基本上是这样的:如果一个波是一个非正弦波，它已经由几个正弦波组成，最典型的是-无限多个.如果信号是非周期性的，则您没有无限数量的分量，而是连续的分量.简而言之，其思想是，每组正弦波都构成一个无限维空间，该空间是由正交矢量的无穷维基本构成的，每个正交矢量都代表一个正弦波.它们在以下意义上是正交的:从负到正无穷大的任意两个乘积的积分为零.您可以将任何信号分解为正弦波分量，这是光谱分析的主要任务.

现在，问题来了:即使您可以将ECG信号的摘要信号分解为一组正弦波分量，但您无法将原始ECG信号彼此分开.这是因为因为它们不是正交的:只有它们的正弦分量才是.粗略地说:即使您可以对每个ECG信号进行频谱分析，即使您可以对具有相同成分的多个ECG信号的总和进行相同的分析，也无法确定其中哪个属于"哪个心电图信号.

有趣的是，在频率空间中，如果在预期形状上有一些必要的先验信息，则可以在一定程度上将频谱曲线从不同来源中分离出来.这种数学技术被用于光谱学中.

在ECG的情况下，原始测量信号取决于时间(而不是频谱)，因此对我而言，这项任务看起来毫无希望.我只是很好奇:几个ECG信号最初如何纠缠在一起?我看过很多次这样的记录.通常会记录来自不同传感器的单个信号.您的任务出了点问题...

请参阅:
http://en.wikipedia.org/wiki/Functional_analysis [ http://en.wikipedia.org/wiki/Spectral_Analysis [ http://en.wikipedia.org/wiki/Fourier_space [ http://en.wikipedia.org/wiki/Fourier_transform [ http://en.wikipedia.org/wiki/FFT [

Basically, this is how it looks: if one wave a non-sinusoidal wave, it is already composed of several sinusoidal waves, most typically -- infinite number of those. If the signal is non-periodic, you have not a countable infinite number of components, but continuum of those. In brief, the idea is that each the set of sinusoidal wave makes an infinite-dimensional space formed by the infinite-dimensional basic of orthogonal vectors, each representing a sinusoidal wave. They are orthogonal in the following sense: integral of the product of any two of them from minus to plus infinity is zero. You can decompose any signal into its sinusoidal component, which is a main task of spectral analysis.

Now, here is the problem: even though you can decompose the summary signal of your ECG signals into a set of sinusoidal components, you cannot separate original ECG signals from each other. This is because they are not orthogonal: only their sinusoidal components are. Roughly speaking: even though you could perform spectral analysis of each ECG signal, and even though you can do the same with the sum of several ECG signal with the same components, there is no a way to determine which of them "belonged" to which ECG signal.

Interestingly, in the space of frequencies, separation of the spectrum curves from different sources is possible, to certain extent, if there is some essential a priory information on the expected shape. Such mathematical technique is used in optical spectroscopy.

In the case of ECG, where the original measured signal is dependency on time (not a spectrum), the task looks hopeless to me. I''m just curious: how happens that several ECG signals was entangled together in first place? I saw such records many times; usually individual signals from different sensors are recorded. Something is wrong with your task…

Please see:
http://en.wikipedia.org/wiki/Functional_analysis[^],
http://en.wikipedia.org/wiki/Spectral_Analysis[^],
http://en.wikipedia.org/wiki/Fourier_space[^],
http://en.wikipedia.org/wiki/Fourier_transform[^],
http://en.wikipedia.org/wiki/FFT[^].

—SA