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Nonuniform filter banks
Multirate
filter banks are used extensively in a number of signal
processing applications such as subband coders for speech
signals, frequency domain speech scramblers, and image
coding. The theory of perfect reconstruction (PR) and near
perfect reconstruction (NPR) filter banks with uniform frequency
partition has been well established. However, in some
applications, uniform filter banks are unable to provide
appropriate time-frequency decomposition. For example, in
the design of the filter banks that approximate the
time-frequency resolution of human ears, nonuniform spacing that
matches
the critical bands is preferred. This nonlinear arrangement is
much useful when the signal energy exhibits bandwidth dependent
distribution among frequency bands.
The
main focus of our group is to analyze and develop efficient
structures and effective design procedures for general
nonuniform filter banks (NUFBs). In
particular, we pay attention to those with linear phase (LP)
property which is crucial in some applications such as image
coding. In the recent work, Dr. Xie proposed an indirect
method to design LP NUFBs with rational decimators based on the
recombination structure. Then, a direct design approach of LP
NPR NUFBs with integer sampling factors was proposed, where the
transition bands of adjacent two analysis/ synthesis filters are
forced to follow a cosine roll-off function to eliminate
the amplitude and aliasing distortions. Later, the idea was
extended to the rational case. Now we are woking on the design
of M-channel
irrational filter banks and another new method to obtain NUFBs
with LP property.
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2-D directional filter banks
Many multidimensional applications such as image enhancement,
denoising, edge detection are germane to the directional
information, so how to process this information is crucial. The
directional filter bank has been proven to be effective in this
field due to the attractive property that they can decompose an
image into directional subbands£each
corresponding to a unique angular orientation, and reconstruct
that image perfectly by using a dual synthesis filter bank.
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wavelet-like filter banks
The theory of the wavelet-like filter bank is just exploring. It
may result in some compromise of the requirements of wavelets
but at the same may
present some useful properties in practical signal processing.
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