可规划相位FIR滤波器的神经网络设计方法

本文针对可规划相频响应的实系数FIR滤波器的逼近问题,采用一个三层复激活函数前馈神经网络来实现。该网络隐层各神经元的激活函数为复指数函数,将滤波器系数作为隐层各神经元到输出层的连接权值,通过对误差函数的最小化来调整权值,并根据网络特性与所要设计的滤波器的特点,提出了一些实际设计中训练样本集选取与误差加权值设置的规则。依托所采用的神经网络,根据上述规则,进行了两例可规划相频特性的实系数FIR滤波器的设计,结果表明所设计滤波器的相频响应较好地满足了设计要求。     

Design of linear phase FIR filters using the LMS algorithm

The application of the stochastic gradient (least mean square) algorithm, the design of linear phase finite impulse response (FIR) filters, is discussed. Analytical results are presented and supported by simulation experiments to demonstrate the superior performance of the LMS algorithm equipped with the linear phase constraint as compared to the standard LMS algorithm     

Design of linear phase FIR filters using fractional derivative constraints

In this paper, the designs of linear phase FIR filters using fractional derivative constraints are investigated. First, the definition of fractional derivative is reviewed briefly. Then, the linear phase FIR filters are designed by minimizing integral squares error under the constraint that the ideal response and actual response have several same fractional derivatives at the prescribed frequency point. Next, the fractional maximally flat FIR filters are designed by letting the number of fractional derivative constraints be equal to the number of filter coefficients. Finally, numerical examples are demonstrated to show that the proposed method has larger design flexibility than the conventional integer derivative constrained methods.     

Efficient determination of FIR Wiener filters with linear phase

The letter deals with the efficient determination of FIR Wiener filters with linear phase. This task is achieved by exploiting the Toeplitz-plus-Hankel structure which is imposed on the normal equations matrix by the phase linearity constraint and the stationarity assumption. It is shown that the design of these filters is ultimately reduced to the computation of optimum FIR Wiener filters by Levinson's algorithm.     

A comparison of LTE channelizers implemented with linear phase m-path recursive filters and FIR filters

Cell sites repeaters may receive a composite signal containing a mix of long term evolution channels with bandwidths of 5, 10, 15, and 20 MHz and be required to rearrange the frequency plan of the channels or to drop and insert specific channels prior to transmitting the altered composite signal. The straight forward approach to this task is to down-convert, and down-sample each channel in the mix and then up-sample and up-convert and merge the new traffic mix. The filters applied to the up and down conversion task as well as the up and down sampling task would likely be linear phase finite impulse response (FIR) filters because of the ease with which the resampling task can be embedded in the filtering task. We present an alternate filter structure formed from linear phase recursive filters and compare their performance and computational complexity with their FIR filter counterparts. We show that the recursive filter version of the channel extractor requires significantly few arithmetic operations and actually outperforms the non-recursive version as demonstrated by the error vector magnitude of the two options.     

Relations between thek-dimensional unconstrained and linear phase FIR Wiener filters

In this note, we show that thek-dimensional linear phase FIR Wiener filter can be obtained from the unconstrained filter with a simple reverse and add operation. The relation between the linear phase and unconstrained phase filters is obtained also in the case of a multichannelk-dimensional system. In this case, the properties of the autocorrelation matrix do not allow the simplifications noted for the single channel case.     

Design of nonrecursive digital filters with linear phase

A new class of selective nonrecursive digital filters with independently prescribed equiripple passband and stopband attenuation and linear phase is obtained by numerical solution of a set of nonlinear equations. Some examples are given, and a comparison is made of the new solutions and those previously known.     

Design of optimal minimum phase FIR filters by direct factorization

An improved method of designing optimal minimum phase FIR filters by directly finding zeros is proposed. The zeros off the unit circle are found by an efficient special purpose root-finding algorithm without deflation. The proposed algorithm utilizes the passband minimum ripple frequencies to establish the initial points, and employs a modified Newton's iteration to find the accurate initial points for a standard Newton's iteration. We show, with examples, that the proposed algorithm can be used to design very long filters (L = 325) with very high stopband attenuations.     

Band-pass filters with linear phase

A set of techniques has been developed which permits the simultaneous realization of flat pass band transmission (±0.15 db experimental) linear phase (to within ±5° experimental) over most (1 - 1/N) of the nominal pass band, where N is the number of "in-band" poles. Outside the pass band, the attenuation skirts are steep; experimentally, 40 db has been obtained within 1/N of the nominal filter bandwidth. Shunt L and/or stray capacitance are easily taken into account in the design; in particular, crystals as well as lumped LC have been used. The procedures can accommodate any amount of series resistance in inductors at the expense of flat loss, without any essential change in the computed values of inductors, capacitors, or resonant frequencies. The sensitivity of the network transmission to component errors is modest; discrepancies in the impedance level or tuning of a given constituent resonance in the network branches affect the characteristic mainly in the vicinity of that resonance.     

