Image Processing Reference
In-Depth Information
shift system are filling the target performance of time-delay. It turns out that calculation
load is light in order of the phase-shift system, the complex IIR system, and the Hilbert
transform system.
load
(MFLOPS)
method
calculation component
estimation equation
Hilbert
transform
R-add: ( tap +1)* fs , R-mul: tap * fs
Ovh: 20%
1.26
( tap =128)
fs *(2* tap +1)*1.2
C-add: ( tap -1)*2+ fs , C-mul:
tap *2* fs
Ovh: 10%
6.74
( tap =128)
complex FIR
fs *(12* tap -4)*1.1
C-add: order *4* fs , C-mul:
order *4* fs
Ovh: 10%
0.84
( order =8)
complex IIR
fs *(24* order )*1.1
12* N * r *1.2*( fs *4/ N )
(FFT shift addition, N /4
shift)
C-add: N * r *3, C-mul: ( N * r /2)*3
Ovh: 20%, R-mul: N *4
1.61
( N =128, r =7)
FFT/IFFT
modulation/
demodulation
C-add: ( tap -1)*2* fs
C-mul: ( tap +2)*2* fs , Ovh: 20%
7.32
( tap =128)
fs *(12* tap -12)*1.2
R-add:
[2* N *(2* N +2* order )+2]* fs
R-mul: 4* N *( N + order )* fs, Ovh:
20%
fs *[4* N *( N + order )
+2*( N -1)]*1.2
0.64
( order =4, N =4)
Phase-shift
R-add: real addition, R-mul: real multiplication, Ovh: over head, C-add: complex addition,
C-mul: complex multiplication, Calculation load is estimated at fs =4kHz
Table 3. Comparison of calculation load
3.4 Comparison of a frequency characteristic and direction separation
Frequency characteristic and direction separation performance are largely dependent on the
filter property that are related to time-delay and calculation load. If the number of filter taps
of FIR and the filter order of IIR are reduced, time-delay and calculation load will decrease.
But these become the trade-off of frequency resolution and frequency characteristic. The
Hilbert transform system frequency characteristic when changing the number of taps is
shown in Fig. 9. The frequency characteristic near the Nyquist and near the DC has
deteriorated, when the number of taps is short. This is the same also about the taps of the
complex FIR system, the modulation/demodulation system and the FFT point number of
the FFT / IFFT system.
In order to compare the direction separation performance, the frequency characteristic
simulation is performed. The frequency characteristics of positive-component (solid line:
forward) and negative-component (dashed line: reverse) are shown in Fig. 10. The target
performance of direction separation is filled except for the phase shift system. The stop-band
property near the low frequency and near the Nyquist frequency is good in the Hilbert
transform system, the complex FIR system, and the FFT/IFFT system. Exclude near the DC
and near the Nyquist frequency, a sufficient separation performance (not less than 30 dB)
and frequency characteristic are acquired by the complex IIR system and the
modulation/demodulation system. The phase-shift system has generally insufficient
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