Digital Signal Processing Reference
In-Depth Information
Chapter 3
Analog Lowpass, Highpass, Bandpass, and
Bandstop Filters
In the last chapter, we were able to determine the normalized approximation
functions for the most common types of analog filters. Our task in this chapter is
to unnormalize those approximation functions in a manner to produce lowpass,
highpass, bandpass, and bandstop filters at the desired frequencies. This
unnormalization will be carried out in such a way that the design of the
normalized approximation functions will be central to the development. Figure 3.1
shows the three-step procedure used in the unnormalization. The simplicity of this
procedure is the fact that the second step is the same for all filter design methods.
Figure 3.1
Procedure for unnormalization.
3.1 UNNORMALIZED LOWPASS APPROXIMATION FUNCTIONS
Even though the normalized approximation functions determined in the previous
chapter are lowpass functions, they still need to be unnormalized to the proper
operational frequency. The first step in the unnormalization procedure, as
indicated in Figure 3.1, is to determine the order of the approximation function
from the unnormalized specifications. The order of approximation function
depends only on the passband and stopband gains and frequencies. The gains for
both the normalized and unnormalized approximation functions will be the same,
the only specifications that change are the passband and stopband edge
frequencies. However, as indicated in Chapter 2, it is not the individual
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