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Filter Approximation

In the earlier sections, we saw several examples of amplitude response curves for various filter types. These always included an “ideal” curve with a rectangular shape, indicating that the boundary between the pass-band and the stop-band was abrupt and that the roll-off slope was infinitely steep. This type of response would be ideal because it would allow us to completely separate signals at different frequencies from one another. Unfortunately, such an amplitude response curve is not physically realizable. We will have to settle for the best approximation that will still meet our requirements for a given application. Deciding on the best approximation involves making a compromise between various properties of the filter’s transfer function, such as, filter order, ultimate roll-off rate, attenuation rate near the cut-off frequency, transient response, ripples, etc.
If we can define our filter requirements in terms of these parameters, we will be able to design an acceptable filter using standard design methods.

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