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I've been reading the Chebyshev filters chapter in The Scientist and Engineer's Guide to Digital Signal Processing and it says

"The Chebyshev filters discussed in this chapter are called type 1 filters, meaning that the ripple is only allowed in the passband. In comparison, type 2 Chebyshev filters have ripple only in the stopband. Type 2 filters are seldom used, and we won't discuss them. "

Why is it that Type 2 filters are uncommon? It seems to me that it's much more useful to have the ripple in the stopband (the bit you don't want) than in the passband (the bit you do want).

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Have a look at this plot from this page at the Mathworks site:

enter image description here

The main issue is, as that page says:

The frequency input to the Chebyshev Type II design function sets the beginning of the stopband rather than the end of the passband.

As you can see, the Chebyshev Type I filter has controllable passband gain out to the cutoff frequency. That is not true for the Type II: Only the stopband gain is controllable there. The passband roll-off for Type II makes it not very interesting for most purposes.

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