9 Bandstop filter transfer function
The transfer function of the bandstop filter can be obtained by mapping the lowpass prototype transfer function, using the following mapping function
The entire procedure for obtaining the bandstop transfer function may include the following steps:

Step 1:
Generate bandpass filter specification

Step 2:
Convert the bandpass filter specification into the symmetrical one
Parameters of the symmetrical specification must satisfy the following conditions:

Step 3:
Convert the symmetrical bandstop specification into the equivalent lowpass prototype using the following expressions

Step 4:
Generate the lowpass prototype transfer function

Step 5:
Map the lowpass prototype transfer function into the desired bandpass transfer function
Sample
The transfer function of the lowpass prototype is obtained as follows:
Such transfer functions occur for the elliptic or inverse Chebyshev approximations. Zeros are complex conjugate; poles are complex conjugate as well. The bandstop transfer function of the filter for which (9.5) is an equivalent lowpass prototype, can be obtained by zdomain frequency mapping. Replacing variable with mapping function
the bandstop filter transfer function can be expressed as follows:
Note, that are complex conjugate zeros and poles of the lowpass prototype transfer function. Therefore, the factors and are real numbers. The pairs and are complex conjugate numbers as well. Consequently, by analogy with (8.6), expression (9.7) can be presented in the form of a rational polynomial with real coefficients, and it satisfies the requirements to the filter transfer function.