Digital Signal Processing Reference
In-Depth Information
APA(K=1), L = 32
APA(K=2), L = 32
APA(K=8), L = 32
APA(K=1), L = 512
APA(K=2), L = 512
APA(K=8), L = 512
−5
−10
−15
−20
−25
0
500
1000
1500
2000
2500
3000
3500
4000
Iteration number
Fig. 4.10
Comparison between NLMS, APA (
K
=
2) and APA (
K
=
8) with filter lengths
L
=
32
and
L
=
512.
μ
=
1and
a
=
0
−5
APA (K=1), a = 0.5
APA (K=2), a = 0.5
APA (K=8), a = 0.5
APA (K=1), a = 0.9
APA (K=2), a = 0.9
APA (K=8), a = 0.9
−10
−15
−20
−25
0
100
200
300
400
500
600
700
800
900
1000
Iteration number
Fig. 4.11
Comparison between NLMS, APA (
K
=
2) and APA (
K
=
8) for AR1 input with pole
in
a
=
0
.
5and
a
=
0
.
9.
μ
=
1and
L
=
32
μ
=
but with
1. For a fixed
L
, the fact that the input is already decorrelated (since
=
a
0) makes the increase in order
K
not very useful to improve convergence. The
filter length makes a strong effect on the convergence speed. The dashed lines show
the predicted steady state error for the NLMS case, which is unaffected by
L
,asit
depends on
v
.
The effect of the input color is studied in Fig.
4.11
, where
L
σ
and
μ
1were
used. For the NLMS, the increase in the input color worsens the speed of convergence
without affecting the steady state error. Increasing the filter order improves the speed
of convergence, although the steady state error is affected. The gain in speed of
convergence is the largest when we move from
K
=
32 and
μ
=
=
1to
K
=
2[
51
], an effect that
is more noticeable with highly colored inputs.
Finally, in Fig.
4.12
we used
μ
=
0
.
25 and
μ
=
1
.
75 with fixed
L
=
512 and
a
the speed of convergence is quite similar
(for a fixed
K
) but the steady state error increases with
=
0
.
5. We see that for these values of
μ
μ
. This confirms the remark
made previously stating the region 0
<μ<
1 as the most convenient to use in
