Image Processing Reference
In-Depth Information
R
4(
n
)
Re
IFFT WR
(
)
FFT X n
(
)
h
4(
n
)
(19)
Modulation/demodulation system:
IQ signal is modulated and frequency is shifted
+fs/4
and
-fs/4
. The positive-component (0 to
+fs/2
) and negative-component (
-fs/2
to
0
) are extracted by LPF. The
+fs/4
shift and the
-fs/4
shift are returned by demodulation. The direction separation outputs are calculated by
formulas (20) and (21). The example of Table 3 is referred to the prior art. The 128-tap FIR
low-pass filter, which has 63/128 cut-off, is used.
Fn
5(
)
Xn
(
) exp
j n
F tap
(
)
exp
j n
(20)
2
2
Rn
5(
)
Xn
(
) exp
j n
F tap
(
)
exp
j n
(21)
2
2
Phase-shift system:
There are two sets of phase-shifter with the transfer characteristic that makes relative phase
difference of IQ-signal 90 degree. The addition-and-subtraction of these outputs is used.
The direction separation outputs are calculated by formulas (22) and (23).
F
6( )
z
Re
X z
( )
Phase
1( )
z
Im
X z
( )
Phase
2( )
z
(22)
R z
6( )
Re
Xz
( )
Phase z
1( )
Im
Xz
( )
Phase z
2( )
(23)
The two sets of phase-shifter are the cascade connection of second-order all-pass filter
arrays. They are denoted by formulas (24) and (25) as a
Phase1 (z)
and a
Phase2 (z).
In the
estimation of Table 3, the cascade connections of four steps of all-pass filters are used.
Moreover, in order to improve the performance near the Nyquist frequency, an interpolator
and a decimator are added before and after phase-shifter. Table 3 is calculated in
N
= 4, and
the FIR filter of
2N
tap is used as an interpolator.
n
1
z
a
k
Phase
1( )
z
(24)
1
1
az
k
1
k
n
1
zb
k
Phase
2( )
z
(25)
1
1
bz
k
1
k
Above six kinds of signal-processing algorithms are confirmed by the simulation. The chirp-
waveform that frequency and a direction are changed is used as an input. The result of a
simulation is shown in Fig. 7. Fig. 7(a) is an input signal and the sign of frequency has
inverted near 200ck (equivalent to the time shown in the Fig. 7 broken line). A solid line is I-
signal and a dotted line is Q-signal. Figures 7(b) to (g) are output waveforms of each signal-
processing system. A solid line is a positive-output (forward) of the Doppler audio, and a
dotted line is a negative-output (reverse) of the Doppler audio. Amplitude of positive-
output becomes large on the right-hand side of a broken line, and it becomes small on the
