# Filter design and sine-waves

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Considering x[n]=1+sin((3*pi*n)/8 + pi/4) + cos ((9*pi*n/24) + pi/4) , please design a filter that will pass the sine-wave portion, but ignore everything else. What is the filter's input response h(t)? In a real filter, what would you have to do differently?

Thanks.

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##### Solution Summary

This solution is the design of a filter that passes the sine-wave portion, using the equation provided as a base, noting the filter's input response and its implications.

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cos((9*pi*n/24)+pi/4)=cos((3*pi*n/8)+pi/4)

First Step:

Multiply x[n] by cos((3*pi*n/8)+pi/4) and then add a DC component 1/2. This means shifting the x(w) to high centre frequencies and adding an ...

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