Optimal design of linear phase FIR digital filters with very flat passbands and equiripple stopbands

A new technique is presented for the design of digital FIR filters, with a prescribed degree of flatness in the passband, and a prescribed (equiripple) attenuation in the stopband. The design is based entirely on an appropriate use of the well-known Reméz-exchange algorithm for the design of weighted Chebyshev FIR filters. The extreme versatility of this algorithm is combined with certain "maximally flat" FIR filter building blocks, in order to generate a wide family of filters. The design technique directly leads to structures that have low passband sensitivity properties

Efficient and multiplierless design of FIR filters with very sharp cutoff via maximally flat building blocks

A new design technique for linear-phase FIR filters, based on maximally flat buildiing blocks, is presented. The design technique does not involve iterative approximations and is, therefore, fast. It gives rise to filters that have a monotone stopband response, as required in some applications. The technique is partially based on an interpolative scheme. Implementation of the obtained filter designs requires a much smaller number of multiplications than maximally flat (MAXFLAT) FIR filters designed by the conventional approach. A technique based on FIR spectral transformations to design new multiplierless FIR filter structures is then advanced, and multiplierless implementations for sharp cutoff specifications are included

Efficient and multiplierless design of FIR filters with very sharp cutoff via maximally flat building blocks

A new design technique for linear-phase FIR filters, based on maximally flat buildiing blocks, is presented. The design technique does not involve iterative approximations and is, therefore, fast. It gives rise to filters that have a monotone stopband response, as required in some applications. The technique is partially based on an interpolative scheme. Implementation of the obtained filter designs requires a much smaller number of multiplications than maximally flat (MAXFLAT) FIR filters designed by the conventional approach. A technique based on FIR spectral transformations to design new multiplierless FIR filter structures is then advanced, and multiplierless implementations for sharp cutoff specifications are included

Performance Analysis of IIR and FIR Filters for 5G Wireless Networks

This paper analyses the performances of the Infinite Impulse Response (IIR) and Finite Impulse Response (FIR) filters. By studying the relationship between filter responses with filter orders and delay, the goal is to choose feasible filters that can accommodate more carriers in a bandwidth thus, the spectral efficiency can be increased. For IIR filtering, we employ filters namely Butterworth, Chebyshev, and Elliptic, while the Equiripple, Bohman, and Hamming are studied for FIR filtering. We evaluate these filters in terms of magnitude response, phase response and group delay, and identify the minimum filter order that characterized nearly to an ideal filter response. The results show that the IIR filter has a steep transition region when compared to the FIR filters under the similar order.  Our performance analysis showed that the IIR filters, with similar filter order of FIR filters, have also the fastest roll-off, small transition region, and low implementation cost. On the other hand, the FIR filters have linear phase response that related to group delay.  Finally, our analysis concluded that Elliptic able to suppress the sidelobes with a minimum order of 10th   and Equiripple have the fastest roll-off and narrowest transition region compare to other tested FIR filter. Thus, make these two types of filter feasible candidates to be implemented in 5G wireless networks

Optimal FIR filter design

The design of Finite Impulse Response (FIR) digital filters that considers both phase and magnitude specifications is investigated. This dissertation is divided into two parts. In Part I we present our implementation of an algorithm for the design of minimum phase filters. In Part II we investigate the design of FIR filters in the complex domain and develop a new powerful design method for digital FIR filters with arbitrary specification of magnitude and phase;Part I considers the design of minimum-phase filters. The method presented uses direct factorization of the transfer function of a companion Parks-McClellan linear-phase filter of twice the length of the desired minimum-phase filter. The minimum-phase filter is derived with excision of half the zeros of the companion linear-phase filter. The zeros of the prototype filter are found using Laguerre\u27s method. We will present our implementation of the design method, and describe some practical aspects and problems associated with the design of minimum-phase filters;Part II investigates the design of optimal Chebychev FIR filters in the complex domain. The design of FIR filters with arbitrary specification of magnitude and phase is formulated into a problem of complex approximation. The method developed is capable of designing filters with real or complex coefficients. Complex impulse response designs are an extension of the real coefficient case based on a proper selection of the approximating basis functions;The minimax criterion is used and the complex Chebychev approximation is posed as a minimization problem in linear optimization. The primal problem is converted to its dual and is solved using an efficient, quadratically convergent algorithm developed by Tang (14). The relaxation of the linear-phase constraint results in a reduction of the number of coefficients compared to linear-phase designs. Linear-phase filters are a special case of our filter design approach. We examine the design of frequency selective filters with or without the conjugate symmetry, the design of one-sided, two-sided, narrowband and fullband Hilbert Transformers and differentiators

Induction motor diagnosis by advanced notch FIR filters and the wigner-ville distribution

