Oversampled FIR and IIR DFT filter banks and Weyl-Heisenberg frames

Bölcskei, Helmut; Hlawatsch, Franz; Feichtinger, H. G.

doi:10.1109/icassp.1996.543920

Cited by 23 publications

(24 citation statements)

References 12 publications

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“…A detailed study of such a factorization problem for both polynomial and rational matrices is given in [56]. Alternatively, the approximative calculation of can be based on a series expansion similar to (16): Using the correspondence between the frame operator and the UFBF matrix , we have [57] VII. SPECIAL CASES In this section, we discuss FB's whose frame operator becomes a simple multiplication operator in the polyphase domain or in the frequency domain, i.e., the polyphase representation or the Fourier transform "diagonalizes" the frame operator.…”

Section: B Construction Of Paraunitary Fb'smentioning

confidence: 99%

“…If the FB corresponds to a UFBF, then an approximative calculation of the minimum norm synthesis FB (which is analogous to the approximation of dual frames described in [33]) can be based on a series expansion of . Indeed, applying the Neumann series expansion [44] to the matrix , the minimum norm synthesis FB is expressed as (16) The convergence of this series expansion follows from frame theory [28] using the correspondence between the frame operator and the UFBF matrix ; it will be faster for snugger frames, i.e., for closer frame bounds . By truncating the expansion (16), the synthesis FB can be approximated with arbitrary accuracy.…”

Section: Approximative Construction Of the Synthesis Filter Bankmentioning

confidence: 99%

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Frame-theoretic analysis of oversampled filter banks

Bölcskei

Hlawatsch

Feichtinger

1998

IEEE Trans. Signal Process.

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Abstract-We provide a frame-theoretic analysis of oversampled finite impulse response (FIR) and infinite impulse response (IIR) uniform filter banks (FB's). Our analysis is based on a new relationship between the FB's polyphase matrices and the frame operator corresponding to an FB. For a given oversampled analysis FB, we present a parameterization of all synthesis FB's providing perfect reconstruction. We find necessary and sufficient conditions for an oversampled FB to provide a frame expansion. A new frame-theoretic procedure for the design of paraunitary FB's from given nonparaunitary FB's is formulated. We show that the frame bounds of an FB can be obtained by an eigenanalysis of the polyphase matrices. The relevance of the frame bounds as a characterization of important numerical properties of an FB is assessed by means of a stochastic sensitivity analysis. We consider special cases in which the calculation of the frame bounds and synthesis filters is simplified. Finally, simulation results are presented.

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Section: B Construction Of Paraunitary Fb'smentioning

confidence: 99%

Section: Approximative Construction Of the Synthesis Filter Bankmentioning

confidence: 99%

Frame-theoretic analysis of oversampled filter banks

Bölcskei

Hlawatsch

Feichtinger

1998

IEEE Trans. Signal Process.

Self Cite

306

324

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“…Note that (compared with critical subsampling) the matrices and , respectively, are unchanged in the oversampled case so that the original phase offset in (13) and (16) is preserved. The matrix is of size , where , and therefore, the polyphase matrices and are of size and , respectively.…”

Section: Polyphase Representation For Oversampled Filter Banksmentioning

confidence: 99%

“…The literature [10], [11], [13] covers only the paraunitary case, where the same prototype is used for analysis and synthesis. However, for relating DFT filter banks to the cosine-modulated banks derived in this paper, it is useful to consider two different prototypes ( and ) also for DFT banks.…”

Section: E Relation To Dft Filter Banksmentioning

confidence: 99%

“…These main aliasing components are not present in the oversampled case, with sufficiently high oversampling. Recently, perfect reconstruction (PR) conditions for oversampled DFT filter banks have been derived, and general relations between oversampled filter banks and frame theory have been investigated [10]- [13]. Due to the modulated nature of DFT and cosine-modulated filter banks, the requirements on the prototypes are somewhat related.…”

Section: Introductionmentioning

confidence: 99%

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Oversampled cosine-modulated filter banks with arbitrary system delay

Kliewer

Mertins

1998

IEEE Trans. Signal Process.

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Abstract-In this paper, design methods for perfect reconstruction (PR) oversampled cosine-modulated filter banks with integer oversampling factors and arbitrary delay are presented. The system delay, which is an important parameter in realtime applications, can be chosen independently of the prototype lengths. Oversampling gives us additional freedom in the filter design process, which can be exploited to find FIR PR prototypes for oversampled filter banks with much higher stopband attenuations than for critically subsampled filter banks. It is shown that for a given analysis prototype, the PR synthesis prototype is not unique. The complete set of solutions is discussed in terms of the nullspace of a matrix operator. For example, oversampling allows the design of PR filter banks having unidentical prototypes (of equal and unequal lengths) for the analysis and synthesis stage. Examples demonstrate the increased design freedom due to oversampling. Finally, it is shown that PR prototypes being designed for the oversampled case can also serve as almost-PR prototypes for critically subsampled cosine-modulated pseudo QMF banks.

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