Image Processing Reference
In-Depth Information
PQ t
() Im () exp( ( ( )))
x t
j

 
sin(
 
t

( ))
(6)
d
Here,  is
/2
when Doppler frequency
 is positive, and  is
/2
when
 is
negative. So
sign  means the polarity. The subtraction-output Forward(t) and the
addition-output Reverse(t) are
()
d
Forward t
PI t
PQ t
sign

t
(7)
()
()
() (
(
) 1) sin(
 
 
( ))
d
d
Re
verse t
()
PI t
()
PQ t
()

(
sign
(
) 1) sin(
 

 
t
( ))
(8)
d
d
From the formulas (7) and (8), when  is positive, only the Forward(t) serves as a non-
zero output. And when  is negative, only the Reverse(t) serves as a non-zero output. Thus,
IQ-signals are separable into positive-component and negative-component. Comparison of
direction separation performance is shown in Fig. 5. The frequency-characteristic in the
velocity range 4kHz (-2kHz to +2kHz) that is well used in diagnosis of the cardiac or
abdomen is shown. A solid line shows the positive-component ( Forward ) and a dashed line
shows the negative-component ( Reverse ). The direction separation performance of the phase-
shift system (conventional analog system) is shown in Fig. 5(a), and the direction separation
performance of the complex IIR filter system (digital system referenced in section 3.2) is
shown in Fig. 5(b).
Reverse
Forward
Frequency
(Hz)
Power (dB)
Forward
Reverse
( )
p
y
(
)
Fig. 5. Direction separation performance
In Fig. 5, a filter-order to which hardware size becomes same is set up. In the complex IIR
filter system, sufficient separation performance (more than 30 dB) is got except for near a
low frequency and near the Nyquist frequency. On the one hand a ringing has occurred by
the phase shift system, there is little degradation near the Nyquist frequency. Although the
direction separation performance near a low frequency and near the Nyquist frequency can
improve if the filter-order is raised in the complex IIR filter system, the processing load
becomes large. It is although the ringing will decrease if range of the phase-shift system is
divided finely, processing load becomes large similarly.
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