Biomedical Engineering Reference
In-Depth Information
FIGURE 5-52
Frequency response
of a low-pass
Butterworth filter.
5.5.5.2 Synthesizing Infinite Impulse Response (IIR) Filters
There is a large body of literature that deals with the synthesis of the common and less
common IIR filter algorithms. However, once again MATLAB synthesizes all common
filter types with minimum effort. For example, the filter for the previous example was
generated with a single command:
[B,A]=butter(3,0.1)
This generates the coefficients of a third-order Butterworth filter with a cutoff fre-
quency of 0.1 (normalized to
f
s
/
2).
In addition to a range of Butterworth filters, MATLAB synthesizes Bessel, Chebyshev,
and elliptical low-pass, high-pass, and band-pass filters of whatever order is required.
However, some care needs to be exercised as numerical issues tend to make high-order
filters unstable.
5.5.5.3 Synthesizing Finite Impulse Response (FIR) Filters
In finite impulse response filters, only the input values are used to produce an output; they
are therefore not recursive.
In this implementation, the shape of the filter is described roughly in terms of the
required amplitude response. So, if the frequency response of the Butterworth filter de-
scribed in the previous section was to be synthesized using a FIR filter, then the following
