Image Processing Reference
In-Depth Information
Fig. 22. SFG of directional filter with allowing for 2-out-of-4 channel selection: FDMUX
approach;
N
=
11
encompasses all complex signal processing to be performed by the modified causal HBF
prototype.
An illustrative example with an underlying HBF prototype filter of length
N
=
+
=
11
is shown in Fig. 22 [Göckler & Groth (2004)]. Due to polyphase decomposition (45) and (46),
sample rate reduction can be performed in front of any signal processing (shimming delays:
z
−
1
). Always two polyphase components of the real and the imaginary parts of the complex
input signal share a delay chain in the direct form implementation of the modified causal
HBF, where all coefficients are either real- or imaginary-valued except for the centre coefficient
h
0
=
n
1
2
e
j
4
.Asaresult,only
N
1
+
3 real multiplications must be performed to calculate a set
of complex output samples at the two (i.e. all) DF output ports. Furthermore, for the FDMUX
DF implementation a total of
(
3
N
−
5
)
/2 delays are needed (not counting shimming delays).
The calculation of
v
p
(
0, 1, 2, 3, is readily understood from the signal flow graph (SFG)
Fig. 22, where for any filter length
Nalwaysone
of these quantities vanishes as a result of
the zero coefficients of (9). Hence, the
I
m
)
,
p
=
4 point IDFT, depicted in Fig. 23(a,b) in detailed
form, requires only 4 real additions to provide a complex output sample at any of the output
ports
o
=
; Fig. 23(b). Channel selection, for instance as shown in Fig. 21, is
simply achieved by selection of the respective two output ports of the SFG of Figs.22 and
23(a), respectively. Moreover, the remaining two unused output ports may be deactivated by
disconnection from power supply.
∈{
0, 1, 2, 3
}