During the last years, several time-frequency decomposition tools have been applied for the diagnosis of induction motors, for those cases in which the traditional procedures, such as motor current signature analysis, cannot yield the necessary response. Among them, the Cohen distributions have been widely selected to study transient and even stationary operation due to their high-resolution and detailed information provided at all frequencies. Their main drawback, the cross-terms, has been tackled either modifying the distribution, or carrying out a pretreatment of the signal before computing its time-frequency decomposition. In this paper, a filtering process is proposed that uses advanced notch filters in order to remove constant frequency components present in the current of an induction motor, prior to the computation of its distribution, to study rotor asymmetries and mixed eccentricities. In transient operation of machines directly connected to the grid, this procedure effectively eliminates most of the artifacts that have prevented the use of these tools, allowing a wideband analysis and the definition of a precise quantification parameter able to follow the evolution of their state. © 1982-2012 IEEE

Computer-Aided Design of Switched-Capacitor Filters

This thesis describes a series of computer methods for the design of switched-capacitor filters. Current software is greatly restricted in the types of transfer function that can be designed and in the range of filter structures by which they can be implemented. To solve the former problem, several new filter approximation algorithms are derived from Newton's method, yielding the Remez algortithm as a special case (confirming its convergency properties). Amplitude responses with arbitrary passband shaping and stopband notch positions are computed. Points of a specified degree of tangency to attenuation boundaries (touch points) can be placed in the response, whereby a family of transfer functions between Butterworth and elliptic can be derived, offering a continuous trade-off in group delay and passive sensitivity properties. The approximation algorithms have also been applied to arbitrary group delay correction by all-pass functions. Touch points form a direct link to an iterative passive ladder design method, which bypasses the need for Hurwitz factorisation. The combination of iterative and classical synthesis methods is suggested as the best compromise between accuracy and speed. It is shown that passive ladder prototypes of a minimum-node form can be efficiently simulated by SC networks without additional op-amps. A special technique is introduced for canonic realisation of SC ladder networks from transfer functions with finite transmission at high frequency, solving instability and synthesis difficulties. SC ladder structures are further simplified by synthesising the zeros at +/-2fs which are introduced into the transfer function by bilinear transformation. They cause cancellation of feedthrough branches and yield simplified LDI-type SC filter structures, although based solely on the bilinear transform. Matrix methods are used to design the SC filter simulations. They are shown to be a very convenient and flexible vehicle for computer processing of the linear equations involved in analogue filter design. A wide variety of filter structures can be expressed in a unified form. Scaling and analysis can readily be performed on the system matrices with great efficiency. Finally, the techniques are assembled in a filter compiler for SC filters called PANDDA. The application of the above techniques to practical design problems is then examined. Exact correction of sinc(x), LDI termination error, pre-filter and local loop telephone line weightings are illustrated. An optimisation algorithm is described, which uses the arbitrary passband weighting to predistort the transfer function for response distortions. Compensation of finite amplifier gain-bandwidth and switch resistance effects in SC filters is demonstrated. Two commercial filter specifications which pose major difficulties for traditional design methods are chosen as examples to illustrate PANDDA's full capabilities. Significant reductions in order and total area are achieved. Finally, test results of several SC filters designed using PANDDA for a dual-channel speech-processing ASIC are presented. The speed with which high-quality, standard SC filters can be produced is thus proven

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

Channelization for Multi-Standard Software-Defined Radio Base Stations

As the number of radio standards increase and spectrum resources come under more pressure, it becomes ever less efficient to reserve bands of spectrum for exclusive use by a single radio standard. Therefore, this work focuses on channelization structures compatible with spectrum sharing among multiple wireless standards and dynamic spectrum allocation in particular. A channelizer extracts independent communication channels from a wideband signal, and is one of the most computationally expensive components in a communications receiver. This work specifically focuses on non-uniform channelizers suitable for multi-standard Software-Defined Radio (SDR) base stations in general and public mobile radio base stations in particular. A comprehensive evaluation of non-uniform channelizers (existing and developed during the course of this work) shows that parallel and recombined variants of the Generalised Discrete Fourier Transform Modulated Filter Bank (GDFT-FB) represent the best trade-off between computational load and flexibility for dynamic spectrum allocation. Nevertheless, for base station applications (with many channels) very high filter orders may be required, making the channelizers difficult to physically implement. To mitigate this problem, multi-stage filtering techniques are applied to the GDFT-FB. It is shown that these multi-stage designs can significantly reduce the filter orders and number of operations required by the GDFT-FB. An alternative approach, applying frequency response masking techniques to the GDFT-FB prototype filter design, leads to even bigger reductions in the number of coefficients, but computational load is only reduced for oversampled configurations and then not as much as for the multi-stage designs. Both techniques render the implementation of GDFT-FB based non-uniform channelizers more practical. Finally, channelization solutions for some real-world spectrum sharing use cases are developed before some final physical implementation issues are considered