True Impulse Response Research Articles

Performance analysis of unconstrained partitioned-block frequency-domain adaptive filters in under-modeling scenarios

The unconstrained partitioned-block frequency-domain adaptive filter (PBFDAF) offers superior computational efficiency over its constrained counterpart. However, the correlation matrix governing the natural modes of the unconstrained PBFDAF is not full rank. Consequently, the mean coefficient behavior of the algorithm depends on the initialization of adaptive coefficients and the Wiener solution is non-unique. To address the above problems, a new theoretical model for the deficient-length unconstrained PBFDAF is proposed by constructing a modified filter weight vector within a system identification framework. Specifically, we analyze the transient and steady-state convergence behavior. Our analysis reveals that modified weight vector is independent of its initialization in the steady state. The deficient-length unconstrained PBFDAF converges to a unique Wiener solution, which does not match the true impulse response of the unknown plant. However, the unconstrained PBFDAF can recover more coefficients of the parameter vector of the unknown system than the constrained PBFDAF in certain cases. Also, the modified filter coefficient yields better mean square deviation (MSD) performance than previously assumed. The presented alternative performance analysis provides new insight into convergence properties of the deficient-length unconstrained PBFDAF. Simulations validate the analysis based on the proposed theoretical model.

Bayes Control of Hammerstein Systems

Abstract In this paper, we consider data driven control of Hammerstein systems. For such systems a common control structure is a transfer function followed by a static output nonlinearity that tries to cancel the input nonlinearity of the system, which is modeled as a polynomial or piece-wise linear function. The linear part of the controller is used to achieve desired disturbance rejection and tracking properties. To design a linear part of the controller, we propose a weighted average risk criterion with the risk being the average of the squared L2 tracking error. Here the average is with respect to the observations used in the controller and the weighting is with respect to how important it is to have good control for different impulse responses. This criterion corresponds to the average risk criterion leading to the Bayes estimator and we therefore call this approach Bayes control. By parametrizing the weighting function and estimating the corresponding hyperparameters we tune the weighting function to the information regarding the true impulse response contained in the data set available to the user for the control design. The numerical results show that the proposed methods result in stable controllers with performance comparable to the optimal controller, designed using the true input nonlinearity and true plant.

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On weak identification in structural VARMA models

We simulate synthetic data from known data generating processes (DGPs) that arise from economic theory, and compare the performance of fitted VAR and VARMA models in estimating the true impulse responses to structural shocks. We show that while the VARMA structures implied by these DGPs are theoretically identified and lead to precise estimates of impulse responses given enough data, their parameters are close to the non-identified ridge in the parameter space, and that makes precise estimation of the impulse responses in small samples typical of macroeconomic data improbable. As a result, VARMA models barely show any advantage over VARs in characterizing the known DGPs in small samples. This is a refinement of the conjecture that near non-stationarity, near non-invertibility or weak identification could be possible reasons for the failure of structural VARMA models in providing good estimates of theoretical impulse responses of particular DSGE models.

Zero Lower Bound and Parameter Bias in an Estimated DSGE Model

This paper examines how and to what extent parameter estimates can be biased in a dynamic stochastic general equilibrium (DSGE) model that omits the zero lower bound constraint on the nominal interest rate. Our experiments show that most of the parameter estimates in a standard sticky-price DSGE model are not biased although some biases are detected in the estimates of the monetary policy parameters and the steady-state real interest rate. Nevertheless, in our baseline experiment, these biases are so small that the estimated impulse response functions are quite similar to the true impulse response functions. However, as the probability of hitting the zero lower bound increases, the biases in the parameter estimates become larger and can therefore lead to substantial differences between the estimated and true impulse responses.

The Zero Lower Bound and Parameter Bias in an Estimated DSGE Model

Summary This paper examines how and to what extent parameter estimates can be biased in a dynamic stochastic general equilibrium (DSGE) model that omits the zero lower bound (ZLB) constraint on the nominal interest rate. Our Monte Carlo experiments using a standard sticky-price DSGE model show that no significant bias is detected in parameter estimates and that the estimated impulse response functions are quite similar to the true ones. However, as the frequency of being at the ZLB or the duration of ZLB spells increases, the parameter bias becomes larger and therefore leads to substantial differences between the estimated and true impulse responses. It is also demonstrated that the model missing the ZLB causes biased estimates of structural shocks even with the virtually unbiased parameters. Copyright © 2015 John Wiley & Sons, Ltd.

