Oversampled Filter Banks Research Articles

Oversampled filter bank channelizer for cryogenic detectors.

We present the field-programmable gate array (FPGA) implementation of an oversampled generalized discrete Fourier transform (GDFT) filter bank (FB), optimized for its usage in the readout of cryogenic detectors, such as microwave kinetic inductance detectors. A polyphase structure is derived underlining the efficiency of complex-valued subband processing, raised by a GDFT modulation. For the latter, a fast Fourier algorithm realization may be used, yielding a highly efficient polyphase implementation for arbitrary integer decimation ratios. The FB is tested through a 16-channel GDFT channelizer. The implementation is based on the Xilinx Zynq family of FPGAs and aims to show the data reuse and flexibility offered by the GDFT channelizer structure. General design criteria are summarized for the 16-channel polyphase FB channelizer. The performance in hardware resource usage is also presented, taking into account one of the main objectives of the current physics experiments, aiming to have an extremely large readout format.

Near Orthogonal Oversampled Graph Filter Banks

A framework for oversampled filter banks for graph signals was recently proposed by Tanaka and Sakiyama (2014). It was shown that M-channel oversampled filter bank which is exactly orthogonal is not possible with polynomial spectral filter functions. The result is an extension of the critically sampled framework of Narang and Ortega (2012). In this work we present a solution that is nearly orthogonal which has the advantage of giving a nearly tight transform, i.e. nearly equal frame bounds. A family of target functions which satisfy the orthogonality condition is constructed using Bernstein polynomials. The design of the spectral filters is easily achieved through an approximation of the target functions. Filters with good spectral characteristics that are nearly orthogonal can be easily obtained using the proposed method.

Q인자 조절 가능 2차원 이산 웨이브렛 변환 필터의 설계와 성능분석

The general wavelet transform has profitable property in non-stationary signal analysis specially. The tunable Q-factor wavelet transform is a fully-discrete wavelet transform for which the Q-factor Q and the asymptotic redundancy r, of the transform are easily and independently specified. In particular, the specified parameters Q and r can be real-valued. Therefore, by tuning Q, the oscillatory behavior of the wavelet can be chosen to match the oscillatory behavior of the signal of interest, so as to enhance the sparsity of a sparse signal representation. The TQWT is well suited to fast algorithms for sparsity-based inverse problems because it is a Parseval frame, easily invertible, and can be efficiently implemented. The transform is based on a real valued scaling factor and is implemented using a perfect reconstruction over-sampled filter bank with real-valued sampling factors. The transform is parameterized by its Q-factor and its over-sampling rate, with modest over-sampling rates being sufficient for the analysis/synthesis functions to be well localized. This paper describes filter design of 2D discrete-time wavelet transform for which the Q-factor is easily specified. With the advantage of this transform, perfect reconstruction filter design and implementation for performance improvement are focused in this paper. Hence, the 2D transform can be tuned according to the oscillatory behavior of the image signal to which it is applied. Therefore, application for performance improvement in multimedia communication field was evaluated.

<formula formulatype="inline"><tex Notation="TeX">$M$</tex> </formula>-Channel Oversampled Graph Filter Banks

This paper proposes $M$ -channel oversampled filter banks for graph signals. The filter set satisfies the perfect reconstruction condition. A method of designing oversampled graph filter banks is presented that allows us to design filters with arbitrary parameters, unlike the conventional critically sampled graph filter banks. The oversampled graph Laplacian matrix is also introduced with a discussion of the entire redundancy of the oversampled graph signal processing system. The practical performance of the proposed filter banks is validated through graph signal denoising experiments.

FINITE IMPULSE RESPONSE DOUBLE DENSITY FILTER BANKS AND FRAMELETS

In this paper, we focus on the design of oversampled filter banks and the resulting framelets. The framelets obtained exhibit improved shift invariant properties over decimated wavelet transform. Shift invariance has applications in many areas, particularly denoising, coding and compression. Our contribution here is on filter bank completion. In addition, we propose novel factorization methods to design wavelet filters from given scaling filters.

Subsampled Factor, Passband Frequency Range and Filter Order Used For Design of Oversampled Filter Bank for 2d Image Analysis

Subsampled Factor, Passband Frequency Range and Filter Order Used For Design of Oversampled Filter Bank for 2d Image Analysis

Instantaneous Erasures in Oversampled Filter Banks: Conditions for Output Perfect Reconstruction

In this paper, we aim at finding the conditions that an oversampled filter bank (OFB) should satisfy, in order to maintain its perfect reconstruction property when erasures happen in the subband domain. This problem has been addressed before mainly from frame-theoretic point of view and only for the case of what we call in this paper classic erasure. In the frame-theoretic approach, the stable filter banks are associated with frames in l2(\BBZ) and a subband erasure is defined as the deletion of the frame expansion coefficients corresponding to the frame vectors resulting from each filter and all its translated versions. This is equivalent to assuming that all the samples of a subband have been completely lost (classic erasure) and this is why in this approach it is always assumed that each channel is either working perfectly or not at all. In this paper, we extend this notion of erasure to a situation where subband channels are allowed to be on or off arbitrarily in each time instance and we define a new type of erasure called instantaneous erasure. Using an approach based on the time-domain analysis of perfect reconstruction property, we introduce general conditions for perfect reconstruction of the output and also the sufficient conditions for two classes of filter banks: Causal OFBs with causal inverse and OFBs with maximum robustness against classic erasure.

