FIR oversampled filter banks and frames in ℓ 2 (Z)

Perfect reconstruction oversampled filter banks are equivalent to a particular class of frames in l/sup 2/(Z). These frames are the subject of this paper. First, the necessary and sufficient conditions of a filter bank for implementing a frame or a tight frame expansion are established, as well as a necessary and sufficient condition for perfect reconstruction using FIR filters after an FIR analysis. Complete parameterizations of oversampled filter banks satisfying these conditions are given. Further, we study the condition under which the frame dual to the frame associated with an FIR filter bank is also FIR and give a parameterization of a class of filter banks satisfying this property. Then, we focus on non-subsampled filter banks. Non-subsampled filter banks implement transforms similar to continuous-time transforms and allow for very flexible design. We investigate the relations of these filter banks to continuous-time filtering and illustrate the design flexibility by giving a procedure for designing maximally flat two-channel filter banks that yield highly regular wavelets with a given number of vanishing moments.

A new approach is presented for the design of two-channel perfect-reconstruction (PR) FIR filter banks employing linear-phase analysis and synthesis filters. The approach guarantees the designed filter bank to be PR through a set of implicit mathematical relationships. Furthermore, the approach formulates the design as an unconstrained quadratic programming problem to simultaneously optimize the frequency responses of the analysis and synthesis filters. The criterion for optimality is least-squares. The design technique is extendable to M-channel (M/spl ges/2), and this extension is currently under development.

There are some applications that require oversampled filter banks, for example, adaptive signal processing using multirate filter banks. Little study was done, however, for such filter banks compared with maximally decimated ones. In this paper, we propose a design method for oversampled filter banks which satisfy the perfect reconstruction and linear phase properties. Moreover, we consider the design method for both orthogonal and biorthogonal ones. When the decimation ratio is not a divisor of the number of channels, we find it impossible for analysis and synthesis filters to have the same frequency responses by considering the mechanism of aliasing cancellation. In other words, biorthogonal filter banks can be designed under an arbitrary decimation ratio, while it is restricted to a divisor of the number of channels in the orthogonal case. We first derive the conditions for perfect reconstruction and linear phase for both biorthogonal and orthogonal ones. Then, we present the design method for both cases. Finally, some design examples are shown. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(10): 78–86, 1997

We propose a new method for design of computationally efficient nonsubsampled multiscale multidirectional filter bank with perfect reconstruction (PR). This filter bank is composed of two nonsubsampled filter banks, for multiscale decomposition and for directional expansion. For multiscale decomposition, we transform the 1-D equivalent sub band filters directly into 2-D equivalent sub band filters. The computational cost is considerably reduced by avoiding the computation of 2-D convolutions. The multidirectional decomposition utilizes fan filters. A new method for design of 2-D zero phase FIR fan filter transformation function is developed. This method also aids the transformation of a 1D filter bank to a 2-D multidirectional filter bank. The potential application of the proposed filter bank is illustrated by comparing the image denoising performance of the proposed filter bank with other design method that exist in available literature.

In this work we look at the class of uniform biorthogonal FIR, IIR and hybrid filter banks with M = 2 channels. When quantization noise passes through the synthesis filter bank, it gets amplified due to the multiplication of synthesis filter norms to the quantization noise in each channel. Better compression, or higher coding gain, can be achieved if the quantization noise amplification is reduced. Scaling down of the synthesis filters to maintain the property of perfect reconstruction does not work so the analysis of the filter bank needs to be scaled up. Minimization of such amplification has been proposed earlier for FIR filter banks. We are proposing an implementable and stable coloring filter for IIR filter bank which is the optimum coloring filter for the assumed filter structure. We deal with an example of a hybrid filter bank based on all pass delay chain structure.

This paper presents the multirate and re-sampling techniques to realize a low-delay, 18-band quasi-ANSI filter bank for digital hearing aids, which not only achieves a rather low computation complexity without a significant increase in the latency, but reduces greatly the total computation complexity for sub-band signal processing followed by the filter bank, such as noise reduction as well as wide dynamic range compression (WDRC). Researches done in the literature all focused on how to reduce the computation complexity of the filter bank. In particular, with the efficient multirate and interpolated FIR (IFIR) approaches for a 10-ms, 18-band quasi-ANSI filter bank, approximately 93% of the multiplications are saved, compared that with a straightforward parallel FIR filters architecture. However, they did not consider the computation complexity of the sub-band signal processing. In this paper, we first investigate realizing the FIR filter bank efficiently by using the multirate re-sampling techniques. To reduce the complexity, the optimized re-sampling factor for each filter band is explored carefully. Then, with the resampling technique, an efficient multirate quasi-ANSI FIR filter bank architecture is proposed. Compare to the state-of-the-art quasi-ANSI filter bank, approximately 17.7% of multiplicative complexity is reduced further and, up to 25% of the total computation complexity for sub-band signal processing followed by the filter bank is saved, but with only a slight increase in latency, i.e. 13.6 ms.

