脑电读书会 | 傅里叶分析与滤波基础
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Hello,
这里是行上行下,我是喵君姐姐~
行上行下读书会已经进行到第七期啦!本期读书会的主题是《事件相关电位基础》(第二版) 第七章 傅里叶分析与滤波基础。
![](http://static.careerengine.us/api/aov2/https%3A_%7C__%7C_mmbiz.qpic.cn_%7C_mmbiz_png_%7C_6G3tEQTiacLukdhPcDAgUq5frianGdbRbjLeHkyX4fvgD5OabibS0ickUucIpIVwIOhlhNC5xoqWRmYLXTmibuvqWPw_%7C_640%3Fwx_fmt%3Dpng.jpg)
第七章主要介绍了傅里叶分析的基础知识,引入了时域和频域这两个ERP数据分析中的重要概念。
在此基础上,作者讲述了滤波的必要性,并深入介绍了时域滤波和频域滤波的基本原理以及二者之间的相互关系。
最后,作者基于自身经验为我们提供了滤波失真的可能情况及可行建议。
PS:
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![](http://static.careerengine.us/api/aov2/https%3A_%7C__%7C_mmbiz.qpic.cn_%7C_mmbiz_png_%7C_6G3tEQTiacLukdhPcDAgUq5frianGdbRbjFwWWicvLdI0sYkZFfxZbiajWK7RYxmo5hbvjVxMtdajmPdUUqQbm8T9A_%7C_640%3Fwx_fmt%3Dpng.jpg)
注:由于我们的精力有限,内容可能难免会有遗漏或错误,欢迎大家批评指正,提出建议,我们一起共同学习和进步~
PART 1
傅里叶分析基础
傅里叶变换:时域 →频域
傅里叶逆变换:频域→时域
![](http://static.careerengine.us/api/aov2/https%3A_%7C__%7C_mmbiz.qpic.cn_%7C_mmbiz_png_%7C_6G3tEQTiacLukdhPcDAgUq5frianGdbRbjEiaBqxnaYapYktGXQrl9tJpPfZ2BAm38RWzXBOibZYK4BEBFYaHcribJg_%7C_640%3Fwx_fmt%3Dpng.jpg)
傅里叶分析的本质是任何波形都可由一组正弦波的累加来重构,甚至是方波。
![](http://static.careerengine.us/api/aov2/https%3A_%7C__%7C_mmbiz.qpic.cn_%7C_mmbiz_png_%7C_6G3tEQTiacLukdhPcDAgUq5frianGdbRbjzibCcU8YdGCDC6sAW4ZPiaF0FEookHicSmKLxspJWtYoQVw4ov5U979AQ_%7C_640%3Fwx_fmt%3Dpng.jpg)
傅里叶分析的不对称性。
![](http://static.careerengine.us/api/aov2/https%3A_%7C__%7C_mmbiz.qpic.cn_%7C_mmbiz_png_%7C_6G3tEQTiacLukdhPcDAgUq5frianGdbRbjibiaOBGcN0xYz0WJBK4SGM0lrzI5qxc4FIcibBp6tNDHejlhHbI1l3r7Q_%7C_640%3Fwx_fmt%3Dpng.jpg)
PART 2
频域滤波基础
![](http://static.careerengine.us/api/aov2/https%3A_%7C__%7C_mmbiz.qpic.cn_%7C_mmbiz_png_%7C_6G3tEQTiacLukdhPcDAgUq5frianGdbRbj9LF9vUYKw92P9h1CZickQYUlMK7bibqR9hgO3jWdykfib9lsfA1X615og_%7C_640%3Fwx_fmt%3Dpng.jpg)
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由于二次滤波是增益相乘,对于滤波顺序可以不必过分纠结。
![](http://static.careerengine.us/api/aov2/https%3A_%7C__%7C_mmbiz.qpic.cn_%7C_mmbiz_png_%7C_6G3tEQTiacLukdhPcDAgUq5frianGdbRbjGmG4BflRr8Bg6QCAmPk25fpRW7ia4ibf4Q6VdkWgEGeGic4ayLox0wyicw_%7C_640%3Fwx_fmt%3Dpng.jpg)
![](http://static.careerengine.us/api/aov2/https%3A_%7C__%7C_mmbiz.qpic.cn_%7C_mmbiz_png_%7C_6G3tEQTiacLukdhPcDAgUq5frianGdbRbjz5WIbP9Cueqe0x2NIwalqgR4EptFkusLh9jsZejcEmgmOYibmY8VSlg_%7C_640%3Fwx_fmt%3Dpng.jpg)
注意区分半振幅截止频率和半功率截止频率。
在学术论文写作中,只汇报截止频率是不够的。
![](http://static.careerengine.us/api/aov2/https%3A_%7C__%7C_mmbiz.qpic.cn_%7C_mmbiz_png_%7C_6G3tEQTiacLukdhPcDAgUq5frianGdbRbjibyJiahAoq90dCloDOX7nMLUoUIibiaSQREA2XAOBS4T7dhOgTNxfP6Hsw_%7C_640%3Fwx_fmt%3Dpng.jpg)
PART 3
时域滤波基础
