Two-channel IIR QMF banks with approximately linear-phase analysisand synthesis filters

Perfect linear-phase two-channel QMF banks require the use of finite impulse response (FIR) analysis and synthesis filters. Although they are less expensive and yield superior stopband characteristics, perfect linear phase cannot be achieved with stable infinite impulse response (IIR) filters. Thus, IIR designs usually incorporate a postprocessing equalizer that is optimized to reduce the phase distortion of the entire filter bank. However, the analysis and synthesis filters of such an IIR filter bank are not linear phase. In this paper, a computationally simple method to obtain IIR analysis and synthesis filters that possess negligible phase distortion is presented. The method is based on first applying the balanced reduction procedure to obtain nearly allpass IIR polyphase components and then approximating these with perfect allpass IIR polyphase components. The resulting IIR designs already have only negligible phase distortion. However, if required, further improvement may be achieved through optimization of the filter parameters. For this purpose, a suitable objective function is presented. Bounds for the magnitude and phase errors of the designs are also derived. Design examples indicate that the derived IIR filter banks are more efficient in terms of computational complexity than the FIR prototypes and perfect reconstruction FIR filter banks. Although the PR FIR filter banks when implemented with the one-multiplier lattice structure and IIR filter banks are comparable in terms of computational complexity, the former is very sensitive to coefficient quantization effects     

Design of stable, causal, perfect reconstruction, IIR uniform DFTfilter banks

Design procedures for stable, causal and perfect reconstruction IIR parallel uniform DFT filter banks (DFT FBs) are presented. In particular a family of IIR prototype filters is a good candidate for DFT FB, where a tradeoff between frequency selectivity and numerical properties (as measured by the Weyl-Heisenberg frames theory) could be made. Some realizations exhibiting a simple and a massively parallel and modular processing structure making a VLSI implementation very suitable are shown. In addition, some multipliers in the filters (both the analysis and synthesis) could be made; powers or sum of powers of 2, in particular for feedback loops, resulting in a good sensitivity behavior. For these reasons as well as for the use of low order IIR filters (as compared with conventional FIR filters), the overall digital filter bank structure is efficient for high data rate applications. Some design examples are provided     

An FIR Channel Estimation Filter with Robustness to Channel Mismatch Condition

This letter proposes a finite impulse response (FIR) channel estimation filter that has robustness against the channel mismatch due to the FIR structure. The channel impulse response is described with a complex state space model and then estimated from received data on the recent time interval. Numerical results show that the FIR channel estimation filter can provide more robust performance than conventional Kalman IIR filters when channel model parameters are not correct.     

Fast Implementation of 3-D Digital Filters Via Systolic Array Processors

In this paper a fast implementation architecture of three-dimensional (3-D) FIR or IIR digital filters via systolic VLSI array processors is described. The modular structure presented is comprised of similar processing elements in a linear cascade configuration with local interconnections. High speed throughput rates are attained due to high concurrency, which is achieved by exploiting both pipelining and parallelism. The considered 3-D FIR and IIR filters may be used for the processing of reconstructed 3-D images and in medical imaging applications.     

Q value analysis of microwave photonic filters

This paper first presents the fundamental principles of the microwave photonic filters.As an example to explain how to implement a microwave photonic filter, a specific finite impulse response (FIR) filter is illustrated.Next, the Q value of the microwave photonic filters is analyzed theoretically, and methods around how to gain high Q value are discussed.Then,divided into FIR filter, first-order infinite impulse response (IIR) filter, and multi-order IIR filter, several novel microwave photonic filters with high Q value are listed and compared.The technical difficulties to get high Q value in first-order IIR filter and multi-order IIR filter are analyzed concretely.Finally, in order to gain higher Q value, a multi-order IIR microwave photonic filter that easily extends its order is presented and discussed.     

General IIR optical filter design for WDM applications usingall-pass filters

A general design algorithm is presented for infinite impulse response (IIR) bandpass and arbitrary magnitude response filters that use optical all-pass filters as building blocks. Examples are given for an IIR multichannel frequency selector, an amplifier gain equalizer, a linear square-magnitude response, and a multi-level response. Major advantages are the efficiency of the IIR filter compared to finite impulse response (FIR) filters, the simplicity of the optical architecture, and its tolerance for loss. A reduced set of unique operating states is discussed for implementing a reconfigurable multichannel selection filter     

Optical half-band filters

This paper proposes two kinds of novel 2×2 circuit configuration for finite-impulse response (FIR) half-band filters. These configurations can be transformed into each other by a symmetric transformation and their power transmittance is identical. The configurations have only about half the elements of conventional FIR lattice-form filters. We derive a design algorithm for achieving desired power transmittance spectra. We also describe 2×2 circuit configurations for infinite-impulse response (IIR) half-band filters. These configurations are designed to realize arbitrary-order IIR half-band filter characteristics by extending the conventional half-band circuit configuration used in millimeter-wave devices. We discuss their filter characteristics and confirm that they have a power half-band property. We demonstrate design examples including FIR maximally flat half-band filters, an FIR Chebyshev half-band filter, and an IIR elliptic half-band filter     

