FIR Coefficients Research Articles

Identification of noisy input-output FIR models with colored output noise

This paper deals with the identification of FIR models corrupted by white input noise and colored output noise. An identification algorithm that exploits the properties of both the dynamic Frisch scheme and the high-order Yule-Walker (HOYW) equations is proposed. It is shown how the HOYW equations allow to define a selection criterion for identifying the input noise variance (and then the FIR coefficients) within the Frisch locus of solutions. The proposed approach does not require any a priori knowledge about the input and output noise variances. The algorithm performance is assessed by means of Monte Carlo simulations.

A Hardware Implementation of the Levinson Routine in a Radio Detector of Cosmic Rays to Improve a Suppression of the Nonstationary RFI

The radio detector system for ultrahigh-energy cosmic rays in the Pierre Auger Observatory operates in the frequency range 30–80 MHz, which is often contaminated by human-made radio-frequency interferences (RFIs). Several filters were used to suppress the RFI: based on the FFT, an IIR notch filter, and an FIR filter based on the linear prediction. The last refreshes the FIR coefficients calculating either in the external ARM processor, internal soft-core NIOS processor implemented inside the field programmable gate aray (FPGA), or hard-core embedded processors [based on Integrated ARM Cortex-A9800 MHz Hardcore Processor System (HPS)] being a silicon part of the FPGA chip. Refreshment times significantly depend on the type of calculation process. For a stationary RFI, the FIR coefficients can be refreshed each minute or rarer. However, an efficient suppression of nonstationary short-term contaminations requires a much faster response. Calculations of FIR coefficients in an external Voipac PXA270M ARM processor take 1–2 s, by the soft-core virtual NIOS processor on the level of hundreds of milliseconds. The HPS allows a reduction of the refreshment time to ~20 ms (for a 32-stage FIR filter). A symmetry of covariance matrix allows one to use the much faster Levinson procedure instead of typical Gauss routine for solving a set of linear equations of time. A hardware implementation of this procedure inside the FPGA fabric as a specialized $\mu \text{C}$ (with 100-MHz clock) requires only ~53 800 clock cycles. We used 64- or 48-b floating-point representations to calculate FIR coefficients. Resources occupation is relatively high, as the design was optimized for a maximal register performance. However, the RFI suppression is very efficient. We expect a significant suppression of even a short-term nonstationary RFI.

Adaptive Linear Predictor FIR Filter Based on the Cyclone V FPGA With HPS to Reduce Narrow Band RFI in Radio Detection of Cosmic Rays

We are presenting a new approach to a filtering of radio frequency interference (RFI) in the Auger Engineering Radio Array (AERA), which studies the electromagnetic part of the extensive air showers. Radio stations can observe radio signals caused by coherent emissions due to geomagnetic radiation and charge excess processes. AERA observes the frequency band from 30 to 80 MHz. This range is highly contaminated by human-made RFI. In order to improve the signal to noise ratio RFI filters are used in AERA to suppress this contamination. The filter has already been tested with real AERA radio stations in the Argentinean Pampas with very successful results. The linear equations were solved either in the virtual soft-core NIOS® processor (implemented in the FPGA chip as a net of logic elements) or in the external Voipac PXA270M ARM processor. The NIOS® processor is relatively slow (50 MHz internal clock), and the calculations performed in an external processor consume a significant amount of time for data exchange between the FPGA and the processor. Tests showed very good efficiency of the RFI suppression for stationary (long-term) contaminations. However, we observed short-time contaminations, which could not be suppressed either by the IIR-notch filter or by the FIR filter based on the linear predictions. For the LP FIR filter, the refresh time of the filter coefficients was too long and the filter did not keep up with the changes in the contamination structure, mainly due to a long calculation time in a slow processors. We propose to use the Cyclone® V SE chip with an embedded micro-controller operating with a 925 MHz internal clock to significantly reduce the refreshment time of the FIR coefficients. First results in the laboratory are very promising.