Optimal Design of Oversampled Synthesis FBs With Lattice Structure Constraints

Oversampled filter banks (FBs) with lattice structure allow fast implementation and guarantee the linear phase and perfect reconstruction property. For such FBs, the synthesis FB is not unique. This nonuniqueness provides extra design freedom for optimal reduction of subband noise required in many applications. However, the existing design methods of synthesis FB for optimal reduction of subband noise cannot guarantee the linear phase and lattice structure property. This paper studies the design of oversampled synthesis FBs with guaranteed lattice structure for optimal reduction of subband noise. Based on a state space parameterization of all synthesis FBs with lattice structure, the explicit formulae are derived to find the optimal solution for noise reduction. Numerical examples are presented to demonstrate the effectiveness of the new design methods obtained.

Wavelet Transform With Tunable Q-Factor

This paper describes a discrete-time wavelet transform for which the Q-factor is easily specified. Hence, the transform can be tuned according to the oscillatory behavior of the signal to which it is applied. The transform is based on a real-valued scaling factor (dilation-factor) and is implemented using a perfect reconstruction over-sampled filter bank with real-valued sampling factors. Two forms of the transform are presented. The first form is defined for discrete-time signals defined on all of Z. The second form is defined for discrete-time signals of finite-length and can be implemented efficiently with FFTs. The transform is parameterized by its Q-factor and its oversampling rate (redundancy), with modest oversampling rates (e.g., three to four times overcomplete) being sufficient for the analysis/synthesis functions to be well localized.

Oversampled Paraunitary DFT Filter Banks: A General Construction Algorithm and Some Specific Solutions

Oversampled filter banks are at the center of essential signal processing systems, either for source coding or for transmission applications. Among this class of filter banks (FBs), the case of oversampled discrete Fourier transform (DFT) filter banks is particularly important since it leads to efficient algorithm implementations. However, up to now, no general construction algorithm has been proposed to exhaustively cover the large set of the various solutions offered by this family of FBs. The paper recalls in detail the precise features of the rectangular paraunitary matrices that are specific of this type of systems. A parametrization method is proposed involving transformations, being either rotations or shifts, that depend upon the oversampling ratio and upon the prototype filter length. This shows that several factorizations exist leading to solutions of different dimension. Orthogonal and paraunitary patterns are introduced and, using a sequence of transformations applied to a pattern (STAP), an algorithm is derived that allows us to get the exhaustive set of solutions for various values of the oversampling ratio and prototype filter length. Furthermore, for some oversampling ratios, explicit expressions of some solutions are also provided that are valid whatever the maximum length of the prototype filter. Finally, design examples for linear and nonlinear phase prototype filters are presented.

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.

Correction to "Performance of Sigma-Delta Quantizations in Finite Frames"

The title of the above cited paper (ibid., vol. 56, no. 8, pp. 4157-4165, Aug. 10) was printed incorrectly. The correct title is On the Use of the First- and Second-order Sigma-Delta Quantizers in the Context of Oversampled Filter Banks.

A Procedure to Adapt Filter Banks to Finite-Length Signals

In this paper, we consider the problem of processing finite-length signals by means of critically sampled or oversampled filter banks. Based on a polyphase matrix factorization of the filter bank, we propose a realization adaptation that does not make any assumption about the signal values outside the support of the input signal, contrary to what is done, for instance, when using zero padding, periodic repetition or extension by symmetry. The proposed procedure has several advantages. In particular, we show that it preserves the perfect reconstruction and the general properties of the filter bank.

Comment on "Parity-Check Matrix Calculation for Paraunitary Oversampled DFT Filter Banks

In a previous paper, Karp, Kieffer, and Duhamel have presented three methods to calculate the parity-check matrix of paraunitary oversampled DFT filter banks. Here is another.

Optimal Noise Reduction in Oversampled PR Filter Banks

This paper studies the optimal noise reduction problem for oversampled filter banks (FBs) with perfect reconstruction (PR) constraint. Both the optimal design and worst case design are considered, where the former caters for the noise with known power spectral density (PSD) and the latter for the noise with unknown PSD. State-space based explicit formulae involving only algebraic Riccati equation and matrix manipulations are provided for the general (IIR or FIR) oversampled PR FBs, and the relations between different cases are analyzed and revealed. Extensive numerical examples are provided to illustrate the proposed design methods and to show their effectiveness.