Design of linear-phase IIR filters via impulse-response gramians

A new method for the design of a linear-phase infinite-impulse-response (IIR) filter is presented. It involves designing a finite-impulse-response (FIR) filter satisfying the given frequency response specifications and subsequently obtaining a significantly lower order IIR filter using model reduction based on impulse-response gramians. The general outline of the method and a brief overview of the existing linear-phase FIR filter design and model-reduction techniques are presented. The impulse-response gramian and the model-reduction algorithm used are presented. The method is illustrated by design examples and is compared with other methods for the design of linear-phase IIR filters using equalizers     

Reduced order IIR approximation to FIR digital filters

An algorithm for designing an infinite-impulse-response (IIR) stable filter using a finite-impulse-response (FIR) given filter, with the objective of reducing the delay and order, is described. The design is in the time domain using the least-squares-inverse algorithm, which is briefly described. In this method, the numerator of the approximated filter is part of the FIR filter itself and no calculations and minimization are needed to find the numerator coefficients (except finding the FIR roots). An error analysis between the given FIR and approximated IIR filters is provided. This error analysis enables the designer to fix a design parameter, often unnoted, keeping the energies of the approximated and original filters equal. Results and two illustrative examples are presented     

Design of low-order linear-phase IIR filters via orthogonalprojection

This paper presents an indirect linear-phase IIR filter design technique based on a reduction of linear-phase FIR filters. The desired filter is obtained by minimizing the L₂ norm of the difference between the original FIR filter and the lower order IIR filter. We first establish a relationship between the Hankel singular values of the discarded part of the FIR filter and the L₂ norm of the corresponding filter approximation error based on model truncation. This result motivates us to propose a simple finite search method that will achieve better approximation results than commonly used truncation methods such as the balanced truncation (BT) and the impulse response gramian (IRG) methods. We then develop an iterative algorithm for finding an optimal IIR filter based on a matrix projection of the original FIR filter. The convergence of the proposed algorithm is established. Filters designed using the proposed algorithm are compared with those obtained by other techniques with respect to the amplitude response and group delay characteristics in the passband. Numerical examples show that the proposed algorithm offers the best performance     

Low-Order IIR Filter Bank Design

The advantage of infinite-impulse response (IIR) filters over finite-impulse response (FIR) ones is that the former require a much lower order (much fewer multipliers and adders) to obtain the desired response specifications. However, in contrast with well-developed FIR filter bank design theory, there is no satisfactory methodology for IIR filter bank design. The well-known IIR filters are mostly derived by rather heuristic techniques, which work in only narrow design classes. The existing deterministic techniques usually lead to too high order IIR filters and thus cannot be practically used. In this paper, we propose a new method to solve the low-order IIR filter bank design, which is based on tractable linear-matrix inequality (LMI) optimization. Our focus is the quadrature mirror filter bank design, although other IIR filter related problems can be treated and solved in a similar way. The viability of our theoretical development is confirmed by extensive simulation.     

Oversampled sigma-delta LMS adaptive FIR filters

Two filter designs for adaptive least mean squares (LMS) filtering with sigma-delta modulated input signals are described. One implementation is multibit multiplier-free and operates entirely at the oversampling frequency of the sigma-delta signals, in the other design only the FIR filter operates at the oversampled frequency while the adaptive filtering algorithm is performed at the Nyquist rate. To circumvent any aliasing problems that may be caused by the downsampling process in the architecture and ensure convergence of the adaptive FIR filter. It is necessary to attenuate the high-frequency sigma-delta quantisation noise that is present. To perform this task a multiplier-free, multistage IIR filter structure is used that requires considerably fewer computations than an equivalent FIR filter. The two adaptive LMS filter designs are analysed and their performance is compared with a conventional PCM system in terms of achievable minimum MSE and adaptation speed     

Design methodology for subdigit pipelined digit-serial IIR filters

A novel architecture for high performance two's complement digit-serial IIR filters is presented. The application of the digit-serial computation to the design of IIR filters introduces delay elements in the feedback loop of the IIR filter. This offers the possibility of pipelining the feedback loop inherent in the IIR filters. To fully explore the advantages offered by the use of digit-serial computation, the digit serial structure is based on the feed forward of the carry digit, which allows subdigit pipelining to increase the throughput rate of the IIR filters. A systematic design methodology is presented to derive a wide range of digit-serial IIR filter architectures which can be pipelined to the subdigit level. This will give designers greater flexibility in finding the best trade off between hardware cost and throughput rate. It is shown that the application of digit-serial computations for the realisation of IIR filters combined with the possibility of subdigit pipelining, results in an increase in the computation speed with a considerable reduction in silicon area consumption when compared to an equivalent bit-parallel IIR filter realisations.     

