Impulse Response Coefficients Research Articles

Channel estimation for asymmetrically clipped optical orthogonal frequency division multiplexing optical wireless communications

A novel channel estimation method for asymmetrically clipped optical orthogonal frequency division multiplexing-based optical wireless communications systems is proposed. Different from the superimposed sequence used in traditional methods, the local matrix and superimposed periodic training are designed rationally. Furthermore, the channel impulse response coefficient of indoor optical wireless diffuse channel can be estimated exactly. The proposed method is not only accurate and simple, but can also allocate time and power flexibly, and improves the bandwidth efficiency.

Efficient Channel Delay Estimation for OFDM Systems over Doubly-Selective Fading Channels

In this paper, we propose an efficient channel delay estimation method for orthogonal frequency-division multiplexing (OFDM) systems, especially over doubly-selective fading channels which are selective in both the symbol time domain and subcarrier frequency domain. For the doubly-selective fading channels in single frequency network (SFN), long and strong echoes exist and thus the conventional discrete Fourier Transform (DFT) based channel delay estimation system often fails to produce the exact channel delay profile. Based on the analysis of the discrete-time frequency response of the channel impulse response (CIR) coefficients in the DFT-based channel delay estimation system, we develop a method to effectively extract the true CIR from the aliased signals by employing a simple narrow-band low-pass filter (NB-LPF). The performance of the proposed system is verified using the COST207 TU6 SFN channel model.

Sharp Transition Multiband Filter in Speech Processing Scheme for Hearing Impaired

Problem statement: A simple analytical approach to the synthesis of a sharp transition, linear phase, multiband FIR filter is presented. The filter magnitude response is modeled using trigonometric functions of frequency. Approach: Employing variable density of ripple cycles in passband and stopband regions with large density of ripples cycles at the sharp transition edges, reduces the abrupt discontinuities at these edges. Results: As a result, Gibb’s phenomenon is reduced in the filter implementation thus giving a flat passband and good stopband attenuation. A closed form expression for impulse response coefficients is obtained. The filter design is easily tunable and allows for variation in transition bandwidth of each band. A speech processing scheme is implemented using a pair of the proposed sharp transition multiband FIR filters to split the speech spectrum into complementary short time spectral bands. Conclusion: The adjacent speech formants are fed dichotically to the two ears to reduce the effect of spectral masking and hence improve speech perception in sensorineural hearing impaired.

Complementary Binary Code Design based on Mismatched Filter

Complementary code (CC) pairs have the interesting characteristic that the superposition of the two related autocorrelation functions (ACFs) has zero sidelobes in range direction. This is an important property for radar applications to avoid range sidelobes. However, CC pairs exist only for limited codeword lengths. Therefore, the general idea of CC design is extended here by applying a mismatched filter (MMF) procedure to the binary phase codeword pairs. There are two objectives considered. The first objective is to design MMF impulse responses to fulfill the zero sidelobe property. The second objective is to find binary phase codeword pairs in cooperation with the MMFs which have a high gain in signal-to-noise ratio (SNR). It is shown that for all codeword lengths (even where the classic CC pair does not exist) there exist binary phase codeword pairs and the related MMF impulse response coefficients which also have the zero sidelobe property. Furthermore, these codeword pairs have high gains in SNR which are nearly the same as for the classic matched filter technique.

Efficient 2-D based algorithms for WLS designs of 2-D FIR filters with arbitrary weighting functions

The impulse response coefficients of a two-dimensional (2-D) finite impulse response (FIR) filter naturally constitute a matrix. It has been shown by several researchers that, two-dimension (2-D) based algorithms that retain the natural matrix form of the 2-D filter's coefficients are computationally much more efficient than the conventional one-dimension (1-D) based algorithms that rearrange the coefficient matrix into a vector. In this paper, two 2-D based algorithms are presented for the weighted least squares (WLS) design of quadrantally symmetric 2-D FIR filters with arbitrary weighting functions. Both algorithms are based on matrix iterative techniques with guaranteed convergence, and they solve the WLS design problems accurately and efficiently. The convergence rate, solution accuracy and design time of these proposed algorithms are demonstrated and compared with existing algorithms through two design examples.

