Transmultiplexing as a Method of Protecting Digital Data Against Unauthorized Reading, in IoT Systems in Particular

The perfect reconstruction cosine/sine-modulated filter banks belonging to the class of modulated filter banks have been studied extensively due to their attractive features (simple structure, analysis and synthesis filters are of equal length, low computational complexity), and consequently, they have received a great interest in audio coding applications. In fact, they are employed in the international speech and audio coding standards and proprietary audio compression algorithms. The oddly and evenly stacked modified discrete cosine transform (MDCT) and the corresponding modified discrete sine transform (MDST), the modulated lapped transform (MLT), the extended lapped transforms (ELTs), and their biorthogonal versions are real-valued cosine/sine-modulated filter banks satisfying the perfect reconstruction property. The modulated complex lapped transform (MCLT) is the complex-valued filter bank whose real part is the MLT or equivalently, the oddly stacked MDCT, and the imaginary part is the oddly stacked MDST. In this chapter, definitions, general properties, and matrix representations of the MDCT/MDST, MLT, ELT, and MCLT filter banks are presented. In order to an analysis/synthesis filter bank be perfect reconstruction, the necessary and sufficient conditions imposed on the analysis and synthesis windowing functions play an important role. Therefore, additionally the windowing procedure and perfect reconstruction (biorthogonal) conditions in the case of identical and (nonidentical) analysis and synthesis windowing functions, design of a windowing function including definitions of commonly windowing functions used in audio coding applications, adaptive switching of transform block sizes and windowing functions, and general perfect reconstruction conditions for the ELT filter bank with multiple overlapping factor both for the orthogonal and biorthogonal cases are derived and/or discussed in detail.

A review is presented first of the evolution of transmultiplexers since about 1966, in the context of a long progression of theoretical advances and developments leading to recent proposals to fundamentally improve OFDM type systems using principles of perfect reconstruction filter (PRF) banks. The equivalence of transmultiplexers to OFDM type multi-user systems is discussed. The desirable goals for performance and implementation of transmultiplexers or multiband, multiuser communication systems that are addressed and met in this paper using filter bank trees are set down. Then modifications and extensions are presented of the designs and architectures of wavelet packet based synthesis and analysis pairs of filter bank trees (Sablatash and Lodge in Digital Signal Process 13: 58–92, 2003) that can be used as transmultiplexers. These exhibit a number of advantages over the previous designs and address three shortcomings of the designs used to illustrate basic principles in Sablatash and Lodge (Digital Signal Process 13:58–92, 2003). The first of these is the asymmetry of the magnitude frequency responses of the multiplexer channels, which is addressed using a symmetric design for a lowpass and highpass quadrature mirror filter (QMF) pair described herein. The second is the problem of minimizing the total delay of the signal in passing through the analysis and synthesis filter banks. This is addressed using an architecture involving DFT polyphase synthesis filter banks to replace the wideband VSB filters at the roots of the two identical synthesis filter bank trees, but results in the multiplexer having fewer levels. In this way a tradeoff is effected of lower delay and complexity with fewer levels of bandwidth on demand. At the receiver matching DFT polyphase analysis filters and the other matching analysis filters are implemented. The third shortcoming is the difficulty in designing a synchronization scheme if the filters in the synthesis and analysis filter banks have non-linear phase. This is addressed by designing linear phase filters that do not affect the ISI to any significant degree for communication purposes, although exact perfect reconstruction is lost, but greatly ease and improve the design of the synchronization scheme. Relationships of this paper and its advantages over recent research studies and IEEE 802.22 standards proposals using PR filter banks for multi-user systems to greatly improve on OFDM systems are discussed.

