Ty Coon>, 1 April 1989 Ty Coon, President of Vice This General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Lesser General Public License instead of this License.

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基于QT、z-fft实现的微型可视化信号运算/变换/处理工具 展开 收起
C++ 等 6 种语言
GPL-2.0
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