A Chebyshev, Butterworth or Bessel is a filter approximation function that generates a Laplace Transform rational polynomial that represent the filter type and order on the complex variable plane (the S-Domain). The complex number that sets the denominator of the rational polynomial equal to zero is called the pole. A 1^{st} order pole has one parameter, a real pole frequency, fp and a 2^{nd} order complex pole has two parameters, a complex pole frequency, fp and a unitless quality factor, Q. A Chebyshev, Butterworth or Bessel filter approximation generate a sequence of 1^{st} and 2^{nd} order (fp, Q) pair parameters used by a filter program to produce a filter circuit. An odd order filter has one real pole and one or more complex pole pair, and an even order filter has one or more complex pole pairs. For example, a 3^{rd} order filter has one real fp parameter and one (fp, Q) complex pole pair and a 4^{th} order filter has two (fp, Q) complex pole pairs.
A Chebyshev, Butterworth or Bessel is a filter approximation function that generates a Laplace Transform rational polynomial that represent the filter type and order on the complex variable plane (the S-Domain). The complex number that sets the denominator of the rational polynomial equal to zero is called the pole. A 1^{st} order pole has one parameter, a real pole frequency, fp and a 2^{nd} order complex pole has two parameters, a complex pole frequency, fp and a unitless quality factor, Q. A Chebyshev, Butterworth or Bessel filter approximation generate a sequence of 1^{st} and 2^{nd} order (fp, Q) pair parameters used by a filter program to produce a filter circuit. An odd order filter has one real pole and one or more complex pole pair, and an even order filter has one or more complex pole pairs. For example, a 3^{rd} order filter has one real fp parameter and one (fp, Q) complex pole pair and a 4^{th} order filter has two (fp, Q) complex pole pairs.