Filterbank design for oversampled filter banks without aliasing in the subbands

Abstract

In this paper we propose a new strategy for the design of real-valued lterbanks which avoids aliasing in the subbands (\inband aliasing") such that applications where two subband signals have to be compared become possible. One example for such an application is subband adaptive ltering, where, with the proposed lterbank structure, the traditionally required crossterm adaptive lters between adjacent subbands can be omitted. The proposed lterbank consists of at least three channels which are subsampled by di erent subsampling ratios.

Design of near perfect reconstruction oversampled filter banks for subband adaptive filters

“…Another way to obtain a filter bank satisfying (2) is to use a realvalued nonuniform OSFB and choose a setup where the bandpass sampling theorem is not violated [12], [13]. For a real-valued signal in the lth channel to be undistorted due to decimation by a factor S l ; an interpretation of the bandpass sampling theorem requires the undecimated subband signal's band to lie entirely between any two consecutive frequency points among f = i11=S l ;i=1; 2; 111;S l 01.…”

“…More information on this type of filter bank can be found in [13], [17]- [19]. If a filter bank with a higher number of channels is required, the presented cosine modulation approach can be used, starting with a higher L0; or different setups can be found which satisfy the bandpass sampling theorem.…”

“…The filter banks have been designed to yield a reconstruction error and an inband alias of about 080 dB, giving a resolution of approximately 13 bits. These specifications are targeted at audio applications, but higher quality designs are easily achievable with the presented algorithms [13]. The parameters settings in the design algorithm are =0 :5 and =1 0 .…”

“…Since the prototype design is identical to the design for complex modulated filter banks, it is not discussed further in this paper. Another OSFB class consists of real-valued nonuniform filter banks [13] which have different subsampling ratios S l in each channel to satisfy the bandpass sampling theorem and avoid inband aliasing. In this case, the analysis filters posses different bandwidths which might be advantageous in, e.g., psychoacoustic coding [14].…”

Aliasing-free criticalsampled filter banks design based on frequency domain decomposition

“…For real-valued bandpass signals, literature [4] presented a new method which required single sideband (SSB) modulation into the baseband prior to decimation. Literature [5] proposed a method for the design of real-valued filter banks, where non-uniform filter banks with unequal decimation ratios was adopted, although it avoided the inband aliasing, the aliasing between adjacent bands existed. In order to achieve perfect reconstruction or near perfect reconstruction original signal and to suppress the aliasing inband completely, many optimal criterion [6], [7] are usually selected to design filter banks, but all these could only decrease aliasing but not cancel it completely.…”