This paper focuses on subband coding schemes based on critically decimated paraunitary filter banks. An additional network with matrix A is introduced on the decoder side. We show here how to optimize its coefficients jointly with the quantization steps in order to reduce the reconstruction mean square error (MSE) on the output signal due to quantization and filtering. This optimization is performed under bit-rate constraint. Of course, the resulting overall MMSE filter bank (including A ≠ I m ) does not allow perfect reconstruction (PR), but the signal-to-noise ratio (SNR) is remarkably better than for the PR solutions. The main advantage of such an approach is to preserve the original structure of the filter bank while improving the SNR. Here, we apply the method to modulated filters which can be implemented at very low cost. Solutions are given by comparing rate-distortion curves for various forms of A, several paraunitary modulated filter banks, and two bit-rate measures.

In this work, the problem of design of M channel biorthogonal FIR perfect reconstruction filter banks (FIRPRFB) is addressed using spectral theory of matrix polynomials. The present characterization covers a broader class of filter banks. Some insightful results on reconstruction delay and length of synthesis filters are presented, both of these parameters can be varied in the present characterization. Simulation results are presented for 2,3,4 channel designs.

In this paper, two methods for designing two-channel causal stable IIR PR filter banks are introduced. The first method makes use of model reduction and constrained optimization to obtain a causal stable IIR filter bank from the structural PR FIR filter bank proposed by Phoong et al (1995). It yields better frequency characteristics than the original FIR filter bank and avoids the dump at /spl pi//2 when allpass filters are used. Using a 1-D to 2-D transformation, a two dimensional PR IIR filter bank can readily be obtained from these prototypes. The second method is based on a constrained optimization technique using the general PR condition. Using this technique, filter banks with low system delay and flexible frequency characteristics can be designed. The technique can also be modified to design causal stable IIR dyadic wavelet bases with added regularity conditions. A number of design examples are used to demonstrate the usefulness of the proposed design methods.

An oversampled linear phase (LP) perfect reconstruction (PR) filter bank (FB) with a lattice structure involving a noise robust building block is presented. The structure is based on the generalized lapped pseudo-biorthogonal transform (GLPBT), which represents a large class of lapped transforms. Given an analysis bank of the GLPBT and a correlation matrix of noise, the proposed synthesis bank reduces the noise component and attains PR. Numerical results show that this class of filter bank is effective in transmission of oversampled data over noisy channels.

An efficient two-step approach is presented for designing two-channel perfect-reconstruction linear-phase FIR filter banks. The first step involves finding a good solution by using an iterative procedure. This iterative procedure is generated by properly modifying the Lagrange-Newton method proposed by Horng and Willson (1992). In the second step, the resulting solution is then used as a good initial solution for further optimization that is carried out by the second algorithm of Dutta and Vidyasagar (1977). Several examples are included illustrating the efficiency of the proposed approach and the resulting two-channel filter banks.

Due to the sample-and-hold nature of liquid crystal display (LCD) image formation, LCDs suffer from motion picture blur. This is especially evident during scenes containing fast motion due to the inherent sample-and-hold nature of LCD image formation. Using models for the human visual system (HVS) we take a signal processing approach to solving this problem by pre-processing the data before it is sent to the display. Whereas previous pre-processing approaches either apply a simple high pass filter or an iterative deconvolution algorithm, this work uses a small collection of efficient linear FIR filters to reduce the amount of perceived motion blur. Specifically, we develop a two-channel non-perfect reconstruction filter bank to reduce the motion dependent low pass effects of the HVS. Perceptual tests indicate that our algorithm reduces the amount of perceived motion blur on LCDs at a lower complexity than the existing deconvolution approach.

This paper proposes design algorithm for real valued, even order oversampled five channel FIR filter banks with selection of frequency bands and filter order, which reduces inband aliasing and amplitude distortion and removal of noise. This filter bank is designed using direct form-II transposed structure. Analysis of two dimensional (2D) image is carried out using five channel oversampled filter bank. This system is suitable for any images format.

This paper introduces design methods for over-sampled perfect reconstruction filter banks with real-valued coefficients. We deal with FIR filter banks in which all analysis filters have the same length. Two methods are presented for designing integer oversampling ratio and rational oversampling ratio filter banks, respectively. In addition, we further consider design of linear phase perfect reconstruction filter banks by the proposed methods. Finally, two design examples are presented to confirm the validity of our approach.

Considers the theory of cosine-modulated 2 dimensional (2-D) perfect reconstruction (PR) filter banks. First, a 2-D digital filter design with half passband, obtained by the sampling matrix, is discussed. Next, 2-D analysis filter banks are realized by cosine-modulating this prototype 2-D digital filter. It is shown that the modulation in the 2-D frequency plane is equivalent to the 1-D modulation. A necessary and sufficient condition for 2-D perfect reconstruction filter banks is derived. If the polyphase filter pairs of the prototype filter have a double-complement, the resulting 2-D filter bank satisfies the condition of perfect reconstruction. >