Image Processing Reference
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Fig. 1. Multirate filtering applying dyadic HBF decimators, a basic filter, and (transposed)
HBF interpolators
Fig. 2. FDM demultiplexer filter bank; LP/HP: lowpass/highpass directional filter block
based on HBF
Fig. 3. Decimating Hilbert-Transformer (a) and its transpose for interpolation by two (b)
Fig. 4. Two-channel conjugated quadrature mirror filter sub-band coder (SBC) filter bank,
where the filters F
(
)
z
are spectral factors of a linear-phase FIR HBF
Mitra & Kaiser (1993); Vaidyanathan (1993)], which may apply the discrete wavelet transform
[Damjanovic & Milic (2005); Damjanovic et al. (2005); Fliege (1993); Strang & Nguyen (1996)].
Digital linear-phase (LP) FIR and MP IIR HBF have thoroughly been investigated during the
last three decades starting in 1974 [Bellanger et al. (1974)] and 1969 [Gold & Rader (1969)],
respectively. An excellent survey of this evolution is presented in [Schüssler & Steffen
(1998)]. However, the majority of these investigations deal with the properties and the
design of HBF by applying allpass pairs [Regalia et al. (1988); Vaidyananthan et al. (1987)],
also comprising IIR HBF with approximately linear-phase response [Schüssler & Steffen
(1998; 2001); Schüssler & Weith (1987)]. Hence, only few publications on efficient structures
e.g. [Bellanger (1989); Bellanger et al. (1974); Lutovac et al. (2001); Man & Kleine (1988);
Milic (2009); Valenzuela & Constantinides (1983)], present elementary signal flow graphs
(SFG) with minimum computational load. Moreover, only real-valued HBF and complex
Hilbert-Transformers (HT) with a centre frequency of f c
2 ) have been
=
f n /4 (
Ω c
=
considered in the past.
The goal of Section 2 of this contribution is to show the existence of a family of real and
complex HBF, where the latter are derived from the former ones by frequency translation,
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