Digital bunch-by-bunch transverse feedback system at SSRF

In order to suppress multi-bunch couple instabilities caused by transverse impedance, a bunch-by-bunch transverse feedback system based on a FPGA digital processor is commissioned at SSRF storage ring. The RF front end has two COD pre-rejected attenuators for increasing the system arrangement and signal noise ratio, and the 3*RF Local signal comes from the BPM’s sum signal using a FIR filter for avoiding the effect of longitudinal oscillation. The digital processor receives the coupled horizontal and vertical oscillation signals in the base band and transforms the coupled signals to the horizontal and vertical feedback signals with two series double-zeroes FIR filters. A matlab GUI is applied for producing the FIR coefficients when the tune is shifted. The horizontal and vertical Kickers have a special design for increasing the shunt impedance. Then the multi-bunch instabilities are suppressed respectively and the minimum damping time is about 0.4 ms.

An Alternative Approach to the Balanced Model Truncation Algorithm for Acoustic Minimum-Phase Inverse Filters Order Reduction

We propose an alternative approach to the Balanced Model Truncation method (standard method). This approach reduces substantially the order of minimum-phase inverse filters for equalizing room acoustics. This method is based on a property of the filter z transform function, which modifies the corresponding FIR coefficients before the application of the standard technique to the modified FIR coefficients filter version. In the standard technique, the Hankel singular values plot is the chief guide for a user for the selection of a reduced filter order. Results for minimum-phase inverse filter corresponding to partial equalization of measured acoustic impulse response show the superiority of the proposed method over the standard technique, in terms of reduced filters order selection.

631 衝撃音を対象とした能動騒音制御

As an adaptive algorithm for active noise control, LMS algorithm is most popular because of its simplicity and small calculation amount. However, LMS algorithm doesn't converge quickly and accurately because it needs high order of FIR model for colored noise, for example impact noise. For this problem, we propose a method using least squares lattice algorithm (LSL algorithm). LSL algorithm has high-speed convergence based on least-squares method, and accurate convergence by autoregressive moving-average (ARMA) estimation. Therefore, LSL algorithm is expected that it has quick and accurate convergence of ANC for impact noise. Also, we attempt to apply this LSL algorithm to a case close to actual environment. In this case, since the acoustic field has secondary path characteristic, the filtered-x algorithm is applied generally. However, filtered-x algorithm cannot apply to LSL algorithm directly because of it does not calculate FIR coefficients but ladder coefficients. Hence, We propose a method that do not use filtered-x algorithm, and show the effectiveness of that in computer simulations.

Noisy FIR Identification as a Quadratic Eigenvalue Problem

This correspondence describes a method for identifying FIR models in the presence of input and output noise. The proposed algorithm takes advantage of both the bias compensation principle and the instrumental variable method. It is based on a nonlinear system of equations whose unknowns are the FIR coefficients and the input noise variance. This system allows mapping the noisy FIR identification problem into a quadratic eigenvalue problem. The identification problem is thus solved without requiring the use of iterative least-squares algorithms. The performance of the proposed approach has been tested and compared with that of other identification methods by means of Monte Carlo simulations.

Multiscale finite impulse response modeling

Multiscale representation of data has shown great shrinkage abilities when used in data filtering. This paper shows that multiscale representation has similar advantages when used in empirical process modeling. One advantage is that it helps separate noise from important features, which helps improve the accuracy of estimated models. Another advantage is the fact that the number of significant cross-correlation function (CCF) coefficients relating the scaled signal approximations of the input and output data shrinks in half (i.e., decreases dyadically) at every subsequent coarser scale. This advantage is very important in FIR modeling because it means that smaller FIR models are needed at coarse scales. This advantage is exploited to develop a Multiscale Finite Impulse Response (MSFIR) modeling algorithm that helps deal with the collinearity problem often encountered in FIR models. The idea is to decompose the input–output data at multiple scales, and using the scaled signals at each scale, construct smaller FIR models with less collinearity, and then select among all scales the optimum estimated model. The developed MSFIR modeling algorithm is finally shown to outperform some of the existing FIR model estimation methods, such as Ordinary Least Squares (OLS) regression, Ridge Regression (RR), and Principal Component Regression (PCR). A key reason for the advantage of MSFIR over RR is that MSFIR shrinks the statistically insignificant CCF coefficients and noise wavelet coefficients (which are statistically zero) towards zero, while RR shrinks the FIR coefficients towards zero, while they are not.