Design of nonuniformly spaced linear-phase FIR filters using mixedinteger linear programming

An optimization problem for designing a nonuniformly spaced linear-phase FIR filter with minimal complexity is formulated and solved by mixed integer linear programming (MILP). Examples illustrate that the proposed method is useful for designing a wide range of filter types and can outperform subset selection-based design methods     

Design of FIR filters with reduced computations

The performance of a symmetric nonrecursive filter can be improved by multiple use of the same filter. The method is based on an Amplitude Change Function (ACF). An approach to the design of nonrecursive filters using an ACF is discussed in this paper. The prototype filter chosen is a Recursive Running Sum (RRS) filter which does not require any multipliers for its implementation. The required filter specifications are met by multiple use of the RRS filters. The overall filter requires a much smaller number of multiplications and adders than the one designed using the conventional method. It is shown that this method provides reduced noise due to coefficient quantization and product quantization compared with the conventional design technique.     

DESIGN OF POLYPHASE WAVE DIGITAL FILTERS WITH APPROXIMATELY LINEAR PHASE

It is well known that IIR digital filters require quite fewer computations,comparedwith FIR filters,in order to meet stringent magnitude specifications when the phase distortioncan be tolerated.An approximately linear phase,however,can be also obtained with the IIRfilter by making use of a technique without increasing the complexity.Based on a certain numberof attenuation zeros in the pass band,a new approach is developed for the design of polyphasewave digital filters with exact magnitude responses and Chebyshev approximation of the desiredphase responses.The minimum number of attenuation zeros is estimated,and some examples areincluded.     

Design of linear phase M-channel perfect reconstruction FIR filterbanks

We propose two approaches to design M channel nonparaunitary filter banks that satisfy perfect reconstruction (PR) and linear phase (LP) properties. In the first approach, the PR condition is imposed on only a high-pass filter. Although this method does not require nonlinear optimization, it has a demerit in that the order of a high-pass filter becomes high. In the second approach, two filters are optimized simultaneously using a Lagrange-Newton method. We can design PR filter banks that have the same length. The PR constraint is also formulated as a linear and nonlinear equation of the analysis filter coefficients. Finally, some design examples are included     

Throughput-maximizing FIR transmit filters for linear dispersivechannels

Optimum finite-impulse response transmit filters for symbol-by-symbol transmission on linear dispersive additive Gaussian noise channels are derived by maximizing the channel throughput, subject to a fixed average input energy constraint. This maximized throughput is compared to that achievable with water-pour and flat transmit filters. The effect of transmit filter optimization on the receiver performance is investigated by considering the popular minimum mean-square error decision-feedback equalizer receiver structure     

Design of discrete coefficient FIR filters by a fast entropy-directed deterministic annealing algorithm

We present an entropy-directed deterministic annealing optimization algorithm and show its applicability to the problem of designing digital filters with discrete coefficients, each implemented as a sum of signed power-of-two terms and additional general hardware constraints. The algorithm is based on analogies from statistical mechanics and is related to the well-known mean field annealing algorithm. It utilizes estimates of conditional entropy to prune the problem during the optimization, thereby reducing the computational time by 30 to 50%. In conjunction with a scheme to compute the value of the objective function as a sequence of updates, this approach leads to a very fast algorithm. As an application example demonstrating the potential of the new method, we consider the design of digital filters with discrete coefficients consisting of a minimum number of signed power-of-two terms.     

Description of FIR digital filters in the form of parallelconnection of linear phase FIRs

The authors aim to show that FIR digital filters can be described in the form of parallel connection of linear phase FIR digital filters. This representation method may be applicable to FIR digital filter design problems, reducing it to linear phase FIR digital filter design problems     

Simple design and realisation of linear phase 2D FIR filters withdiamond frequency support

A simple design method for linear-phase 2D FIR filters with diamond frequency support is proposed. The method is based on a 1D halfband linear-phase FIR filter design and offers some flexibility in the choice of specifications; the resulting realisation is efficient in terms of computational cost. A design example is also included     

Lowpass digital filters with linear phase

A method of synthetising lowpass recursive digital filters is given in the letter. The method relies on the properties of orthogonal functions on the z plane and the impulse response of an ideal lowpass linear phase filter. Considerable saving in computation and storage appears to have been achieved by this method compared with the nonrecursive (with window functions) truncation method.     

A polynomial-time algorithm for designing FIR filters withpower-of-two coefficients

This paper presents a polynomial-time algorithm for designing digital filters with coefficients expressible as sums of signed power-of-two (SPT) terms. Our proposal is based on an observation that under certain circumstances, the realization cost of a filter with SPT coefficients depends only on the total number of SPT terms, regardless of how the terms distribute among the coefficients. Therefore, the number of SPT terms for each coefficient is not necessarily limited to a fixed number. Instead, they should be allowed to vary subject to a given number of total SPT terms for the filter. This provides the possibility of finding a better set of coefficients. Our algorithm starts with initializing all the quantized coefficient values to zero. It chooses one SPT term at a time and allocates it to the currently most deserving coefficient to minimize the L^∞ distance between the SPT coefficients and their corresponding infinite wordlength values. This process of allocating the SPT terms is repeated until the total number of SPT terms for the filter is equal to a prescribed number. For each filter gain, the time complexity is a second-order polynomial in the number of coefficients to be optimized and is a first-order polynomial in the filter wordlength     

Design of digital FIR notch filters

A new procedure for designing digital FIR notch filters for a specified notch frequency ω_d and 3-dB rejection bandwidth Δω has been proposed. Design formulae for computing the required weights and the length N for the filter have been derived. Illustrative examples confirming the new approach are also given