A new class of two-channel biorthogonal filter banks and waveletbases

Proposes a novel framework for a new class of two-channel biorthogonal filter banks. The framework covers two useful subclasses: i) causal stable IIR filter banks. ii) linear phase FIR filter banks. There exists a very efficient structurally perfect reconstruction implementation for such a class. Filter banks of high frequency selectivity can be achieved by using the proposed framework with low complexity. The properties of such a class are discussed in detail. The design of the analysis/synthesis systems reduces to the design of a single transfer function. Very simple design methods are given both for FIR and IIR cases. Zeros of arbitrary multiplicity at aliasing frequency can be easily imposed, for the purpose of generating wavelets with regularity property. In the IIR case, two new classes of IIR maximally flat filters different from Butterworth filters are introduced. The filter coefficients are given in closed form. The wavelet bases corresponding to the biorthogonal systems are generated. the authors also provide a novel mapping of the proposed 1-D framework into 2-D. The mapping preserves the following: i) perfect reconstruction; ii) stability in the IIR case; iii) linear phase in the FIR case; iv) zeros at aliasing frequency; v) frequency characteristic of the filters     

Frequency domain synthesis of IIR digital filters by means of associated FIR filters

This correspondence describes a synthesis technique for IIR digital filters which allows the use of approximation methods already developed for designing FIR filters. The technique is based on the definition, by means of a suitable transformation, of a FIR filter associated to the desired IIR filter. An example of application is given and the related results are briefly discussed.     

Design of doubly complementary filters with approximate linearphase

A new procedure for the design of a real doubly complementary (DC) pair of digital filters obtained from an all-pass structure is presented. The filter design is based on a zero-phase FIR filter design with multi-band frequency specifications and approximate linear-phase characteristic. The resulting complex or real all-pass filter structure is guaranteed to be stable. Some examples illustrating the design method including comparisons with conventional approximately linear phase IIR filters are also shown     

DSSS系统中基于WHT的自适应干扰抑制

本文提出了一种新的DSSS系统自适应干扰抑制方案。针对Wigner-Ville分布的不足,采用WHT来分析接收信号,并从中提取干扰瞬时频率以设计时变IIR滤波器。和通常采用的线性相位FIR滤波器相比,IIR滤波器具有理想的点阻特性。仿真结果证实IIR滤波器的BER性能好于FIR滤波器。     

A technique for realizing linear phase IIR filters

A real-time IIR filter structure is presented that possesses exact phase linearity with 10~1000 times fewer general multiplies than conventional FIR filters of similar performance and better magnitude characteristics than equiripple or maximally flat group delay IIR filters. This structure is based on a technique using local time reversal and single pass sectioned convolution methods to realized a real-time recursive implementation of the noncausal transfer function H(z^-1). The time reversed section technique used to realize exactly linear phase IIR filters is described. The effects of finite section length on the sectional convolution are analyzed. A simulation methodology is developed to address the special requirements of simulating a time reversed section filter. A design example is presented, with computer simulation to illustrate performance, in terms of overall magnitude response and phase linearity, as a function of finite section length. Nine example filter specifications are used to compare the performance and complexity of the time reversed section technique to those of a direct FIR implementation     

Interpolated LIR Mth-band filter design with allpass subfilters

We propose a new allpass-based structure for the IIR Mth-and 2Mth-band filters. These filters consist of M allpass filters and an interpolation filter (sum of two allpasses). Consequently, the proposed structure is very efficient in implementation. By choosing the allpass phase appropriately, the resulting phase response of the IIR Mth-band filter becomes approximately linear. An example is designed and compared with FIR Mth-band filters     

Revisiting the doppler filter of LEO satellite GNSS receivers for precise velocity estimation

The theoretical aspects of the precise velocity determination of Low Earth Orbit (LEO) satellites’on board Global Navigation Satellite Systems (GNSS) receivers are derived. It shows that the receiver’s Phase Lock Loop (PLL) is required to feature extremely small group delay within its low frequency band, which is in contrast to existing work that proposed wide band linear phase filters. Following this theory, a Finite Impulse Response (FIR) filter is proposed. To corroborate, the proposed FIR filter and an Infinite Impulse Response (IIR) filter lately proposed in literals are implemented in a LEO satellite onboard GNSS receiver. Tests are conducted using a third party commercial GPS signal generator. The results show that the GNSS receiver with the proposed FIR achieves 11 mm/s R.M.S precision, while the GNSS receiver with the IIR filter has a filter-caused velocity error that can not be ignored for space borne GNSS receivers.