Digital Signal Processing Reference
In-Depth Information
Figure 15.6
Mean power of the regularization noise versus normalized reference sine-wave
frequency
k
were calculated under the sampling conditions em-
ulating the specifics of massive data acquisition from a variable number of sig-
nal sources. Specifically, the power of the regularization errors
These estimation errors
ε
ε
k
are given in
Figure 15.6 for the case where the single tone signal is characterized by frequency
f
s
and amplitude
A
The mean sampling rate
f
ms
depends both on the reference
frequency
f
r
and the number
n
of signal sources as
f
ms
=
.
f
r
/
n
. In this case the
errors
ε
k
are calculated for various values of
n
while the mean sampling rate
f
ms
is kept constant and equal to 2.18753
f
x
. To keep the mean sampling rate
f
ms
constant, the reference frequency
f
r
is appropriately changed for each
n
value.
Note that
n
is equal to the reference frequency normalized with regard to the
mean sampling rate
n
=
f
r
/
f
ms
.
This means that the power
P
ε
of the regulariza-
ε
tion noise
(
t
k
), given for the growing numbers of signal sources, also indicates
its dependence on the normalized reference frequency.
It can be seen from the diagram obtained and displayed in Figure 15.6 that
the mean power of the regularization noise, even in the worst case, decreases
quickly at relatively small numbers
n
of the signal sources encoded in this way. It
seems that in many cases of data acquisition from multiple signal sources that the
regularization approach should be applicable if the number is about 10 and more.
The feasibility and rationale of this approach is further illustrated in Figure 15.7.
