Filter Bank Fusion Frames

In this paper we characterize and construct novel oversampled filter banks implementing fusion frames. A fusion frame is a sequence of orthogonal projection operators whose sum can be inverted in a numerically stable way. When properly designed, fusion frames can provide redundant encodings of signals which are optimally robust against certain types of noise and erasures. However, up to this point, few implementable constructions of such frames were known; we show how to construct them using oversampled filter banks. In this work, we first provide polyphase domain characterizations of filter bank fusion frames. We then use these characterizations to construct filter bank fusion frame versions of discrete wavelet and Gabor transforms, emphasizing those specific finite impulse response filters whose frequency responses are well-behaved.Comment: keywords: filter banks, frames, tight, fusion, erasures, polyphas

M-channel cosine-modulated wavelet bases

The 13th International Conference on Digital Signal Processing, Santorini, Greece, 2-4 July 1997In this paper, we propose a new M-channel wavelet bases called the cosine-modulated wavelets. We first generalize the theory of two-channel biorthogonal compactly supported wavelet bases to the M-channel case. A sufficient condition for the M-channel perfect reconstruction filter banks to construct M-channel compactly supported wavelet bases is given. By using this condition, a family of orthogonal and biorthogonal M-channel cosine-modulated wavelet bases is constructed by iterations of cosine-modulated filter banks (CMFB). The advantages of the approach are their simple design procedure, efficient implementation and good filter quality. A method for imposing the regularity on the cosine-modulated filter banks is also introduced and design example is given.published_or_final_versio

M-Channel compactly supported biorthogonal cosine-modulated wavelet bases

In this correspondence, we generalize the theory of compactly supported biorthogonal two-channel wavelet bases to M -channel. A sufficient condition for the M-channel perfect reconstruction filter banks to construct M-channel biorthogonal bases of compactly supported wavelets is derived. It is shown that the construction of biorthogonal Af-channel wavelet bases is equivalent to the design of a Af-channel perfect reconstruction filter bank with some added regularity conditions. A family of M-channel biorthogonal wavelet bases based on the cosinemodulated filter bank (CMFB) is proposed. It has the advantages of simple design procedure, efficient implementation, and good filter quality. A new method for imposing the regularity on the CMFB's is also introduced, and several design examples are given. ©1998 IEEE.published_or_final_versio

Theory and design of arbitrary-length biorthogonal cosine-modulated filter banks

IEEE International Symposium on Circuits and Systems, Hong Kong, China, 9-12 June 1997The design and generalization of Perfect-reconstruction (PR) cosine-modulated filter banks (CMFB) have been studied extensively due to its low design and implementation complexity. In this paper, the theory and design of arbitrary-length biorthogonal CMFB is considered. This is a generalization of the method used in [5] for designing arbitrary length orthogonal CMFB and has the advantage of simple design procedure. We also propose a systematic design method so that biorthogonal CMFB with longer length can be obtained.published_or_final_versio

A rational subdivision scheme using cosine-modulated wavelets

This paper proposes a rational subdivision scheme using cosine-modulated wavelets. Subdivision schemes constructed from iterated filter banks can be used to generate wavelets and limit functions for multiresolution analysis. The proposed subdivision scheme is based on a kind of nonuniform filter banks called recombination nonuniform filterbanks (RN FB). It is shown that if the component FBs in a RNFB are wavelet FBs, then the necessary condition for convergence to limit functions in the subdivision scheme is also satisfied. Therefore, the design of different rational subdivision schemes is considerably simplified. An efficient RNFB, called RN cosine modulated FBs (CMFB), constructed from uniform CMFBs and cosinemodulated transmultiplexers (TMUX) are further investigated. Using a design technique for designing RN CMFB and cosine modulated wavelets (CMW) previously reported by the authors, very smooth limit functions can be generated from the rational subdivision scheme. A design example is given to illustrate the proposed method.published_or_final_versio

Wavelet methods in speech recognition

In this thesis, novel wavelet techniques are developed to improve parametrization of speech signals prior to classification. It is shown that non-linear operations carried out in the wavelet domain improve the performance of a speech classifier and consistently outperform classical Fourier methods. This is because of the localised nature of the wavelet, which captures correspondingly well-localised time-frequency features within the speech signal. Furthermore, by taking advantage of the approximation ability of wavelets, efficient representation of the non-stationarity inherent in speech can be achieved in a relatively small number of expansion coefficients. This is an attractive option when faced with the so-called 'Curse of Dimensionality' problem of multivariate classifiers such as Linear Discriminant Analysis (LDA) or Artificial Neural Networks (ANNs). Conventional time-frequency analysis methods such as the Discrete Fourier Transform either miss irregular signal structures and transients due to spectral smearing or require a large number of coefficients to represent such characteristics efficiently. Wavelet theory offers an alternative insight in the representation of these types of signals. As an extension to the standard wavelet transform, adaptive libraries of wavelet and cosine packets are introduced which increase the flexibility of the transform. This approach is observed to be yet more suitable for the highly variable nature of speech signals in that it results in a time-frequency sampled grid that is well adapted to irregularities and transients. They result in a corresponding reduction in the misclassification rate of the recognition system. However, this is necessarily at the expense of added computing time. Finally, a framework based on adaptive time-frequency libraries is developed which invokes the final classifier to choose the nature of the resolution for a given classification problem. The classifier then performs dimensionaIity reduction on the transformed signal by choosing the top few features based on their discriminant power. This approach is compared and contrasted to an existing discriminant wavelet feature extractor. The overall conclusions of the thesis are that wavelets and their relatives are capable of extracting useful features for speech classification problems. The use of adaptive wavelet transforms provides the flexibility within which powerful feature extractors can be designed for these types of application