卷积(convolution, 另一个通用名称是德文的Faltung)的名称由来，是在于当初定义它时，定义成
integ(f1(v)*f2(t-v))dv，积分区间在0到t之间。举个简单的例子，大家可以看到，为什么叫“卷积”了。比方说在(0，100)间积分，用简单的辛普生积分公式，积分区间分成100等分，那么看到的是f1(0)和f2(100)相乘，f1(1)和f2(99)相乘，f1(2)和f2(98)相乘，.........
等等等等，就象是在坐标轴上回卷一样。所以人们就叫它“回卷积分”，或者“卷积”了。
卷积的过程就是相当于把信号分解为无穷多的冲击信号，
然后进行冲击响应的叠加。
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对于CSP来说，
http://s11/middle/4a033b094ae0ae0c0b75a&690图解 举例 恒星形成率 SFR SFH" TITLE="卷积的物理意义、数学意义 图解 举例 恒星形成率 SFR SFH" />
上面的卷积意思是：
http://s5/middle/4a033b094ae0ae8fa6714&690图解 举例 恒星形成率 SFR SFH" TITLE="卷积的物理意义、数学意义 图解 举例 恒星形成率 SFR SFH" />
数学意义及其他：
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http://mathworld.wolfram.com/images/spacer.gif图解 举例 恒星形成率 SFR SFH" />
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- 以下来自 WolframMath：
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A convolution is an integral that expresses the amount of
overlap of one function http://mathworld.wolfram.com/images/equations/Convolution/Inline1.gif图解 举例 恒星形成率 SFR SFH" /> as it is shifted over another function
http://mathworld.wolfram.com/images/equations/Convolution/Inline2.gif图解 举例 恒星形成率 SFR SFH" />. It therefore "blends" one function with
another. For example, in synthesis imaging, the measured dirty map
is a convolution of the "true" CLEAN map with the dirty beam (the
Fourier
transform of the sampling distribution). The convolution is
sometimes also known by its German name, faltung
("folding").
Convolution is implemented in Mathematica
as Convolve[f,
g, x, y] and
DiscreteConvolve[f, g, n,
m].
Abstractly, a convolution is defined as a product of functions
http://mathworld.wolfram.com/images/equations/Convolution/Inline4.gif图解 举例 恒星形成率 SFR SFH" /> that are objects in the algebra of
Schwartz
functions in http://mathworld.wolfram.com/images/equations/Convolution/Inline5.gif图解 举例 恒星形成率 SFR SFH" />. Convolution of two functions
http://mathworld.wolfram.com/images/equations/Convolution/Inline8.gif图解 举例 恒星形成率 SFR SFH" /> is given by
where the symbol http://mathworld.wolfram.com/images/equations/Convolution/Inline11.gif图解 举例 恒星形成率 SFR SFH" />.
Convolution is more often taken over an infinite range,
(Bracewell 1965, p. 25) with the variable (in this case
http://mathworld.wolfram.com/images/equations/Convolution/Inline18.gif图解 举例 恒星形成率 SFR SFH" />) implied, and also occasionally written as
http://mathworld.wolfram.com/images/equations/Convolution/Inline19.gif图解 举例 恒星形成率 SFR SFH" />.
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The animations above graphically illustrate the convolution of
two boxcar
functions (left) and two Gaussians
(right). In the plots, the green curve shows the convolution of the
blue and red curves as a function of http://mathworld.wolfram.com/images/equations/Convolution/Inline20.gif图解 举例 恒星形成率 SFR SFH" />, the position indicated by the vertical
green line. The gray region indicates the product http://mathworld.wolfram.com/images/equations/Convolution/Inline23.gif图解 举例 恒星形成率 SFR SFH" /> is precisely the convolution. One feature
to emphasize and which is not conveyed by these illustrations
(since they both exclusively involve symmetric functions) is that
the function http://mathworld.wolfram.com/images/equations/Convolution/Inline24.gif图解 举例 恒星形成率 SFR SFH" /> must be mirrored before lagging it across
http://mathworld.wolfram.com/images/equations/Convolution/Inline25.gif图解 举例 恒星形成率 SFR SFH" /> and integrating.
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以上来自 WolframMath。
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加载中，请稍候......
加载中…
(2011-04-02 09:25:27) 
