Digital Filters - Digital Signal Processing: A Practitioner's Approach - page 46

1.4

1.2 Passband ripple

1

0.8
0.6

Corner frequency

0.4
0.2

Filter roll-off

0

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Figure 3.1 Filter specifications

The unit dB/octave is from music and acoustics. The unit dB/decade is from
control engineering; it is slowly becoming more prevalent in filter design. Most of
the programs available demand the order of the filter. A simple rule of thumb is if N
is the order of the system, then the corresponding slope at the cut-off frequency is
20N dB/decade. A quick reference to Figure 3.1 shows a typical filter specification
in the frequency domain. We specify the filter using

Passband or stopband ripple in dB
Corner frequency or cut-off frequency
Roll-off defined in dB/decade

3.2 Moving-Average Filters
Moving-average (MA) filters are the simplest filters and can be well understood
without much difficulty. The basic reason is that there is no feedback in these filters.
The advantage is that they are always stable and easy to implement. On the other
hand, filters with feedback elements but no feedforward elements are called
autoregressive (AR) filters. Here are some examples.

3.2.1 Area under a Curve
The most common MA filters are used for finding the area under a portion of a
curve by the trapezium rule or Simpson's rule, represented as

u k þ u k 1
2

u k ¼ trapezium rule ; ð 3 : 1 Þ

u k þ 4u k 1 þ u k 2
3

u k ¼ Simpson's rule ; ð 3 : 2 Þ

where f u k g is the input and f

u k g the output. The objective of these two filters is to
find the area between the points by finding out the weighted mean ( u k ) of the

ordinates.