Image Processing Reference
In-Depth Information
sides correspond to the baseline-shift shown in Table 5.
FB
and
RB
indicate the bandwidths
on the positive (forward) and negative (reverse) sides, whereas
FBC
and
RBC
, the center
frequencies on the same sides, respectively. These are normalized using
fs
. Although five
stages were used from the baseline shift range of -0.5 to +0.5 in this example, a small setup is
possible with the actual Doppler ultrasound system.
4.3 Three kinds of digital signal-processing ideas
4.3.1 The modulation/demodulation system
The block diagram of the modulation/demodulation system is shown in Fig. 14. The IQ-
signal is modulated with two sets of quadrature modulators. Thereby, the frequency of the
signal induces a
+FBC
shift on the positive-side and a
-RCB
shift on the negative-side. Next,
Nyquist frequency is doubled by zero insertion, and applying band limitations on the
positive and negative sides demodulates signals. The input signal (equivalent to (A) in Fig.
12) with the aliasing spectrum in Fig. 15(a) is modulated, and the spectra indicating the
+FBC
, and
-RCB
shifts of the frequency of the signal are shown in Figures 15(b) and 15(c),
respectively. A positive-side component and a negative-side component are extracted by
carrying out a baseline-shift and applying a band limitation using the bandwidths of
FB
and
R
in the passage regions of
LPF1 (z)
and
LPF2 (z).
The spectra of the
LPF1 (z)
and
LPF2 (z)
outputs are shown in Figures 15(d) and 15(e). Since sampling frequency has
doubled after an LPF output, the direction separations on the positive and negative sides
that shift the frequencies of
-FBC/2
and
+RCB/2
by demodulation, and are denoted by
BPF1
(z)
and
BPF2 (z)
in Fig. 15(f) are realizable. Although the spectrum in Fig. 15 (equivalent to
the aliasing (A) in Fig. 12) is outputted to the negative side for the Nyquist frequency
fs/2
, it
can extract the positive-side component beyond the Nyquist frequency in Fig. 15( f). The
operation was changed and performed in the calculation example shown in Table 7. For
response improvement, we did not use a FIR filter for LPF but the 8th IIR filter with an
equivalent performance.
Zer o
Insertion
Complex
LPF1(z)
Forward Signal
IQ-Input
×
×
Real(Forward)
exp(-π
・
FBC
・
j)
exp(+π
・
FBC/2
・
j)
2・
fs
Reverse Signal
Zer o
Insertion
Complex
LPF2(z)
×
×
Real(Reverse)
exp(+π
・
RBC
・
j)
exp(-π
・
RBC/2
・
j)
2・
fs
Band Width
Center Freq.
Table
BLS
Fig. 14. Block diagram of the modulation/demodulation system