![](http://static.careerengine.us/api/aov2/https%3A_%7C__%7C_mmbiz.qpic.cn_%7C_mmbiz_png_%7C_6G3tEQTiacLukdhPcDAgUq5frianGdbRbjAGbQ7SrEO0gj5RLy2nsbPXxibfyrLewPqPx945XjS9UVH2Wmsy5oGIA_%7C_640%3Fwx_fmt%3Dpng.jpg)
![](http://static.careerengine.us/api/aov2/https%3A_%7C__%7C_mmbiz.qpic.cn_%7C_mmbiz_png_%7C_6G3tEQTiacLukdhPcDAgUq5frianGdbRbjLyVZeLicdrpXgWDQJUqZM4utkQtXBx2apLQGO5Rbib15eeRO31bg1lJg_%7C_640%3Fwx_fmt%3Dpng.jpg)
![](http://static.careerengine.us/api/aov2/https%3A_%7C__%7C_mmbiz.qpic.cn_%7C_mmbiz_png_%7C_6G3tEQTiacLukdhPcDAgUq5frianGdbRbjicsA9iazX4pyH1qT5VYGzoL1a9bNtkXzMbDO9wR0tzc2kObRF2plykOQ_%7C_640%3Fwx_fmt%3Dpng.jpg)
![](http://static.careerengine.us/api/aov2/https%3A_%7C__%7C_mmbiz.qpic.cn_%7C_mmbiz_png_%7C_6G3tEQTiacLukdhPcDAgUq5frianGdbRbjTw3S3hqr4wjyYFGjOorRDrFk2AribyO5p1cxWs16tSoQU6ibRJkY0KUA_%7C_640%3Fwx_fmt%3Dpng.jpg)
PART 4
由滤波引起的失真
![](http://static.careerengine.us/api/aov2/https%3A_%7C__%7C_mmbiz.qpic.cn_%7C_mmbiz_png_%7C_6G3tEQTiacLukdhPcDAgUq5frianGdbRbjR8LaGxUl3xicIaSPswQW1Tz00QxLdXZ35WnXDCHR79ruibs74VpsBTvQ_%7C_640%3Fwx_fmt%3Dpng.jpg)
![](http://static.careerengine.us/api/aov2/https%3A_%7C__%7C_mmbiz.qpic.cn_%7C_mmbiz_png_%7C_6G3tEQTiacLukdhPcDAgUq5frianGdbRbjJ29icciaH3xexFDs3UKic75f6sF2p0QCg48G2VzRfRJj8egLJV5o1k8pw_%7C_640%3Fwx_fmt%3Dpng.jpg)
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PART 5
关于滤波的一些建议
![](http://static.careerengine.us/api/aov2/https%3A_%7C__%7C_mmbiz.qpic.cn_%7C_mmbiz_png_%7C_6G3tEQTiacLukdhPcDAgUq5frianGdbRbjJLKaRkbZsBibHLZzD1dQPQENlQ3Xzic9bvDev0NV5fu1ZUeK7pibgv4dw_%7C_640%3Fwx_fmt%3Dpng.jpg)
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![](http://static.careerengine.us/api/aov2/https%3A_%7C__%7C_mmbiz.qpic.cn_%7C_mmbiz_png_%7C_6G3tEQTiacLukdhPcDAgUq5frianGdbRbjiaSiadEN22ypZSTrKSWt1aCfPk8kVkMoF2swIYd8wrB12l3mVuBLW7Iw_%7C_640%3Fwx_fmt%3Dpng.jpg)
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书中Luck基于自身经验提供了宝贵的一般性建议,正式科研中更重要的是要参考自己领域的相关研究,提高研究之间的可比性!
第七期参与人员名单
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通过本章的学习,相信大家对于傅里叶分析有了进一步的了解,期待我们下一期的学习哟~
![](http://static.careerengine.us/api/aov2/https%3A_%7C__%7C_mmbiz.qpic.cn_%7C_mmbiz_png_%7C_v2lTA0mRBt7ywFjFSSUtF8HcdW84pJDW2jbFsfEc6xCXJBf3yKvukdcoUe1l1g9VAkCIBZKqD1R4XRlAtM0QyA_%7C_640%3Fwx_fmt%3Dpng.jpg)
注:由于我们的精力有限,内容可能难免会有遗漏或错误,欢迎大家批评指正,提出宝贵建议,我们一起共同学习和进步~
参考文献:
[1] Steven J. Luck.(2009) 事件相关电位基础 (洪祥飞, 刘岳庐译). 上海: 华东师范大学出版社.
排版:蛐蛐
编辑:华华
校对:喵君姐姐
![](http://static.careerengine.us/api/aov2/https%3A_%7C__%7C_mmbiz.qpic.cn_%7C_mmbiz_png_%7C_v2lTA0mRBt7ywFjFSSUtF8HcdW84pJDWCPYXhuMfmicjzWeNyLS2ssqL04Net8kaRGePwccvhVFaTnzzBFzeSnA_%7C_640%3Fwx_fmt%3Dpng.jpg)
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