Image denoising using 2-D separable oversampled DFT modulated filter banks

The direction-frequency selectivity of two-dimensional (2-D) separable oversampled discrete Fourier transform (DFT) modulated filter banks, showing that such 2-D filter banks can provide fine frequency tiling and efficient image representations with direction-frequency selectivity, is analysed. Moreover, the doubly local Wiener filtering is extended to the case using two 2-D separable oversampled DFT modulated filter banks, where the empirical subband energy distributions of the image are estimated by the two sets of directional windows matching the direction-frequency selectivity of the subband filters. The proposed algorithm is of low computational complexity and exhibits a great capability to preserve inhomogeneous textures, owing to the fact that 2-D separable DFT modulated bases are suited to represent oscillating patterns in images. The experimental results show that the proposed denoising algorithm is competitive with the existing algorithms with comparable computational complexity. Particularly, for images with abundant inhomogenous texture, it gives larger output peak signal-to-noise ratios (PSNRs) and achieves better visual effect in texture regions of images.

Wavelet Codes: Detection and Correction Using Kalman Estimation

Wavelet codes encoded by uniform oversampled filter banks where the wavelet coefficients represent code symbols are decoded employing Kalman fixed-lag estimation procedures. The code symbol error estimates are based on the mean-squared error (MSE) criterion and are first used to detect the presence of large numerical errors. Then the correction of symbols uses these Kalman estimators directly. The wavelet code symbols are corrupted by low levels of processing noise continuously and occasionally by large disruptive errors, e.g., impulsive noise. The modeling variables have time-varying statistics allowing both types of errors to be handled naturally. Kalman time-varying tracking filters, which use wavelet syndromes as their measurement inputs, develop the fixed-lag smoothed estimates for the larger errors. The syndromes are also modeled as corrupted by processing noise modeling computational failure errors, large and small. Hypothesis detection methods are used to locate large errors and their statistics must include Kalman mismatch characteristics to be valid. Estimators from several adjacent lag positions assist in the detection procedures. Simulation results show correction accuracy in the time domain as well as on a MSE basis. Large classes of wavelet codes are designed using binary convolutional codes as starting points from which the proper filter weights for encoding and syndrome evaluating are determined.

Quantization of Filter Bank Frame Expansions Through Moving Horizon Optimization

This paper describes a novel approach to quantization in oversampled filter banks. The new technique is based on moving horizon optimization, does not rely on an additive white noise quantization model and allows stability to be explicitly enforced in the associated nonlinear feedback loop. Moreover, the quantization structure proposed here includes SigmaDelta and linear predictive subband quantizers as a special case and, in general, outperforms them.

Flexible Frequency-Band Reallocation: Complex Versus Real

This paper discusses a new approach for implementing flexible frequency-band reallocation (FFBR) networks for bentpipe satellite payloads which are based on variable oversampled complex-modulated filter banks (FBs). We consider two alternatives to process real signals using real input/output and complex input/output FFBR networks (or simply real and complex FFBR networks, respectively). It is shown that the real case has a lower overall number of processing units, i.e., adders and multipliers, compared to its complex counterpart. In addition, the real system eliminates the need for two Hilbert transformers, further reducing the arithmetic complexity. An analysis of the computational workload shows that the real case has a smaller rate of increase in the arithmetic complexity with respect to the prototype filter order and number of FB channels. This makes the real case suitable for systems with a large number of users. Furthermore, in the complex case, a high efficiency in FBR comes at the expense of high-order Hilbert transformers; thus, trade-offs are necessary. Finally, the performance of the two alternatives based on the error vector magnitude (EVM) for a 16-quadrature amplitude modulation (QAM) signal is presented.

Computation of the Para-Pseudoinverse for Oversampled Filter Banks: Forward and Backward Greville Formulas

Frames and oversampled filter banks have been extensively studied over the past few years due to their increased design freedom and improved error resilience. In frame expansions, the least square signal reconstruction operator is called the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dual</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">frame,</i> which can be obtained by choosing the synthesis filter bank as the para-pseudoinverse of the analysis bank. In this paper, we study the computation of the dual frame by exploiting the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Greville</i> formula, which was originally derived in 1960 to compute the pseudoinverse of a matrix when a new row is appended. Here, we first develop the backward Greville formula to handle the case of row deletion. Based on the forward Greville formula, we then study the computation of para-pseudoinverse for extended filter banks and Laplacian pyramids. Through the backward Greville formula, we investigate the frame-based error resilient transmission over erasure channels. The necessary and sufficient condition for an oversampled filter bank to be robust to one erasure channel is derived. A postfiltering structure is also presented to implement the para-pseudoinverse when the transform coefficients in one subband are completely lost.