Parameters of Butterworth, Tschebyscheff, and elliptic prototype reference transfer functions in discrete-time frequency transformations

Explicit relationships are presented for the parameters of the normalized lowpass discrete-time prototype reference transfer function suitable for the derivation of denormalized lowpass, highpass, bandpass, and bandstop discrete-time transfer functions having Butterworth, Chebyshev, and elliptic loss-frequency characteristics. These parameters include the required order of the discrete-time prototype reference transfer function as well as the required passband and stopband edge frequencies for its loss-frequency characteristics