Minimum Phase FIR Research Articles

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.

Static and Dynamic Characteristics of DC-DC Converter Using a Digital Filter

This paper presents the regulation and dynamic characteristics of the dc-dc converter with digital PID control, the minimum phase FIR filter or the IIR filter, and then the design criterion to improve the dynamic characteristics is discussed. As a result, it is clarified that the DC-DC converter using the IIR filter method has superior performance characteristics. The regulation range is within 1.3%, the undershoot against the step change of the load is less than 2% and the transient time is less than 0.4ms with the IIR filter method. In this case, the switching frequency is 100kHz and the step change of the load R is from 50 Ω to 10 Ω. Further, the superior characteristics are obtained when the first gain, the second gain and the second cut-off frequency are relatively large, and the first cut-off frequency and the passing frequency are relatively low. Moreover, it is important that the gain strongly decreases at the second cut-off frequency because the upper band pass frequency range must be always less than half of the sampling frequency based on the sampling theory.

A comparison of steady‐state characteristics of buck‐type DC‐DC converter using DSP

AbstractIn this paper, we describe the relationship between the control constants and the output voltage regulation characteristics of a buck DC/DC converter for a digital control system using P‐I‐D control, the minimum phase FIR filter, and the moving average constructed from digital signal processors. Furthermore, the digital control method and its control constants were studied comparatively from the perspective of suppressing the oscillations based on the limit cycle. We found that when an 8‐bit analog‐to‐digital (A‐D) converter having a quantization width of about 80 mV was used, we could obtain excellent results similar to the minimum phase FIR filter and the moving average, achieve an excellent output voltage regulation of less than 1.3% for fluctuations from a light load to the rated 2 A for the target 10 V, and suppress oscillations to less than 20 mV. In the P‐I‐D control method, adequate output voltage regulation characteristics were obtained, but oscillations could not be suppressed. © 2007 Wiley Periodicals, Inc. Electron Comm Jpn Pt 1, 90(5): 1–10, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecja.20357

Design of Equiripple Minimum Phase FIR Filters with Ripple Ratio Control

In this paper, we present a numerical method for the equiripple approximation of minimum phase FIR digital filters. Many methods have been proposed for the design of such filters. Many of them first design a linear phase filter whose length is twice as long, and then factorize the filter to obtain the minimum phase. Although these methods theoretically guarantee its optimality, it is difficult to control the ratio of ripples between different bands. In the conventional lowpass filter design, for example, when different weights are given for its passband and stopband, one needs to iteratively design the filter by trial and error to achieve the ratio of the weights exactly. To address this problem, we modifies well-known Parks-McClellan algorithm and make it possible to directly control the ripple ratios. The method iteratively solves a set of linear equations with controlling the ratio of ripples. Using this method, the equiripple solutions are obtained quickly.

A novel algorithm for the design of selective FIR filters with arbitrary amplitude and phase characteristics

In this paper, a novel analytic technique is presented for the design of finite impulse response digital filters with simultaneous amplitude and phase requirements. The design process relies on the interpolation concept and is based on the generation of arbitrary amplitude and phase polynomials. The new class of FIR filters lays in between the exact linear phase filters at all frequencies and the minimum phase FIR filters based on the amplitude approximation only. It interpolates arbitrary (e.g., linear) phase response in the passband and arbitrary amplitude characteristics in pass- and stopbands. The introduced class of filters can be used on the amplitude and phase equalization of both FIR and IIR digital filters. Illustrative examples are included in order to investigate the main properties of these filters and to demonstrate that the proposed design method leads to a significant saving in the arithmetic computations.

Quasi-equiripple approximation of minimum phase FIR filters by updating desired response

The authors present a new numerical method for the Chebyshev approximation of minimum phase FIR digital filters. This method is based on solving a least squares (LS) problem iteratively. At each iteration, the desired response is transformed so as to have an equiripple magnitude error. This method makes it possible to design minimum phase FIR filters whose magnitude error is quasi-equiripple. Using this method, a quasi-equiripple solution is obtained very quickly. Since the proposed methods do not require any time-consuming optimisation procedure, they require less computational complexity than conventional methods. Finally, some examples to illustrate the advantage of the proposed methods are shown.

Minimum-phase FIR filters for delay-constrained noise reduction

A flexible method of reducing white noise in measurement signals by means of real-time digital filtering is presented. Compared to the widely used averaging filter, the new approach significantly reduces the delay of the step response of a filter, measured typically al the 50% level of the full step. The optimum filter coefficients are obtained analytically as a function of a single weighting parameter.

Lowpass minimum phase filter design using IFIR filters

A design procedure for minimum-phase FIR filters using an interpolated FIR (IFIR) filter is proposed. The IFIR technique allows two linear-phase filters of much lower order to be designed thereby making it easier to apply mipizing than is possible in high order FIR prototype filters. In this way, the problem of finding the roots of high order polynomials is overcome.

