Factorability of lossless time-varying filters and filter banks

We study the factorability of linear time-varying (LTV) lossless filters and filter banks. We give a complete characterization of all, degree-one lossless LTV systems and show that all degree-one lossless systems can be decomposed into a time-dependent unitary matrix followed by a lossless dyadic-based LTV system. The lossless dyadic-based system has several properties that make it useful in the factorization of lossless LTV systems. The traditional lapped orthogonal transform (LOT) is also generalized to the LTV case. We identify two classes of TVLOTs, namely, the invertible inverse lossless (IIL) and noninvertible inverse lossless (NIL) TVLOTs. The minimum number of delays required to implement a TVLOT is shown to be a nondecreasing function of time, and it is a constant if and only if the TVLOT is IIL. We also show that all IIL TVLOTs can be factorized uniquely into the proposed degree-one lossless building block. The factorization is minimal in terms of the delay elements. For NIL TVLOTs, there are factorable and unfactorable examples. Both necessary and sufficient conditions for the factorability of lossless LTV systems are given. We also introduce the concept of strong eternal reachability (SER) and strong eternal observability (SEO) of LTV systems. The SER and SEO of an implementation of LTV systems imply the minimality of the structure. Using these concepts, we are able to show that the cascade structure for a factorable IIL LTV system is minimal. That implies that if a IIL LTV system is factorable in terms of the lossless dyadic-based building blocks, the factorization is minimal in terms of delays as well as the number of building blocks. We also prove the BIBO stability of the LTV normalized IIR lattice

A practical approach for the design of nonuniform lapped transforms

We propose a simple method for the design of lapped transforms with nonuniform frequency resolution and good time localization. The method is a generalization of an approach previously proposed by Princen, where the nonuniform filter bank is obtained by joining uniform cosine-modulated filter banks (CMFBs) using a transition filter. We use several transition filters to obtain a near perfect-reconstruction (PR) nonuniform lapped transform with significantly reduced overall distortion. The main advantage of the proposed method is in reducing the length of the transition filters, which leads to a reduction in processing delay that can be useful for applications such as real-time audio coding

Role of anticausal inverses in multirate filter-banks. I. System-theoretic fundamentals

In a maximally decimated filter bank with identical decimation ratios for all channels, the perfect reconstructibility property and the nature of reconstruction filters (causality, stability, FIR property, and so on) depend on the properties of the polyphase matrix. Various properties and capabilities of the filter bank depend on the properties of the polyphase matrix as well as the nature of its inverse. In this paper we undertake a study of the types of inverses and characterize them according to their system theoretic properties (i.e., properties of state-space descriptions, McMillan degree, degree of determinant, and so forth). We find in particular that causal polyphase matrices with anticausal inverses have an important role in filter bank theory. We study their properties both for the FIR and IIR cases. Techniques for implementing anticausal IIR inverses based on state space descriptions are outlined. It is found that causal FIR matrices with anticausal FIR inverses (cafacafi) have a key role in the characterization of FIR filter banks. In a companion paper, these results are applied for the factorization of biorthogonal FIR filter banks, and a generalization of the lapped orthogonal transform called the biorthogonal lapped transform (BOLT) developed

Performance Analysis of Discrete Wavelet Multitone Transceiver for Narrowband PLC in Smart Grid

Smart Grid is an abstract idea, which involves the utilization of powerlines for sensing, measurement, control and communication for efficient utilization and distribution of energy, as well as automation of meter reading, load management and capillary control of Green Energy resources connected to the grid. Powerline Communication (PLC) has assumed a new role in the Smart Grid scenario, adopting the narrowband PLC (NB-PLC) for a low cost and low data rate communication for applications such as, automatic meter reading, dynamic management of load, etc. In this paper, we have proposed and simulated a discrete wavelet multitone (DWMT) transceiver in the presence of impulse noise for the NB-PLC channel applications in Smart Grid. The simulation results show that a DWMT transceiver outperforms a DFT-DMT with reference to the bit error rate (BER) performance

The Stationary Phase Approximation, Time-Frequency Decomposition and Auditory Processing

The principle of stationary phase (PSP) is re-examined in the context of linear time-frequency (TF) decomposition using Gaussian, gammatone and gammachirp filters at uniform, logarithmic and cochlear spacings in frequency. This necessitates consideration of the use the PSP on non-asymptotic integrals and leads to the introduction of a test for phase rate dominance. Regions of the TF plane that pass the test and don't contain stationary phase points contribute little or nothing to the final output. Analysis values that lie in these regions can thus be set to zero, i.e. sparsity. In regions of the TF plane that fail the test or are in the vicinity of stationary phase points, synthesis is performed in the usual way. A new interpretation of the location parameters associated with the synthesis filters leads to: (i) a new method for locating stationary phase points in the TF plane; (ii) a test for phase rate dominance in that plane. Together this is a TF stationary phase approximation (TFSFA) for both analysis and synthesis. The stationary phase regions of several elementary signals are identified theoretically and examples of reconstruction given. An analysis of the TF phase rate characteristics for the case of two simultaneous tones predicts and quantifies a form of simultaneous masking similar to that which characterizes the auditory system.Comment: Submitted to IEEE Trans Signal Processing 14th Aug 201

Zero-Delay Rate Distortion via Filtering for Vector-Valued Gaussian Sources

We deal with zero-delay source coding of a vector-valued Gauss-Markov source subject to a mean-squared error (MSE) fidelity criterion characterized by the operational zero-delay vector-valued Gaussian rate distortion function (RDF). We address this problem by considering the nonanticipative RDF (NRDF) which is a lower bound to the causal optimal performance theoretically attainable (OPTA) function and operational zero-delay RDF. We recall the realization that corresponds to the optimal "test-channel" of the Gaussian NRDF, when considering a vector Gauss-Markov source subject to a MSE distortion in the finite time horizon. Then, we introduce sufficient conditions to show existence of solution for this problem in the infinite time horizon. For the asymptotic regime, we use the asymptotic characterization of the Gaussian NRDF to provide a new equivalent realization scheme with feedback which is characterized by a resource allocation (reverse-waterfilling) problem across the dimension of the vector source. We leverage the new realization to derive a predictive coding scheme via lattice quantization with subtractive dither and joint memoryless entropy coding. This coding scheme offers an upper bound to the operational zero-delay vector-valued Gaussian RDF. When we use scalar quantization, then for "r" active dimensions of the vector Gauss-Markov source the gap between the obtained lower and theoretical upper bounds is less than or equal to 0.254r + 1 bits/vector. We further show that it is possible when we use vector quantization, and assume infinite dimensional Gauss-Markov sources to make the previous gap to be negligible, i.e., Gaussian NRDF approximates the operational zero-delay Gaussian RDF. We also extend our results to vector-valued Gaussian sources of any finite memory under mild conditions. Our theoretical framework is demonstrated with illustrative numerical experiments.Comment: 32 pages, 9 figures, published in IEEE Journal of Selected Topics in Signal Processin

Speculative Thread Framework for Transient Management and Bumpless Transfer in Reconfigurable Digital Filters

There are many methods developed to mitigate transients induced when abruptly changing dynamic algorithms such as those found in digital filters or controllers. These "bumpless transfer" methods have a computational burden to them and take time to implement, causing a delay in the desired switching time. This paper develops a method that automatically reconfigures the computational resources in order to implement a transient management method without any delay in switching times. The method spawns a speculative thread when it predicts if a switch in algorithms is imminent so that the calculations are done prior to the switch being made. The software framework is described and experimental results are shown for a switching between filters in a filter bank.Comment: 6 pages, 7 figures, to be presented at American Controls Conference 201