Minimum-phase Finite Impulse Response Research Articles

Minimum phase finite impulse response filter design

The design of minimum phase finite impulse response (FIR) filters is considered. The study demonstrates that the residual errors achieved by current state-of-the-art design methods are nowhere near the smallest error possible on a finite resolution digital computer. This is shown to be due to conceptual errors in the literature pertaining to what constitutes a factorable linear phase filter. This study shows that factorisation is possible with a zero residual error (in the absence of machine finite resolution error) if the linear operator or matrix representing the linear phase filter is positive definite. Methodology is proposed able to design a minimum phase filter that is optimal—in the sense that the residual error is limited only by the finite precision of the digital computer, with no systematic error. The study presents practical application of the proposed methodology by designing two minimum phase Chebyshev FIR filters. Results are compared to state-of-the-art methods from the literature, and it is shown that the proposed methodology is able to reduce currently achievable residual errors by several orders of magnitude.

Design of multiplierless minimum-phase FIR filters using palindromic polynomials and sharpening

Minimum phase (MP) filters have all zeros inside the unit circle and have a minimum group delay and a minimum energy delay properties, especially useful in communication systems. The special class of MP filters has all zeros inside and on the unit circle. This paper presents a method for design of this class of MP FIR (Finite Impulse Response) digital filters without multipliers The method is based on palindromic polynomials and sharpening technique. The coefficients of palindromic polynomials are presented as a sum of powers of two, and consequently can be implemented by using only adders and shifts, resulting in a multiplierless design. Two classes of palindromic polynomials, having all zeros on the unit circle, are considered. Next, the sharpening technique was applied to improve the magnitude characteristic and to move zeros inside of unit circle. The choice of the design parameters is also presented. All zeros, of the designed MP filter, are inside or on the unit circle. Method is illustrated with one example.

Design of Minimum-Phase FIR Filter: An Evolutionary Approach

In this communication, one novel attempt has been made towards the design of minimum-phase finite impulse response (FIR) filter using one evolutionary computation technique, named differential evolution (DE) algorithm. Mean square error (MSE) between the frequency samples of the ideal filter and the designed filter in the pass-band and stop-band region and the minimum average error (MAE) between the frequency samples in the transition-band region had been considered for the formulation of the objective function in the optimization process. Performance of the optimization technique has been monitored in terms of convergence characteristics for four different orders of FIR filter under consideration. Robustness of our proposition has been firmly established in the sense that the proposed algorithm can be suitably tuned for the design of low-pass, high-pass or band-pass FIR filter of different specifications. Supremacy of the proposed algorithm over other existing techniques for the design of minimum-phase FIR filter has been substantiated by means of frequency response and pole-zero diagrams.

Minimum-phase fir precoder design for multicasting over MIMO frequency-selective channels

To maximize the throughput of frequency-selective multicast channel, the minimum-phase Finite Impulse Response (FIR) precoder design is investigated in this paper. This problem can be solved in two steps. Firstly, we focus on designing a nonminimum-phase FIR precoder under the criterion of maximizing the throughput, and develop two efficient algorithms for the FIR precoder design from perspectives of frequency domain and time domain. In the second step, based on the theory of spectral factorization, the nonminimum-phase FIR precoder is transformed into the corresponding minimum-phase FIR precoder by a classic iterative algorithm without affecting the throughput. Numerical results indicate that the achievable rate of the proposed design has remarkable improvement over that of existing schemes, moreover, the group delay introduced by the FIR precoder is minimized.

Processing of transient signals from damage in CFRP composite materials monitored with embedded intensity-modulated fiber optic sensors

In this research study, intensity-modulated fiber optic sensors, whose working principle is based on the microbending concept, are used to monitor the damage in C/epoxy laminates during tensile loading. The use of advanced signal processing techniques based on time–frequency analysis is explained in order to get information on the damage developing in the composite. The signal Short Time Fourier Transform (STFT) has been computed and several robust noise reduction algorithms have been applied. Principally, Wiener adaptive filtering, improved spectral subtraction filtering, minimum-phase FIR (Finite Impulse Response) filtering and Singular Value Decomposition (SVD)-based filtering have been used. An energy and frequency-based detection criterion is introduced to detect transient signals that can be correlated with the Modal Acoustic Emission (MAE) results and thus damage in the composite material. Hints are that time–frequency analysis and Hankel Total Least Square (HTLS) method can also be used for damage characterisation (delamination, matrix cracking and fiber breaking).

