On the eigenfilter design method and its applications: a tutorial

The eigenfilter method for digital filter design involves the computation of filter coefficients as the eigenvector of an appropriate Hermitian matrix. Because of its low complexity as compared to other methods as well as its ability to incorporate various time and frequency-domain constraints easily, the eigenfilter method has been found to be very useful. In this paper, we present a review of the eigenfilter design method for a wide variety of filters, including linear-phase finite impulse response (FIR) filters, nonlinear-phase FIR filters, all-pass infinite impulse response (IIR) filters, arbitrary response IIR filters, and multidimensional filters. Also, we focus on applications of the eigenfilter method in multistage filter design, spectral/spacial beamforming, and in the design of channel-shortening equalizers for communications applications

Efficient reconstruction of band-limited sequences from nonuniformly decimated versions by use of polyphase filter banks

An efficient polyphase structure for the reconstruction of a band-limited sequence from a nonuniformly decimated version is developed. Theoretically, the reconstruction involves the implementation of a bank of multilevel filters, and it is shown that how all these reconstruction filters can be obtained at the cost of one Mth band low-pass filter and a constant matrix multiplier. The resulting structure is therefore more general than previous schemes. In addition, the method offers a direct means of controlling the overall reconstruction distortion T(z) by appropriate design of a low-pass prototype filter P(z). Extension of these results to multiband band-limited signals and to the case of nonconsecutive nonuniform subsampling are also summarized, along with generalizations to the multidimensional case. Design examples are included to demonstrate the theory, and the complexity of the new method is seen to be much lower than earlier ones

Linear Phase FIR Low Pass Filter Design Based on Firefly Algorithm

In this paper, a linear phase Low Pass FIR filter is designed and proposed based on Firefly algorithm. We exploit the exploitation and exploration mechanism with a local search routine to improve the convergence and get higher speed computation. The optimum FIR filters are designed based on the Firefly method for which the finite word length is used to represent coefficients. Furthermore, Particle Swarm Optimization (PSO) and Differential Evolution algorithm (DE) will be used to show the solution. The results will be compared with PSO and DE methods. Firefly algorithm and Parks–McClellan (PM) algorithm are also compared in this paper thoroughly. The design goal is successfully achieved in all design examples using the Firefly algorithm. They are compared with that obtained by using the PSO and the DE algorithm. For the problem at hand, the simulation results show that the Firefly algorithm outperforms the PSO and DE methods in some of the presented design examples. It also performs well in a portion of the exhibited design examples particularly in speed and quality

Optimization design of mth-band FIR filters with application to image processing

Cone programming (CP) is a class of convex optimization technique, in which a linear objective function is minimized over the intersection of a set of affine constraints. Such constraints could be linear or convex, equalities or inequalities. Owing to its powerful optimization capability as well as flexibility in accommodating various constraints, the cone programming finds wide applications in digital filter design. In this thesis, fundamentals of linear-phase M th-band FIR filters are first introduced, which include the time-domain interpolation condition and the desired frequency specifications. The restriction of the interpolation matrix M for linear-phase two-dimensional (2-D) M th-band filters is also discussed by considering both the interpolation condition and the symmetry of the impulse response of the 2-D filter. Based on the analysis of the M th-band properties, a semidefinite programming (SOP) optimization approach is developed to design linear-phase 1-0 and 2-D M th-band filters. The 2-D SOP optimization design problem is modeled based on both the mini-max and the least-square error criteria. In contrast to the 1-D based design, the 2-D direct SDP design can offer an optimal equiripple result. A second-order cone programming (SOCP) optimization approach is then presented as an alternative for the design of M th-band filters. The performances as well as the design complexity of these two design approaches are justified through numerical design examples. Simulation results show that the performance of the SOCP approach is better than that of the SDP approach for 1-D M th-band filter design due to its reduced computational complexity for the worst-case, whereas the SDP approach is more appropriate for the 2-D M th-band filter design than the SOCP approach because of its efficient and simple optimization structure. Moreover, the designed M th-band filters are proved useful in image interpolation according to both the visual quality and the peak signal-to-noise ratio (PSNR) for the images with different levels of details

Design of multichannel nonrecursive digital filters with applications to seismic reflection data

Imperial Users onl

Multirate digital filters, filter banks, polyphase networks, and applications: a tutorial

Multirate digital filters and filter banks find application in communications, speech processing, image compression, antenna systems, analog voice privacy systems, and in the digital audio industry. During the last several years there has been substantial progress in multirate system research. This includes design of decimation and interpolation filters, analysis/synthesis filter banks (also called quadrature mirror filters, or QMFJ, and the development of new sampling theorems. First, the basic concepts and building blocks in multirate digital signal processing (DSPJ, including the digital polyphase representation, are reviewed. Next, recent progress as reported by several authors in this area is discussed. Several applications are described, including the following: subband coding of waveforms, voice privacy systems, integral and fractional sampling rate conversion (such as in digital audio), digital crossover networks, and multirate coding of narrow-band filter coefficients. The M-band QMF bank is discussed in considerable detail, including an analysis of various errors and imperfections. Recent techniques for perfect signal reconstruction in such systems are reviewed. The connection between QMF banks and other related topics, such as block digital filtering and periodically time-varying systems, based on a pseudo-circulant matrix framework, is covered. Unconventional applications of the polyphase concept are discussed

Unified eigenfilter approach: with applications to spectral/spatial filtering

The eigenfilter approach is extended to solve general least-squares approximation problems with linear constraints. Such extension unifies previous work in eigenfilters and many other filter design problems, including spectral/spatial filtering, one-dimensional or multidimensional filters, data independent or statistically optimal filtering, etc. With this approach, various filter design problems are transformed into problems of finding an eigenvector of a positive definite matrix that is determined by filter design specifications. This approach has the advantage that many filter design constraints can be incorporated easily. A number of design examples are presented to show the usefulness and flexibility of the proposed approach

Quo Oxygen Sensor: Linear and Non-Linear Filtering Approaches to Noise Reduction

A system for measurement of oxygen consumption (V02) and determination of respiratory quotient (RQ: RQ = VO2/VCO2) is currently being developed by a joint project between Novametrix Inc. (Wallingford CT) and the University of Utah Department of BioEngineering. The system may prove to be highly useful on \u27extended duration space flight to monitor the metabolic rate of astronauts. The system employs a novel oxygen partial pressure sensor based on oxygen luminescence quenching technology for real-time measurement of respiratory oxygen concentration. This paper addresses the sensors\u27s signal vs. noise properties. The signal to noise (SIN) ratio of the sensor has been found to degrade progressively with increasing oxygen partial pressure (pO2) with the degradation appearing to become problematic at oxygen partial pressures above approximately 60%. In order to improve the (high pO2) SIN ratio of the sensor, a number of signal processing techniques were investigated. These techniques were selected based on a qualitative assessment of the sensor\u27s unique signal processing requirements and the effectiveness of the techniques was quantitatively characterized for comparison purposes. The techniques included linear as well as non-linear filtering strategies. The linear filtering strategies investigated consisted of two classes of notch filters while the more disparate non-linear filters consisted of classes of polynomial (Voltera series) filters, median and median-related filters, order statistic filters, morphological filters and weighted majority with minimum range filters. Each of the filters investigated were optimized using actual sensor data to improve sensor SIN ratio performance while maintaining adequate sensor dynamics. A number of candidate filters with varying degrees of computational complexity and noise suppression effectiveness are proposed for the sensor. Future studies will evaluate the performance of these filters within the framework of candidate oxygen consumption algorithms