Image Processing Reference
In-Depth Information
N
1
1
(cos( )
2
2

B
co ( )

B
)
ij
ij
N
4
m
0
N
1
1
1
2
2
cos (
 
)
(
B
cos(
 
)
B
)
ij
ij
4
N
m
0
2
2
2
N
1
1
2
1
g
2
cos (

)
(
B
NNN
)
cos(
)
(3.25)
ij
ij
4
12
m
N
0
2
2
2
1
1
2
1
g
2
cos (
 
)
(
B
NNN
)
ij
4
12
m
0
2
2
2
1
2
g
2
cos (
 
)
(
)
ij
4
NN
12
2
 represent standard deviation of Gaussian random variable, Signal Noise Ratio
2
2
g
Where
V
SN
, and here the V is the amplitude of input signal, let amplitude resolution of a-bit
2
21
digitize and quantization step be , here variable 'a' can be 8~24. We have
( Ken
a
V
Mochizuki, 2007). Applying this equation to formula (3.25) term by term, we obtain
2
2
1
1
2
V
2
2
cos (
 
)
(
)
(3.26)
e
ij
2
4
N
12
SN
Where  is the standard deviation of measurement initial phase difference. The standard
deviation of digital correlation algorithms depends on the sampling frequency N, SNR
and amplitude resolution 'a', as understood from formula (3.26). Here the noise of
amplitude resolution can be ignored if the 'a' is sufficiently bigger than 16-bit and the
SNR is smaller than 100 dB. The measurement accuracy for this method is mostly related
to SNR of signal. This method has been tested that has the strong anti-disturbance
capability.
4. System noise floor and conclusion
To evaluate the noise floor, we designed the platform when the test signal and reference
signal were distributed in phase from a single signal generator. The signal generator at
10MHz and the beat-frequency value of 100Hz were set. For this example obtained the Allan
deviation (square root of the Allan variance (DAVID A, HOWE)) of
  
( )
4.69
E
14
at
y
 second.
The measurement ability could be optimized further by improving the performance of OG.
Because the reference of the system is drove by the output of OG.
Since the digital correlation techniques can smooth the effects of random disturbance of the
MBFG, it can achieve higher measurement accuracy than other methods even if on the same
MBFG.
 second and
1
  
( )
1.27
E
15
at
1000
y
Search WWH ::




Custom Search