Scene adaptive coders are constituted by the cascade of a linear transform, scalar quantization, entropy coding and a buffer controlled by a feedback loop for bit rate regulation. The main contribution of this paper is to derive an analytical criterion evaluating the performances of any perfect reconstruction linear transform in the frame of scene adaptive coding. This criterion is, thereafter, used in order to optimize linear multiresolution transforms. The optimization adapts the filters parameters to the codec features and to the statistics of the 2-D sources; so, the authors call these transforms adapted multiresolution transforms (AMTs). The transforms under study are implemented by a cascade of separable perfect-reconstruction (PR) FIR two-band filter banks that can change at each resolution level. Two types of filter banks are envisaged: the PR orthogonal quadrature mirror filter (QMF) bank, which allows to implement the orthogonal AMT and the PR linear-phase filter (LPF) bank, which implements the biorthogonal AMT. They perform the optimization of the filters in their factorized lattice form, taking the finite length of the multipliers into account. Their criterion also allows them to show the performances achieved by these two linear multiresolution transforms compared to other linear (multiresolution) transforms. >

The modified DFT (MDFT) filter bank is a highly efficient pseudo-QMF filter bank with almost perfect reconstruction. It has been shown that the MDFT filter bank provides a computational efficiency which is comparable with or in some cases even higher than that of the well-known cosine modulated filter bank. Additionally, the MDFT filter bank opens new applications as subband coding or as a transmultiplexer filter bank. The paper shows how almost perfect reconstruction is achieved in the MDFT filter bank, i.e. how adjacent-spectrum aliasing is cancelled, how nonadjacent-spectrum is suppressed, and how amplitude distortions are minimized. >

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 real-time 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.

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

Optimal duration-bandwidth localized antisymmetric biorthogonal wavelet filters

There has been considerable interest in the design of multidimensional (MD) filter banks. MD filter banks find application in subband coding of images and video data. MD filter banks can be designed by cascading one-dimensional (1D) filter banks in the form of a tree structure. In this case, the individual analysis and synthesis filters are separable and the filter bank is called a separable filter bank. MD filter banks with nonseparable filters offer more flexibility and usually provide better performance. Nonetheless, their design is considerably more difficult than separable filter banks. The purpose of this paper is to provide an overview of developments in this field on the design techniques for MD filter banks, mostly two-dimensional (2D) filter banks. In some image coding applications, the 2D two-channel filter banks are of great importance, particularly the filter bank with diamond-shaped filters. We will present several design techniques for the 2D two-channel nonseparable filter banks. As the design of MD filters are not as tractable as that of 1D filters, we seek design techniques that do not involve direct optimization of MD filters. To facilitate this, transformations that turn a separable MD filter bank into a nonseparable one are developed. Also, transformations of 1D filter banks to MD filter banks are investigated. We will review some designs of MD filter banks using transformations. In the context of 1D filter bank design, the cosine modulated filter bank (CMFB) is well-known for its design and implementation efficiency. All the analysis filters are cosine modulated versions of a prototype filter. The design cost of the filter bank is equivalent to that of the prototype and the implementation complexity is comparable to that of the prototype plus a low-complexity matrix. The success with 1D CMFB motivate the generalization to the 2D case. We will construct the 2D CMFB by following a very close analogy of 1D case. It is well-known that the 1D lossless systems can be characterized by state space description. In 1D, the connection between the losslessness of a transfer matrix and the unitariness of the realization matrix is well-established. We will present the developments on the study of 2D lossless systems. As in 1D case, the 2D FIR lossless systems can be characterized in terms of state space realizations. We will review this, and then address the factorizability of 2D FIR lossless systems by using the properties of state space realizations.

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.

A proficient approach to the design of Quadrature Mirror Filter (QMF) Bank is studied and an algorithm is offered for straightforward accomplishment of QMF bank with near perfect reconstruction. Objective function is built upon perfect reconstruction condition. The cutoff frequency is repetitively varied to adjust the filter coefficients using the anticipated algorithm and reconstruction error is minimized. Using the optimal value of cutoff frequency the prototype filter is designed and other filters of the bank is considered from that single prototype filter. Kaiser and Dolph-Chebyshev window functions are used to investigate the betterment of the design method. The performance of the projected design method are evaluated in terms of computation time required i.e. CPU time, Perfect Reconstruction Error (PRE), Magnitude Square Error (MSE) and Number of Iterations (NOI). The proposed algorithm is simple, easy to implement, and linearly converges to optimal solution. Finally, the sub-band decomposition of an audio signal is done using the filter bank.

