A Little on Filter Topologies

If you ve had enough of digital filters, difference equations, the z-plane, and all that for now, you can skip the next sections and go on to Chapter 4. However, if you just can t get enough of this stuff, read on for some notes about implementing digital filters. 

Noting that the numerator is of third order, and the denominator is of fourth order, we can factor each into first and second order filter segments  

Now that we ve factored it, we can compare the sections to our standard BiQuad forms given in Equation 3.11 and see that this filter gives us two resonances one at r = 0.99,/= 3/8 SRATE and one at r=0.99,/ = 7/8 SRATE. It also gives us one complex zero pair at r = 1.0,/= 5/7 SRATE. Finally, it implements a single zero at/= 0. Since the transfer function is just a product of these, we can rewrite it as a chain of simple filter segments  

Ken Stieglitz. A Digital Signal Processing Primer. Menlo Park Addison Wesley, 1996. 

Lawrence Rabtner and Bernard Gold. Theory and Application of Digital Signal Processing. Englewood Cliffs Prentice Hall, 1974. 

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