Image Processing Reference
In-Depth Information
2
2 sin(
n
/2)
hn
1(
)
 
(
n
0)
(11)
n
0
(
n
0)
Complex FIR system:
There is a report of the Doppler audio separation processing using a complex FIR filter.
However, since there is no description about a filter coefficient, we designed in a frequency
domain and transformed into FIR coefficient in time domain using inverse Fourier
transform. The output of complex FIR system is denoted by formulas (12) and (13). In the
estimation of Table 3, the 128-tap coefficient sequence with the pass band of
fs
/ 128
to
is used.

63
fs
/ 128
Fn Xn HFn ap
2(
)
(
)
2(
)
(12)
Rn Xn HRn ap
2(
)
(
)
2(
)
(13)
Complex IIR system:
Based on the shift theory of Fourier transform, frequency shift is applied to z operators. A
real-LPF transfer function is changed into the positive-BPF and the negative-BPF. The
complex IIR transfer functions become a formulas (14) and (15).
Fz HFzXz
3( )
3( )
( )
(14)
Rz HRzXz
3()
3()
()
(15)
When the transfer function of real LPF is set to RLPF (z), transfer functions of HF3 (z') and
FR3 (z'') are calculated by transformed operators. In the estimation of Table 3, the filter with
the 8th order Butterworth type is used.
HF
3( )
z
RLPF
3(
z
')
where
z
'
 
j z
(16)
HR
3( )
z
RLPF
3( '')
z
where
'' zj z
 
(17)
FFT/IFFT system:
The IQ-signal is separated by the positive-filter and negative-filter in a frequency domain.
Next, the separated spectra are returned to waveforms in time domain by inverse-FFT.
There is a report of this system aiming at the Doppler noise rejection. For the continuous
output after inverse-FFT, a shift addition of the time waveform is carried out in time
domain. The outputs of this system can be denoted by formulas (18) and (19). In estimation
of Table 3, FFT/IFFT point number is set to 128, and used the frequency filter of
fs
/ 128
to
 for separation. Moreover, Hamming window ( h4 ) is applied, and 32 time-
series are shift-added.
63
fs
/ 128
Fn
4(
)
Re
IFFTWF
(
)
FFTXn
(
)
hn
4(
)
(18)
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