ABSTRACT
We are now ready to consider the systematic design of nonrecursive filters. The design method is based on the Figure 16.I, which has 6 parts. On the upper left is a sketch of the ideal filter you wish to have. It can be a low pass, a high pass, a band pass, a band stop, a notch filter, or even a differentiator. For other than differentiator filters you usually want either 0 or 1 as the height in the various intervals, while for the differentiator you want iω since the derivative of the eigenfunction is
hence the desired eigenvalues are the coefficient iω. For a differentiator there is likely to be a cutoff at some frequency because, as you can see, differentiation magnifies, multiplies by ω, and is larger at the high frequencies, which is where the noise usually is, Figure 16.II. See also Figure 15.II.
