#### bubulescu

##### Member level 3

For a low-pass prototype Chebyshev type I filter, if the ripple in the pass-band is Rp, then the corner frequency will be @-Rp, but if the ripple needs to be less than the attenuation (e.g. Rp=-1 A=-2), one would use this formula:

\[ \omega_{sc} = \frac{\omega_p}{cosh \left(\frac{1}{N} acosh \left( \frac{\epsilon_p}{\epsilon_r} \right) \right)} \]

and, for a high-pass transformation, there will be \[\omega_p \] multiplied by [...], instead of division.

The way I'm using the general transfer function for band-pass is:

\[ H(s) = \frac{a_{1_1} s}{s^2 + b_{1_1} s + b_{0_1} } \cdot \frac{a_{1_2} s}{s^2 + b_{1_2} s + b_{0_2} ) \cdot ... \]

(and, for the band-stop, they will have s^2+a0), adapted to fit the bandwidth requirements for being greater than, or less than 2 (normalized). As you can see I cannot apply the frequency scaling like for the low- or high-pass filters.

So, what I'd like to know is how to use frequency scaling for band-pass/band-stop filters.

Thank you in advance,

Vlad