Page 159 - DSP Integrated Circuits

144 Chapter 4 Digital Filters

The cutoff angle, according to Equation (4.31), is

The corresponding lumped element filter shall have a normalized cutoff fre-
quency:

A ladder filter of Butterworth type with cutoff frequency o) c has the element
values

The element values in the lumped element filter are

Using the analogy between the lumped element filter and the transmission
line filter, the characteristic resistances can be determined. We get

4.15 WAVE-FLOW BUILDING BLOCKS

The basic building blocks for the reference filter are unit elements that are either
open- or short-circuited at the far end. According to Equation (4.30), the frequency
response of such a unit element filter is periodic with a period of 2it/T, i.e., the same
as for a digital filter. The signals and components of the unit element filter can be
mapped to a digital filter by sampling with sample period, T = T. In the following
sections, we will derive the wave-flow equivalents to some common circuit ele-
ments and interconnection networks.