Adaptive clutter filtering for ultrasound color flow imaging

In this article, we present an adaptive clutter rejection method for selecting different clutter filters in ultrasound color flow imaging. A single clutter filter is typically used to reject the clutter. Because the clutter characteristics vary in both space and time, the single clutter filter approach has difficulty in providing optimum clutter rejection in ultrasound images. To achieve more accurate velocity estimation, we have developed a method to select a clutter filter adaptively at each location in an image from a set of predefined filters. Selection criteria have been developed based on the underlying clutter characteristics and the properties of various filters ( e.g., minimum-phase finite impulse response, projection-initialized infinite impulse response and polynomial regression). We have incorporated our adaptive clutter rejection method in an ultrasound system. We have found that our adaptive method can reduce the mean absolute error between the estimated and true flow velocities significantly compared with the conventional methods, in which a single clutter filter is used throughout the entire image. With in vivo abdominal data, we obtained an average gain of 5.0 dB in signal-to-clutter ratio (SCR), compared with the conventional method. These preliminary results indicate that the proposed adaptive method could improve the accuracy of flow velocity estimation in ultrasound color flow imaging through the improvement in SCR and the reduction in bias. (E-mail: ykim@u.washington.edu)

Equiripple minimum phase FIR filter design from linear phase systems using root moments

In this brief we propose to design a minimum phase finite-impulse response (FIR) digital filter transfer function from a given equiripple linear phase FIR transfer function which has identical amplitude. The brief deals with two important issues. The first issue is that we are concentrating on very high degree polynomials for which factorization procedures for root extraction are unreliable. A novel approach is taken, that involves the use of a set of parameters called root moments of a polynomial, derivable directly from the polynomial coefficients that immensely facilitate the factorization of polynomials of very large order. The second issue is that the polynomials we deal with have roots on the unit circle. In the paper we propose a method to overcome this problem. The results of the proposed design scheme are very encouraging as far as robustness and computational complexity are concerned.

Closed-form correlative coding (CFC/sub 2/) blind identification of MIMO channels: isometry fitting to second order statistics

We present a blind closed-form consistent channel estimator for multiple-input multiple-output (MIMO) systems that uses only second order statistics. We spectrally modulate the output of each source by correlative coding it with a distinct filter. The correlative filters are designed to meet the following desirable characteristics: no additional power or bandwidth is required; no synchronization between the sources is needed; the original data rate is maintained. We first prove an identifiability theorem: under a simple spectral condition on the transmitted random processes, the MIMO channel is uniquely determined, up to a phase offset per user, from the second order statistics of the received data. We then develop the closed-form algorithm that attains this identifiability bound. We show that minimum-phase finite impulse response filters with arbitrary memory satisfy our sufficient spectral identifiability condition. This results in a computationally attractive scheme for retrieving the data information sequences after the MIMO channel has been identified. We assess the performance of the proposed algorithms by computer simulations. In particular, the results show that our technique outperforms the previously introduced transmitter-induced conjugate cyclostationarity approach when there are carrier frequency misadjustments.

Frequency-domain design method for linear-phase and minimum-phase FIR equalizers

First the author shows that generally, the attenuation of equalizers should be optimized rather than their magnitude responses. Then he presents an algorithm for the design of linear-phase finite-impulse response (FIR) filters with Chebyshev approximation of desired attenuation functions. The design is quite similar to the Parks-McClellan algorithm, with two decisive deviations. The first concerns the choice of a weighting function, and secondly, the Remez algorithm is modified in order to be able to approximate also nontrivial attenuation functions. Finally, the design is extended to minimum-phase FIR filters, which can also equalize the phase response of minimum-phase systems. It is shown here that phase optimization is a consequence of attenuation optimization.

Blind identification of FIR systems using third order cumulants

A variety of real systems can be represented (either completely or in part) by the finite impulse response (FIR) systems. The parameters of such a system as well as the phase are often required in many practical situations. Non-minimum phase (NMP) systems may be identified correctly from the higher order cumulants which contain the non-minimum phase information. Five estimators based on third-order cumulants are discussed for the identification of (minimum or nonminimum phase) FIR systems from the observed noisy output which has been contaminated by zero-mean symmetric white noise of unknown variance. Two of these algorithms employ both non-linear optimisation and third-order cumulant matching techniques, and the other three are based on the method of least squares but using a specific relation between the third-order cumulants and the parameters of FIR systems. Results from extensive simulations are presented to highlight the salient features and to make comparison with some published results.

Finding the zeros of linear phase FIR frequency sampling digital filters

The need for finding the zeros of FIR filters often arises in digital signal processing applications. If we want to convert linear phase finite-impulse response (FIR) filters into minimum phase FIR filters [1], [2], the problem of finding the zeros of the filter is encountered. This problem has been addressed in [3], but not solved. Here we introduce the idea of using frequency sampling filters for obtaining its zeros. The advantage of using this kind of filter resides in the fact that all the zeros on the unit circle are known. Furthermore, the zeros off the unit circle can be obtained with some simple processing. This type of filter is especially useful when high-order narrow-band filters are involved. Finding the zeros of very high-order equirriple low-pass filters can be a difficult, if not impossible, task.