This paper presents a generalized novel design of a family of multiplier free orthogonal wavelet filter banks (FBs) with low complexity. In the proposed method, maximum number of zeros at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$z=-1$ </tex-math></inline-formula> is ensured for a desired length of analysis and synthesis filters. A new class of technique is proposed to obtain dyadic filter coefficients based on double shifting orthogonality property with allowable deviation from original filter coefficients. This is achieved by slightly altering perfect reconstruction (PR) condition to obtain dyadic filter coefficient. A general closed form expression is formulated using double shifting orthogonality property to reduce the error between original filter coefficients and proposed dyadic filter coefficients. The designed wavelet FB improved time-frequency product, Sobolev regularity and frequency selectivity (low energy in error) over well known existing wavelet FBs. In addition, a fixed point VLSI architecture is proposed for the designed family of orthogonal wavelet FBs. The suggested architecture is designed and implemented on Kintex7 FPGA board. The proposed family of orthogonal wavelet FBs is multiplier less with significantly reduced adders, shifters and dynamic power dissipation. The performance of the proposed wavelet FB is validated on two different applications namely image compression and medical image retrieval. The proposed FBs are tested on well known datasets such as CLASSIC, EPFL, RAISE, and FiveK for image compression and on three different medical image databases such as NEMA, OASIS, and EXACT09 for image retrieval.

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. >

A filter bank is presented, which is based on coupled all-pass filters. The special properties of the filter bank are approximately linear phases of the subbands, perfect reconstruction and a low group delay. The synthesis filter bank is just a simple summation. The filter bank represents a generalization of the well-known lattice wave digital filters (LWDFs). For this reason, most properties of the wave digital filters are maintained, for instance, their excellent stability behavior and an extremely low sensitivity coefficient (see Fettweis, A., Proc. IEEE, vol.74, no.2, p.270-327, 1986). The design of the all-pass filters is performed by an iterative procedure. Finally, the filter bank is illustrated by means of a design example.

We study the fundamentals of time-varying filter banks (TVFB). Using a polyphase approach to TVFBs, we are able to show some unusual properties that are not exhibited by the conventional LTI filter banks. For example, we can show that for a perfect reconstruction (PR) TVFB, the losslessness of analysis bank does not always imply that of the synthesis bank, and replacing the delay z-1 in an implementation of a lossless linear time-variant (LTV) system with z-L for integer L in general will result in a nonlossless system. Moreover, we show that interchanging the analysis and synthesis filters of a PR TVFB will usually destroy the PR property, and a PR TVFB in general will not generate a discrete-time basis for l2. Furthermore, we show that we can characterize all TVFBs by characterizing multi-input multi-output (MIMO) LTV systems. A useful subclass of LTV systems, namely the lossless systems, is discussed in detail. All lossless LTV systems are invertible. Moreover, the inverse is a finite impulse response (FIR) if the original lossless system is an FIR. Explicit construction of the inverses is given. However, unlike in the LTI case, we show that the inverse system is not necessarily unique or invertible. In fact, the inverse of a lossless LTV system is not necessarily lossless. Depending on the invertibility of their inverses, the lossless systems are divided into two groups: (i) invertible inverse lossless (IIL) systems and (ii) noninvertible inverse lossless (NIL) systems. We show that an NIL PR TVFB will only generate a discrete-time tight frame with unity frame bound. However if the PR FB is IIL, we have an orthonormal basis for ℓ2. In a companion paper, some of these results are used to derive deeper properties of lossless TVFB including factorization theorems.

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.