A Per-Survivor Processing Receiver for MIMO Transmission Systems With One Unknown Channel Order Per Output

The order of a communications channel is the length of its impulse response. Recently, several works have tackled the problem of estimating the order of a frequency-selective multiple-input-multiple-output (MIMO) channel. However, all of them consider a single order, despite the fact that a MIMO channel comprises several subchannels (specifically, as many as the number of inputs times the number of outputs), each one possibly with its own order. In this paper, we introduce an algorithm for maximum-likelihood sequence detection (MLSD) in frequency- and time-selective MIMO channels that incorporates full estimation of the MIMO channel impulse response (CIR) coefficients, including one channel order per output. Simulation results following the analytical derivation of the algorithm suggest that the proposed receiver can achieve significant improvements in performance when transmitting through a MIMO channel that effectively comprises subchannels of different lengths.

Modeling and tracking temporal fluctuations for underwater acoustic communications

High-rate, phase-coherent communications through the underwater acoustic channel requires implicitly or explicitly tracking the fluctuations of the channel impulse response. Current techniques estimate the time-varying channel impulse response using observations of signals that have propagated through the channel over some averaging interval and often rely on some method of representing the time variability in the channel. For example, the work by Stojanovic that enabled phase-coherent communications through the underwater channel represented the time-variation as a common phase rotation (Doppler shift) of all taps of the channel impulse response. The tracking of channel fluctuations involves a fundamental trade-off between the number of independent parameters used to represent both the channel impulse response coefficients (i.e., the dimensionality of the estimation problem) and their temporal variations, the rate of channel fluctuations that can be tracked, and the signal to noise ratio (SNR). This talk will present new and review established techniques for modeling time variability and reducing dimensionality in underwater acoustic channel. The performance of these approaches as a function of SNR and rate of channel fluctuation will be compared and their computational complexity will be discussed.

Heart detection and diagnosis based on ECG and EPCG relationships

A new design of a system for preliminary detection of defective hearts is proposed which is composed of two subsystems, in which one is based on the relationship between the electrocardiogram (ECG) and phonocardiogram (PCG) signals. The relationship between both signals is determined as an impulse response (h(n)) of a system, where the decision is made based on the linear predictive coding coefficients of a heart’s impulse response. The other subsystem uses a phase space approach, in which the mean squared error between the distance vectors of the phase space of the normal heart and abnormal heart is judged by the likelihood ratio test (Λ) value, on which the decision is made. The advantage of the proposed system is that a heart’s diagnosis system based on the ECG and EPCG signals can lead to high performance heart diagnostics.

General non-recursive coefficients calculation formula for sinc N filter

A general non-recursive formula is proposed for calculating impulse response coefficients of sinc N filter, which is made by N cascade-connected sinc filters with length of M. It is demonstrated that this formula is valid for all coefficients and suitable for general cases. Using it, different from other methods, each coefficient is independent to others and can be accessed directly due to its non-recursive characteristic.

An adaptive method for consistent estimation of real-valued non-minimum phase zeros in stable LTI systems

An adaptive algorithm, consisting of a recursive estimator for a finite impulse response model having two non-zero lags only, and an adaptive input are presented. The model is parametrized in terms of the first impulse response coefficient and the model zero. For linear time-invariant single-input single-output systems with real rational transfer functions possessing at least one real-valued non-minimum phase zero of multiplicity one, it is shown that the model zero converges to such a zero of the true system. In the case of multiple non-minimum phase zeros, the algorithm can be tailored to converge to a particular zero. The result is shown to hold for systems and noise spectra of arbitrary degree. The algorithm requires prior knowledge of the sign of the high frequency gain of the system as well as an interval to which the non-minimum phase zero of interest belongs.

A digital energy spectroscopy based on FIR filter

We designed a universal digital energy spectroscopy based on online digital signal processing. A prototype system was built and tested. Signals from radiation detectors were processed via a digital filter whose coefficients could be modified without changing the hardware. The paper introduces the hardware design of the digital energy spectroscopy system as well as the full set of software consisting of the selection of the coefficients of the finite impulse response (FIR) filter and the coding in the field-programmable gate array (FPGA). The system was tested with the high purity germanium (HPGe) detector. The results showed that this prototype can achieve an energy resolution close to that of a traditional multi-channel analyzer (MCA) with a much higher counting rate.

