Digital Signal Processing Reference
In-Depth Information
50
0
1
−50
0
0
10
20
30
40
50
60
−1
(b) Sample Number of Real Output
0
20
40
60
50
(a) Sample Number of Input
0
+
−50
Input (Real)
0
10
20
30
40
50
60
(c) Sample Number of Imaginary Output
64
63
63
1
0.5
0
1
−0.5
−1
−1
0
1
Magnitude
Angle(Degrees)
(d) Real
Figure 4.33:
(a) Input sequence, a unit step sequence; (b) Real part of output sequence, an increasing
ramp; (c) Imaginary part of output sequence, identically zero; (d) The pole, plotted in the complex plane.
oscillate and the filter seems to ignore the remainder of the input signal as the frequency passes beyond
the pole's resonant frequency.
Reducing the pole's magnitude to 0.95, however, gives the filter a stable response, as shown in
Fig. 4.35.
4.12.5 LEAKY INTEGRATOR
A single-pole IIR with a real pole at frequency zero having a magnitude less than 1.0 is often termed a
Leaky Integrator
, and finds frequent use as a signal averager. Often, when the leaky integrator is used to
average a signal, the input signal is scaled before it enters the summing junction so that the steady state
unit step response is 1.0. The equation of a Leaky Integrator as employed in signal averaging is
y
[
n
]=
βx
[
n
]+
(
1
−
β)y
[
n
−
1
]
(4.21)
where 0
<β<
1
.
0. Thus in the example above, with the pole at 0.9, we have (1-
β
) = 0.9, which implies
that
β
= 0.1, and the steady state unit step response is 1.0. When used as a signal averager,
β
is chosen