Control-relevant design of periodic test input signals for iterative open-loop identification of multivariable FIR systems

In this paper, the problem of control-relevant test input design for iterative system identification is considered. Two approaches are presented for the L-optimal input test signal design by Cooley and Lee (2001). which minimizes the a posteriori closed-loop error based on a priori information given by the data already collected from previous iterations. To simplify the computation, we limit our design to a period signal of period n, which is the number of FIR coefficients. The first approach is direct time-domain search for optimal test input values, which can be formulated as a nonconvex optimization or a concave Quadratic Program. The second approach considers frequency domain solution of the L-optimal design problem to obtain the optimal discrete spectra of the test signals, which is subsequently realized as a periodic signal.

On the hierarchical least-squares algorithm

A so-called hierarchical recursive least-squares (HRLS) algorithm was suggested in a recent letter in an attempt to reduce the computational burden and improve the convergence rate of the classical RLS algorithm. The discussion of HRLS in the original letter, however, has several unclear points; in particular no clear explanation was offered for the good simulation results reported. In this letter we provide some analysis of the HRLS to determine when this algorithm may be expected to work or fail. It turns out that the input to the channel must be a white sequence, otherwise HRLS may yield grossly biased estimates of the channel FIR coefficients.

Adaptive IIR filter initialization via hybrid FIR/IIR adaptive filter combination

A novel hybrid adaptive FIR/IIR filter configuration is presented. The aim is to reduce the main obstacles limiting the use of adaptive IIR filters: namely convergence and stability. The hybrid scheme attempts to exploit the good qualities of both system adaptive FIR filters (good convergence and stability) and those for adaptive IIR filters (sharp transition bands, lower order, and complexity). In this paper, the hybrid scheme is presented for a system identification problem, and the task is achieved in three main steps: (a) A training signal is applied to an adaptive FIR filter to achieve a near optimum approximation; (b) the FIR coefficients are mapped through the balanced model reduction technique to a smaller set of coefficients initializing an adaptive IIR filter; (c) there is a process of fine tuning (small adaptive stepsize) the adaptive IIR coefficients for further approximation precision. The IIR filter in the hybrid scheme makes use of the Steiglitz McBride algorithm that assures the stability of the filter. Furthermore, the convergence to the minimum error performance is enforced by the fact that the adaptive IIR filter is operating close to the optimum, requiring very small pole perturbation. The hybrid scheme is compared against the adaptive IIR filter initialized with a set of zero coefficients.

Recovery of single source signal from noisy and reverberant environments using second-order statistics

In this paper, a new approach for blind system identification is presented. Our model involves a single unknown source and two signal receivers under a reverberant and noisy environment, and the system is described by an FIR equation plus an additive noise. We mainly focus on the recovery of the source signal and the estimation of the FIR coefficients in the presence of a larger amount of noise by making use of the received data. Under some reasonable assumptions, we have found that the second-order statistics is sufficient for the identification. In our experimental work, we have investigated the effects of some factors on the accuracy of estimating the FIR coefficients. Additionally, we have compared our method with the Widrow's approach and found that our algorithm has a better performance and there is no limitation on the type and the strength of noise even when the SNR is very small (e.g. SNR=−11 dB). Our proposed recursive algorithm also inherits better convergence properties.

Frequency division algorithm for multi-path ghost cancellation

The frequency division algorithm for multi-path ghost cancellation is described through the frequency-domain optimization method for analog and digital TV transmission. Some guidelines for the frequency division method are provided. A novel method to calculate the FIR and IIR coefficients of the deghost systems from the results of the frequency division is proposed. The simulation results are presented by using a Grand Alliance vestigial sideband channel model.

Efficient structurally symmetric algorithms for least squares FIR filters with linear phase

Two novel least-squares algorithms are derived for the computation of the FIR coefficients of multichannel filters with linear (affine) phase. One is for block processing and requires 2 Np+4.25 p/sup 2/ additions and 2 Np+3p/sup 2/ multiplications, with N being the number of input data samples and p the order of the filter. The second algorithm computes the linear (affine) phase filter's coefficients in an adaptive manner with a computational complexity of 8.5 p additions and 6.5 p multiplications per time recursion. Thus, a reduction in computational complexity of the order of 40-50% is obtained compared to previously derived algorithms. A Fortran subroutine is presented for the time recursive algorithm.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>