An optimal adaptive filtering algorithm with a polynomial prediction model

A new approach to the optimal adaptive filtering is proposed in this paper. In this approach, a polynomial prediction model is used to describe the time-variant/invariant impulse response coefficients of an identified system. When the polynomial prediction model is viewed as the state equations of the identified impulse response coefficients and the relationships between the inputs and outputs of the system are regarded as the measurements of the states, our adaptive filtering can be achieved in the framework of the Kalman filter. It is understood that Kalman filter is optimal in the sense of the MAP (maximum a posteriori), ML (most likelihood) and MMSE (minimum mean square error) under the linear and Gaussian white noise conditions. As a result, our algorithm is also optimal in the statistical senses as Kalman filter does, provided that the impulse response coefficients can be modeled by a polynomial. Not only do the analytical results of the algorithm but also the simulation results show that our algorithm outperforms the traditional known algorithms.

On the design of multi notch filters

A methodology for designing FIR multi notch filters (NFs) derived from second-order prototype IIR NFs is suggested. Rejection bandwidth for the designed filter can be controlled by suitable choice of ‘r’, the pole radius of the IIR prototype NFs. The suggested multi NF can also be adapted to eliminate second-, third- and fourth-order harmonics of periodic noise besides the fundamental noise frequency component. A special case when two notch frequencies ω1 and ω2 are such that [(cosω1)(cosω2) = − 1/2] has also been discussed. The IIR multi NF design for this special case results in reduction of the number of multipliers without affecting the response of the desired NF. For the aforereferred condition, the required coefficients of impulse response of FIR multi notch filter get reduced to almost half in number resulting in reduced computations. The number of zero coefficients further reduces with increase in ‘r’ value. In addition, the frequency response becomes better, with reduced ripples in the pass bands, when ‘r’ is increased and length ‘L’ of the FIR NF is chosen appropriately. Copyright © 2010 John Wiley & Sons, Ltd.

Subspace Approach to Identification of Step-Response Model from Closed-Loop Data

We investigate direct estimation of step-response models from closed-loop data using subspace identification. Necessary information concerning impulse-response coefficients is embedded in subspace matrices. Therefore, the step-response coefficients can be directly obtained from this matrix by integration without the need of extracting state space models first, as the conventional subspace identification does. Since the estimated subspace matrix contains more than one set of impulse-response coefficients, a question arises about how to best synthesize them to obtain an optimal estimate of the impulse-response coefficients and subsequently the step-response coefficients. For this purpose, a reformulation of the subspace identification problem is required for which the variance of all elements in the related subspace matrix can be evaluated. The calculated variances are then used to perform a weighted averaging on the estimated impulse-response coefficients to attenuate the noise influence on the final step-response model estimation. Monte Carlo simulations and pilot-scale experiments are provided to illustrate the proposed method.

IMPULSE RESPONSES OF FRACTIONALLY INTEGRATED PROCESSES WITH LONG MEMORY

Fractionally integrated time series, which have become an important modeling tool over the last two decades, are obtained by applying the fractional filter$(1 - L)^{ - d} = \sum\nolimits_{n = 0}^\infty {b_n } L^n$to a weakly dependent (short memory) sequence. Weakly dependent sequences are characterized by absolutely summable impulse response coefficients of their Wold representation. The weightsbndecay at the ratend−1and are not absolutely summable for long memory models (d> 0). It has been believed that this rate is inherited by the impulse responses of any long memory fractionally integrated model. We show that this conjecture does not hold in such generality, and we establish a simple necessary and sufficient condition for the ratend−1to be inherited by fractionally integrated processes.

Design of Second Order Digital FIR Full-Band Differentiators Using Weighting Coefficients

