Image Processing Reference
In-Depth Information
audio is expanded, and the positive-side component in Fig. 17 (b) and the negative-side
component in Fig. 17 (c) are obtained. In the calculation example shown in Table 7, we
perform 128-point FFT and 256-point inverse-FFT. Moreover, we perform the shift-
addition of 32 time series data to which the Hamming window is applied after inverse-FFT.
Power
freq.
WF(ω)
Power
-fs
-fs /2
0
+ fs /2
+fs
FB
freq .
(b) IFFT forward component extracted by WF( ω )
0
-fs
-fs /2
+ fs /2
+fs
fs
fs
BLS
Power
WR(ω)
freq.
R B C
FBC
0
-fs
-fs /2
+ fs /2
+fs
RB
FB
RB
(a) spectrum of IQ-input
(c) IFFT reverse component extracted by WF(ω)
Fig. 17. Frequency design of the FFT/IFFT system
4.3.3 The complex IIR filter system
The signal processing block diagram of the complex IIR filter system is shown in Fig. 18.
Zero insertion is carried out with a pre-treatment, and Nyquist frequency is increased. Next,
two complex band-pass filters separate both components directly. The frequency
characteristics of the transfer functions Hf (z) and Hr (z) with the bandwidths of FB and RB
(one side bandwidth) for LPF are shown in Figures 19(a) and 19(b). On the basis of the
Fourier transform shift theory, the frequency shifts ( FBC and RBC ) are applied to z
operators, and a transfer function of LPF changes to the positive-side and a negative-side
band-pass
filters.
Operator
z
is
transformed
to
zz
'
 
e (

j BC
)
and
  . The frequency characteristics of the complex band-pass filters Hf (z')
and Hr (z'') enable the +FBC and -RBC frequency shifts are shown in Fig. 19(c). In the
calculation example shown in Table 7, we use the 8th Butterworth filter by considering the
response of direction separation.
zz
''
exp(
j
C
)
X
IQ-Input
Forward Signal
Complex
BPF Hf(z')
Zero
Insertion
Real(Forward)
2・ fs
Reverse Signal
Complex
BPF Hr(z' ' )
Band Width
Center Freq.
Table
BLS
Real(Reverse)
2・ fs
Fig. 18. Block diagram of the complex IIR filter system
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