Passive cascaded-lattice structures for low-sensitivity FIR filter design, with applications to filter banks

A class of nonrecursive cascaded-lattice structures is derived, for the implementation of finite-impulse response (FIR) digital filters. The building blocks are lossless and the transfer function can be implemented as a sequence of planar rotations. The structures can be used for the synthesis of any scalar FIR transfer function H(z) with no restriction on the location of zeros; at the same time, all the lattice coefficients have magnitude bounded above by unity. The structures have excellent passband sensitivity because of inherent passivity, and are automatically internally scaled, in an L_2 sense. The ideas are also extended for the realization of a bank of MFIR transfer functions as a cascaded lattice. Applications of these structures in subband coding and in multirate signal processing are outlined. Numerical design examples are included

Frequency response modeling and control of flexible structures: Computational methods

The dynamics of vibrations in flexible structures can be conventiently modeled in terms of frequency response models. For structural control such models capture the distributed parameter dynamics of the elastic structural response as an irrational transfer function. For most flexible structures arising in aerospace applications the irrational transfer functions which arise are of a special class of pseudo-meromorphic functions which have only a finite number of right half place poles. Computational algorithms are demonstrated for design of multiloop control laws for such models based on optimal Wiener-Hopf control of the frequency responses. The algorithms employ a sampled-data representation of irrational transfer functions which is particularly attractive for numerical computation. One key algorithm for the solution of the optimal control problem is the spectral factorization of an irrational transfer function. The basis for the spectral factorization algorithm is highlighted together with associated computational issues arising in optimal regulator design. Options for implementation of wide band vibration control for flexible structures based on the sampled-data frequency response models is also highlighted. A simple flexible structure control example is considered to demonstrate the combined frequency response modeling and control algorithms

FPGA Implementation of Higher Order FIR Filter

The digital Finite-Impulse-Response (FIR) filters are mainly employed in digital signal processing applications. The main components of digital FIR filters designed on FPGAs are the register bank to save the samples of signals, adder to implement sum operations and multiplier for multiplication of filter coefficients to signal samples. Although, design and implementation of digital FIR filters seem simple but the design bottleneck is multiplier block for speed, power consumption and FPGA chip area occupation. The multipliers are an integral part in FIR structures and these use a large part of the chip area. This limits the number of processing elements (PE) available on the chip to realize a higher order of filter. A model is developed in the Matlab/Simulink environment to investigate the performance of the desired higher order FIR filter. An equivalent FIR filter representation is designed by the Xilinx FIR Compiler by using the exported FIR filter coefficients. The Xilinx implementation flow is completed with the help of Xilinx ISE 14.5. It is observed how the use of higher order FIR filter impacts the resource utilization of the FPGA and it’s the maximum operating frequency

On the spectral factor ambiguity of FIR energy compaction filter banks

This paper focuses on the design of signal-adapted finite-impulse response (FIR) paraunitary (PU) filter banks optimized for energy compaction (EC). The design of such filter banks has been shown in the literature to consist of the design of an optimal FIR compaction filter followed by an appropriate Karhunen-Loe/spl grave/ve transform (KLT). Despite this elegant construction, EC optimal filter banks have been shown to perform worse than common nonadapted filter banks for coding gain, contrary to intuition. Here, it is shown that this phenomenon is most likely due to the nonuniqueness of the compaction filter in terms of its spectral factors. This nonuniqueness results in a finite set of EC optimal filter banks. By choosing the spectral factor yielding the largest coding gain, it is shown that the resulting filter bank behaves more and more like the infinite-order principal components filter bank (PCFB) in terms of numerous objectives such as coding gain, multiresolution, noise reduction with zeroth-order Wiener filters in the subbands, and power minimization for discrete multitone (DMT)-type nonredundant transmultiplexers

Study of numeric Saturation Effects in Linear Digital Compensators

Saturation arithmetic is often used in finite precision digital compensators to circumvent instability due to radix overflow. The saturation limits in the digital structure lead to nonlinear behavior during large state transients. It is shown that if all recursive loops in a compensator are interrupted by at least one saturation limit, then there exists a bounded external scaling rule which assures against overflow at all nodes in the structure. Design methods are proposed based on the generalized second method of Lyapunov, which take the internal saturation limits into account to implement a robust dual-mode suboptimal control for bounded input plants. The saturating digital compensator provides linear regulation for small disturbances, and near-time-optimal control for large disturbances or changes in the operating point. Computer aided design tools are developed to facilitate the analysis and design of this class of digital compensators

On prefilters for digital FIR filter design

A new family of digital prefilter structures is introduced, based on the Dolph-Chebyshev function. These prefilters can be combined with appropriately designed "equalizer" filters based on equiripple methods, leading to efficient FIR digital filter designs. Design examples are included, demonstrating the simplicity of the resulting designs, as compared to conventional equiripple designs

Towards an optimised VLSI design algorithm for the constant matrix multiplication problem

The efficient design of multiplierless implementations of constant matrix multipliers is challenged by the huge solution search spaces even for small scale problems. Previous approaches tend to use hill-climbing algorithms risking sub-optimal results. The proposed algorithm avoids this by exploring parallel solutions. The computational complexity is tackled by modelling the problem in a format amenable to genetic programming and hardware acceleration. Results show an improvement on state of the art algorithms with future potential for even greater savings

Lattice structures for optimal design and robust implementation of two-channel perfect-reconstruction QMF banks

A lattice structure and an algorithm are presented for the design of two-channel QMF (quadrature mirror filter) banks, satisfying a sufficient condition for perfect reconstruction. The structure inherently has the perfect-reconstruction property, while the algorithm ensures a good stopband attenuation for each of the analysis filters. Implementations of such lattice structures are robust in the sense that the perfect-reconstruction property is preserved in spite of coefficient quantization. The lattice structure has the hierarchical property that a higher order perfect-reconstruction QMF bank can be obtained from a lower order perfect-reconstruction QMF bank, simply by adding more lattice sections. Several numerical examples are provided in the form of design tables

Synthesis and realization of noncausal digital filters.

Chok-ki Chan.Bibliography: leaves 117-122Thesis (Ph.D.) - Chinese University of Hong Kong, 198