2021-Brubaker, Phil - Optimum Matched Filter Design (Transfer Function)

By Phil B Brubaker

Optimal Designs Enterprise

Download (PDF)

Licensed according to this deed.

Published on


Optimum Matched Filter (Transfer Function)

(Nested Processes ... Each Process controlled by a Solver)

Problem Description

The transfer function H(s) is the Laplace transform of the output signal Yout(s)* divided by the Laplace transform of the input signal Yin(s)*: that is H(s)=   where each signal's transform is assumed to be a ratio of polynomials.  Thus, H(s) can likewise be stated in the form:

Equation 2.1  Generalized H(s)

Assuming the numerator and denominator can be factored, yields H(s) in the general form

Equation 2.2  Factored Transfer Function

where each Zi is known as a "zero" and the Pi as a "pole" of the transfer function.  Zi and Pi are complex points in the Laplace domain.

A realizable transfer function must have poles and zeros with their conjugate points.  That is, poles and zeros come in pairs.  If a pole or zero is located at the complex point si + jwi, then its conjugate is located at si - jwi.  Thus, a generalized transfer function is stated as

Equation 2.3  Generalized Transfer Function H(s)

Given n-data points from a Bode plot (see Figure 2.1 below) that define the mainlobe of the desired transfer function, find the optimal Pole/Zero constellation such that H(s) has equal sidelobe peak amplitudes in a Bode plot and curve fits the given data in the mainlobe.

Bode Plot: Mainlobe with 3 Sidelobes


For more, read attached PDF file.

Links:    Slide Show    Website    Download

Your Turn!

Have a Filter design to solve?  Please state it here and use graphs, pictures, etc. to get your problem well stated and understood by those reading it.

Cite this work

Researchers should cite this work as follows:

  • Phil B Brubaker (2021), "2021-Brubaker, Phil - Optimum Matched Filter Design (Transfer Function)," https://www.simiode.org/resources/8361.

    BibTex | EndNote