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Fig. 30. Identity for elimination of P -fold interfractional PS-SP cascades
Fig. 31. Parallelisation of unit delay (a) and M -fold down-sampler (b) with zero time offset
( p
=
0)
identities [Groth (2003)], the contiguous PM -fold down-samplers of the SP demultiplexer
have a relative time offset of M .
4.2 Parallelisation of SBC-FDFMUX filter bank
Subsequently, we deploy the parallelisation of the high rate FDMUX front-end section of
the versatile tree-structured SBC-FDFMUX FB for flexible channel and bandwidth allocation
[Abdulazim & Göckler (2005); Abdulazim et al. (2007)]. The first three hierarchically cascaded
stages of the FDMUX are shown in Fig.
32 in block diagram form applying BP. In
each stage,
1, 2, 3, the respective input spectrum is split into two subbands of equal
bandwidth in conjunction with decimation by two. For convenience of presentation, all DF
have identical coefficients and, in contrast to Section 3, are assumed as critically sampling
2-channel DFT PP FB with zero frequency offset (cf. [Abdulazim et al. (2007)]). The branch
filter transfer functions H
ν =
0, 1, represent the two PP components of the prototype
filter [Göckler & Groth (2004); Vaidyanathan (1993)] where, by setting z ν
λ (
z
ν )
,
λ =
e j Ω ( ν ) with
:
=
e j Ω ( ν )
Ω ( ν ) =
ν =
λ (
)
2
π
f / f ν and
1, 2, 3, the respective frequency responses H
are obtained,
ν
which are related to the operational sampling rate f ν of stage
. The respective DF lowpass
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