Constrained least square design of FIR filters without specified transition bands

This paper puts forth the notion that explicitly specified transition bands have been introduced in the filter design literature in part as an indirect approach for dealing with discontinuities in the desired frequency response. We suggest that the use of explicitly specified transition bands is sometimes inappropriate because to satisfy a meaningful optimality criterion, their use implicitly assumes a possibly unrealistic assumption on the class of input signals. This paper also presents an algorithm for the design of peak constrained lowpass FIR filters according to an integral square error criterion that does not require the use of specified transition bands. This rapidly converging, robust, simple multiple exchange algorithm uses Lagrange multipliers and the Kuhn-Tucker conditions on each iteration. The algorithm will design linear- and minimum-phase FIR filters and gives the best L/sub 2/ filter and a continuum of Chebyshev filters as special cases. It is distinct from many other filter design methods because it does not exclude from the integral square error a region around the cut-off frequency, and yet, it overcomes the Gibbs' phenomenon without resorting to windowing or 'smoothing out' the discontinuity of the ideal lowpass filter.

Minimum-phase filter design from linear-phase startpointvia balanced model truncation

A new practical design approach for minimum-phase FIR or IIR filters, setting out from a high dimensionality FIR linear-phase prototype is described. The novelty of this technique lies in overcoming the inherent problem of finding the roots of a high order polynomial with repeated and/or very closely clustered roots.

Improved design of minimum-phase FIR digital filters by cepstrum and fast Hartley transform

An equiripple minimum-phase FIR filter is designed using the cepstrum and the fast Hartley transform (FHT). This fast procedure is performed entirely in the real domain and requires only two short-length FHT computations. This method avoids complicated phase wrapping and greatly reduces the aliasing error.

Design of minimum phase FIR digital filters

Minimum phase FIR filters are known to have certain practical advantages, e.g. minimum group delay, reduced order for given gain specifications, and lower coefficient sensitivity, when compared with the more common linear phase filters. In the paper, a new adaptive method for designing such filters is presented. The algorithm requires a gain specification in a manner identical to the linear phase case. Conditions for optimality are investigated in terms of the zeros' configuration, equiripple characteristics, minimax and LMS criteria. The result is a very flexible minimum phase FIR filter design technique, with the potential to accommodate a number of different filter structures and types. It is thought to be the second, after the transformation of linear to minimum phase approach, able to guarantee optimum Chebyshev solutions.

Design of minimum-phase FIR digital filter through cepstrum

A method to design an equiripple minimum-phase FIR filter using the cepstrum is described. This method avoids the complicated polynomial root-finding algorithm of Herrman and Schuessler (1970), or the phase-unwrapping algorithm associated with the complex cepstrum of Mian and Nainar (1982). The differential cepstrum method proposed by Pei and Lu (1986) has aliasing problems and requires the computation of three FFTs. The proposed method requires only two FFT computations and avoids the processing of phase.

Design of optimal minimum phase FIR filters by direct factorization

Abstract 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.

Design of minimum-phase FIR digital filters by differential cepstrum

The differential cepstrum is introduced to design equiripple minimum phase FIR filters by using cepstral deconvolution; this fast procedure only takes three FFT computation and avoids the complicated phase wrapping and polynomial root-finding algorithms.

Comments on "A fast procedure to design equiripple minimum-phase FIR filters"

It is shown that the approximation problem for minimum-phase FIR filters with arbitrary specifications on the attenuation can be solved by a method published in [3] although that method is based on the same idea of that developed in the above \footnote[1]{paper}, it is simpler and also easier to apply.

Optimal design of minimum-phase FIR filters

The paper presents a new method for the optimal design of minimum phase FIR filters. First, a constrained approximation procedure is used to obtain the magnitude function and the transmission zeros in the stopband(s). Next, the zeros of the transfer function inside the unit circle are calculated via a low-degree polynomial factorization. For low-pass filters, a straightforward exchange algorithm is presented which achieves the constrained approximation step; a convergence proof is given and it is shown that the algorithm can be implemented via a simple modification of the Parks-McClellan program. The efficacy of the method is illustrated by a numerical example. Attention is drawn to the fact that bandpass filters may in principle require more sophisticated means.

Design of linear or minimum-phase fir filters by constrained chebyshev approximation

Constrained Chebyshev approximation is a known mathematical problem, and Remes' type algorithms for finding the solution have been described. It is shown in this paper that the classical Parks-McClellan program can be converted into a general program for constrained approximation. The program can serve for the design of both linear and minimum phase FIR digital filters.

Accelerated design of linear or minimum phase FIR filters with a Chebyshev magnitude response

An accelerated version of the well known program of Parks and McClellan for the design of linear-phase FIR filters is combined with an improved cepstral procedure to find the corresponding minimum-phase solution. Among three possibilities of speeding up the program, two recently published ones are shown to be doubtful, although a third and new one proves useful. The minimum-phase part follows the method preferred from two methods proposed previously, with some improvements. Further improvements, implemented already or yet to be investigated, are given.

A fast procedure to design equiripple minimum-phase FIR filters

A fast procedure is given to design equiripple minimum-phase FIR filters following the technique proposed by Herrmann and Schuessler [1]: Use is made of cepstral deconvolution, carried out through FFT, to avoid the polynomial root-finding problem inherent in the method.