Image Processing Reference
In-Depth Information
Digital signal processing program retrieves the stored data from disk and carries out the
processing. Frequency measurement includes dual-channel phase difference and single
frequency measurement modes in the digital signal processing program. The program will
run different functions according to the select mode of users. Single frequency measurement
mode can acquire frequency values and the Allan deviation of every input signal source. In
addition, the dual-channel phase difference mode can output the phase difference between
two input signals.
The output program manages the interface that communicate with other instruments,
exports the data of user interesting to disk or graph. Text files of these data are available if
the user need to analyze data in the future.
3.5 Measurement precision
The dual-mixer and digital correlation algorithms are applied to DFSA. In this system, has
symmetrical structure and simultaneously measurement to cancel out the noise of common
offset reference source. (THOMAS E. PARKER, 2001) So the noise of common offset source
can be ignored. The errors of the Multi-Channel Digital Frequency Stability Analyzer relate
to thermal noise and quantization error (Ken Mochizuki, 2007 & Masaharu Uchino, 2004).
The cross-correlation algorithm can reduce the effect of circuit noise floor and improve the
measurement precision by averaging amount of sampling data during the measurement
interval. In addition, this system is more reliability and maintainability because the structure
of system is simpler than other high-precision frequency measurement system. This section
will discuss the noise floor of the proposed system.
To evaluate the measurement precision of DFSA, we measured the frequency stability when
the test signal and reference signal came from a single oscillator in phase (L.Sojdr, J. Cermak,
2003). Ideally, between the test channel and reference were operated symmetrically, so the
error will be zero. However, since the beat signals output from MBFG include thermal noise,
the error relate to white Gaussian noise with a mean value of zero.
Although random disturbance noise can be removed by running digital correlation
algorithms in theory, we just have finite number of sampling data available in practice. So it
will lead to the results that the cross-correlation between the signal and noise aren't
completely uncorrelated. Then the effect of random noise and quantization noise can't be
ignored. We will discuss the effect of ignored on measurement precision in following
chapter.
According to above formula (3.7) introduction, the frequency drift could be acquired by
measuring the beat-frequency signal at frequency. But in the section 3.2.2, the beat signal is
no noise, and that is inexistence in the real world. When the noises are added in the beat
signal, it should be expressed like:
f
f
b
i
vn
()
V
sin(2
n
)
gn
()
lni
(),
1,2,3 .
(3.8)
i
i
i
i
i
N
Where
i
vn
represents beat-frequency signal,
()
V
indicates amplitude of channel i,
f
is the
nominal frequency of beat-frequency signal, unknown frequency drift
of source under
test in channel i, denotes the initial phase of channel i. Here
N
is sampling frequency of
analog-to-digital converter (ADC),
i
i
gn
denotes random noise of channel i,
()
i
ln
is
()
