Structural Health Monitoring Using Smart Sensors - ideals ...

zj =
yjM + l i
jM+l i /L
= hjM+l i -Lmxm
j=0,
m= jM + l i – N +
L
(5.20)
By introducing l i
, the beginning point of the downsampled signal can be finely adjusted.
If the time difference at the start of sensing is taken into account by l i
, the synchronization
accuracy of signals is not limited by the original sampling period.
Resampling is then combined with linear interpolation to achieve the necessary
accuracy. The integer, M is replaced by a real number, M r
. The upsampling rate, L a
,
must remain an integer. M r
and L a
are not uniquely determined. These values are chosen
so that L a
is not too large. A large value of L a
requires a high-order lowpass filter, as is
the case for the normal polyphase implementation of resampling. Using these upsampling
and downsampling factors, resampling is performed. Upsampling is same as before.
However, the downsampling process shown in Eq. (5.20) cannot be directly applied,
because of the noninteger downsampling factor. Output data points to be calculated do not
necessarily correspond to points on the upsampled signal. Output data points often fall
between upsampled data points. Linear interpolation is used to calculate output values as
follows:
zj
= yp l
p u
– p j
+ yp u
p j
– p l
=
p l
L a
hp l
– L a
mxm
p u
– p j
m= p l – N +
L a
p u
L a
+ hp u
– L a
mxm
p j
– p l
m= p u – N +
L a
p j
= jM r
+ l i
p l
= jM r
+ l i
p u
= p l
+
(5.21)
In this way, resampling of an arbitrary noninteger rational factor can be achieved. When
L a
is not too small, the approximation of linear interpolation gives reasonable results. A
value of L a
ranging from 20 to 150 is employed in algorithmic testing and shown to give
reasonable results.
Implementation on Imote2s
The proposed resampling approach is employed to address issues toward
synchronized sensing. This approach is first overviewed.
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