Most methods for the FIR differentiator design, published so far, have rather complex algorithms, requiring significant computing time. In addition, their design procedures and equations differ for the cases of even and odd differentiator length. FIR differentiators (filters) designed by these methods mostly have the passband group delay level corresponding to that of the linear phase FIR filters. In that sense, the design procedure of the first and higher order FIR full-band differentiators, proposed in this paper, is not only more efficient, but general too. Its efficiency consists in the direct (by this means - faster) determination of numerical values of their impulse response coefficients. Its generality consists in the fact that this method uses the same procedure and formulas for the design of differentiators with both even and odd length (without any mutual difference). (In order to avoid confusion, in the following text, the order of differentiation will be denoted by k, while the length of the FIR structure will be denoted by N). In addition, FIR differentiators designed by this method have approximately constant passband group delay level, which is lower than that of the corresponding linear phase FIR differentiators. These characteristics are enabled due to the fact that full-band differentiators, designed by the presented method, possess neither the (anti) symmetric feature of their impulse response coefficients, nor the strictly linear phase. The proposed method is based on the simultaneous approximation of the prescribed magnitude and group delay responses. The method presents an approach for the FIR differentiator frequency response approximation, directly in the complex, and not in the real domain. Two weighting coefficients, αR and αI, for the approximation of the real and imaginary part of the frequency response, respectively, are introduced. In the convenient manner, they are incorporated into properly and specifically defined quadratic measure error of the FIR differentiator’s frequency response approximation. This manner enables adjusting (decreasing) contributions of the frequency response real and imaginary part approximation errors to the total approximation error. Performing a proper analysis of the real and imaginary part approximation errors (of designed FIR differentiator frequency responses), values of these two parameters, giving a small variation of the group delay response, are obtained simultaneously with very small magnitude response error in the passband. In order to illustrate the proposed method effectiveness, numerical design examples of the second order FIR full-band differentiators are given.

Simultaneous Confidence Regions for Impulse Responses

Abstract Inference about an impulse response is a multiple testing problem with serially correlated coefficient estimates. This paper provides a method to construct simultaneous confidence regions for impulse responses and conditional bands to examine significance levels of individual impulse response coefficients given propagation trajectories. The paper also shows how to constrain a subset of impulse response paths to anchor structural identification and how to formally test the validity of such identifying constraints. Simulation and empirical evidence illustrate the new techniques. A broad summary of asymptotic analytic formulas is provided to make the methods easy to implement with commonly available statistical software.

Design of Optimal Comb FIR Filters-Speed and Robustness

An extension to the analytical design of digital equiripple comb FIR filters is presented here. The filters are optimal in Chebyshev sense. The design runs from the filter specification through the degree formula to the impulse response coefficients, which are evaluated by an extremely efficient recursive algorithm. The proposed design method outperforms the standard procedures in terms of speed and robustness.

Multiple-point statistical room correction for audio reproduction: Minimum mean squared error correction filtering

This paper treats the problem of correction of loudspeaker and room responses using a single source. The objective is to obtain a linear correction filter, which is robust with respect to listener movement within a predefined region-of-interest. The correction filter is based on estimated impulse responses, obtained at several positions, and a linear minimum mean squared error criteria. The impulse responses are estimated using a Bayesian approach that takes both model errors and measurement noise into account, which results in reliable impulse response estimates and a measure of the estimation errors. The correction filter is then constructed by using information from both the estimated impulse response coefficients and their associated estimation errors. Furthermore, in the optimization criteria a time-dependent reflection filter is introduced, which attenuates the high frequency parts of the reflected responses, that is, the parts of the responses that cannot be compensated with a single source system. The resulting correction filter is shown to significantly improve both the temporal and spectral properties of the responses compared to the uncorrected system, and, furthermore, the obtained correction filter has a low level of pre-ringing.

Wavelet-Based Semiblind Channel Estimation for Ultrawideband OFDM Systems

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Ultrawideband (UWB) communications involve very sparse channels, because the bandwidth increase results in a better time resolution. This property is used in this paper to propose an efficient algorithm that jointly estimates the channel and the transmitted symbols. More precisely, this paper introduces an <emphasis emphasistype="boldital"> expectation-maximization</emphasis> (EM) algorithm within a wavelet-domain Bayesian framework for semiblind channel estimation of multiband orthogonal frequency division multiplexing based UWB communications. A prior distribution is chosen for the wavelet coefficients of the unknown channel impulse response to model a sparseness property of the wavelet representation. This prior yields, in maximum <emphasis emphasistype="boldital">a posteriori</emphasis> estimation, a thresholding rule within the EM algorithm. We particularly focus on reducing the number of estimated parameters by iteratively discarding “insignificant” wavelet coefficients from the estimation process. Simulation results using UWB channels that were issued from both models and measurements show that, under sparseness conditions, the proposed algorithm outperforms pilot-based channel estimation in terms of the mean square error (MSE) and bit error rate (BER). Moreover, the estimation accuracy is improved, whereas the computational complexity is reduced compared with traditional semiblind methods. </para>