This example will look at a moving average system.
Some notes about this system:
- It is lowpass
-
It has linear phase with jumps of
π radians when the sinc function
changes sign
-
The duration of the filter is inversely proportional to
its bandwidth
-
This filter is finite impulse response (FIR)
-
It cannot be built with passive R, L, C circuits
-
We do not have independent control over all four design
specifications
We are going to design a moving average filter with the
following design specs:
ω
p
=100π
ω
p
100
,
e
s
=0.1
e
s
0.1
,
e
p
=0.1
e
p
0.1
With this specification, we are allowing
ω
s
ω
s
to be a dependant variable (since we need one). We can now
find the equation for this moving average system.
We begin with
|Hiω|=1.1sinωT2ωT2
H
ω
1.1
ω
T
2
ω
T
2
(1)
We will now solve for
TT
with
|Hi100π|=1.1sin50πT50πT=0.9
H
100
1.1
50
T
50
T
0.9
(2)
For these specs,
T≃0.007
T
0.007
.
This means that
|Hiω|
H
ω
does not stay below
e
s
=0.1
e
s
0.1
until
ω
s
≃771π
ω
s
771
.
It is very clear from this representation that the
transition band is huge (
671π
671
). This is a very bad filter, especially when you
consider that it cannot be implemented with passive
circuitry. Fortunately better filters
(e.g. Butterworth, Chebyshev and Elliptical) do exist.