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I've done research and could not find any resources on this topic.

I have message signal composed of more sinusoids. Then I preform amplitude modulation, that is multiply that signal with higher frequency carrier signal, and obtain modulated signal. Then to demodulate that signal, I multiply the signal with same carrier signal, and obtain demodulated version of signal. Then I should pass the signal through low pass filter, to obtain signal identical to message signal.

If I do this by matlab using fdesing.lowpass it is fine I get good output, but how to do this low pass filter by hand on paper, if I just ignore frequencies higher than the maximum frequency in message signal I don't get same amplitudes.

I multiply signals by using inverse Euler formula for $\cos$.

Any link or help would be appreciated.

If I didn't make myself clear, let me now and I will try to write an example (which I omit for now because I don't see here any latex support for writing mathematical equations).

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    $\begingroup$ Latex support is enabled. Write away ! $\endgroup$ – Peter K. Nov 19 '13 at 5:05
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how to do this low pass filter by hand on paper?

You can use very simple low pass filter - Moving average. Filter is quite simple - it is sum of N sample of signal divided by N. If length of filter will be equal to period of carrier signal then performance of this filter will be good.

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