Digital Signal Processing Reference
In-Depth Information
0
0
(
a
)
(
b
)
-10
-10
-20
-20
= 0.95
= 1.05
-30
-30
-40
-40
= 0.995
-50
= 1.005
-50
-60
-60
-70
-70
-80
-80
0
0.2
0.4
0.6
0.8
1
0
0.2
0.4
0.6
0.8
1
N
ormalised Frequency,
F
Normalized Frequency,
F
N
ormalised Frequency,
F
Normalized Frequency,
F
Figure 2.32
Effect of manipulating the central coefficient in an odd-length filter. (a) Reduction of
h
L
/2+1
by 0.5% (
= 0.995) and 5% (
= 0.95). (b) Increase of
h
L
/2+1
by 0.5% (
= 1.005) and 5% (
=
1.05).
2.12 SUMMARY
This chapter discussed the method used to design the filters that will be presented
in the following chapters. All filters were designed using the Gaussian window. In
particular, the design rules were presented along with the limitations of the
technique. However, it was suggested that in most product development
applications, especially where there is little time to weigh the benefits of several
filter designs, the window technique proves useful. Moreover, it was felt that
some basic implementation tools should also form part of the presentation. This
was done by reviewing actual filter designs that focused on time and frequency
domain implementations, as well as decimation, cascading, and interpolation,
along with their algorithms. Noise was also considered where white noise
propagation through the filter was used as a good working model. In Chapters 3 to
5, the coefficients for low-pass, high-pass, and band-pass filters, in addition to
their general performance features, will be given in a data sheet format.
Differentiators and Hilbert Transformers will be treated separately in Chapters 6
and 7.