On Optimality Limits of Channel-Structured Estimation in Multicarrier Systems

The channel-structure-based estimation has proved its capacity to enhance the performance over channels that exhibit a sparse impulse response. In this paper, it is shown that, below a signal-to-noise ratio (SNR) limit, the channel estimation performance, based on its true impulse response structure, is no more optimal in the mean square error (MSE) sense. The orthogonal frequency-division multiplexing (OFDM) transmission framework is considered, where the MSE analysis of the channel frequency response is first elaborated. Then, the SNR threshold lower bounding the interval over which the structured channel estimation is optimal is derived. Finally, an approximation leads to a new form of the threshold, which is more suitable for prediction in practice. The analysis handles both of the block- and the comb-type channel estimation and accounts for possible spectral-shaping incorporation.

Local Linear Impulse Responses for a Small Open Economy*

AbstractTraditional vector autoregressions derive impulse responses using iterative techniques that may compound specification errors. Local projection techniques are more robust to this problem, and Monte Carlo evidence has suggested they provide reliable estimates of the true impulse responses. We use local linear projections to investigate the dynamic properties of a model for a small open economy, New Zealand. We compare impulse responses from projections to those from standard techniques, and consider the implications for monetary policy. We pay careful attention to the dimensionality of the model, and focus on effects of policy on gross domestic product, interest rates, prices and exchange rates.

Correct and rapid impulse response calculation as a precondition for auralization.

For almost 20 years auralization procedures have become more and more common, but the simulated acquisition of needed impulse responses (IRs) is still a crucial point during a design process. Different methods have been developed over time with different assumptions and approximations. Until now we observe time‐consuming procedures to calculate true IRs especially in large halls. In this paper new algorithms are reported to calculate IRs in multi‐thread mode with one computer or better via a network with a set of CPUs working in parallel. So calculations in large halls may be reduced from 8–10 h with one CPU to 10–20 min with multi‐core computers. Via internet routines a master‐slave network is used to allow parallel networking on the same file. Examples are shown using eight remote‐controlled quad‐core computers, i.e., 32 CPUs at the same time. This way the auralization procedure is becoming a daily and quickly usable function. It opens the way to convert an auralization toy into a real tool.

A Misspecification-Robust Impulse Response Estimator

This paper proposes an alternative methodology to estimating impulse response function. The proposed method does not impose parametric restrictions on the estimated impulse response function as the conventional method does. Instead, the impulse responses are estimated by regressing the series of interest on the residuals obtained from prior-stage “long autoregression”. Our Monte Carlo simulations demonstrate that the proposed estimator is capable of capturing the shapes of a wide range of impulse response functions without requiring that a correctly specified model be used in estimating the innovations. On the other hand, the inference under the conventional impulse response estimator can be quite misleading if the estimation models are misspecified. The advantage of the proposed impulse response estimator over the conventional one is most relevant when the true impulse response function exhibits rich dynamics, but the size of the sample proscribes the use of large-order estimation models.

Sign Restrictions in Structural Vector Autoregressions: A Critical Review

The paper provides a review of the estimation of structural vector autoregressions with sign restrictions. It is shown how sign restrictions solve the parametric identification problem present in structural systems but leaves the model identification problem unresolved. A market and a macro model are used to illustrate these points. Suggestions have been made on how to find a unique model. These are reviewed. An analysis is provided of whether one can recover the true impulse responses and what difficulties might arise when one wishes to use the impulse responses found with sign restrictions. (JEL C32, C51, E12)

An ultrasonic imaging speckle-suppression and contrast-enhancement technique by means of frequency compounding and coded excitation

A method for improving the contrast resolution of B-mode images is proposed by combining the speckle-reduction technique of frequency compounding (FC) and the coded excitation and pulse-compression technique called resolution enhancement compression (REC). FC suppresses speckle but at the expense of a reduction in axial resolution. Using REC, the axial resolution and bandwidth of the imaging system was doubled. Therefore, by combining REC with FC (REC-FC), the tradeoff between axial resolution and contrast enhancement was extended significantly. Simulations and experimental measurements were conducted with a single-element transducer (f/2.66) having a center frequency of 2.25 MHz and a -3-dB bandwidth of 50%. Simulations and measurements of hyperechoic (+6 dB) tissue-mimicking targets were imaged. Four FC cases were evaluated: full-, half-, third-, and fourth-width of the true impulse response bandwidth. The image quality metrics used to compare REC-FC to conventional pulsing (CP) and CP-FC were contrast-to-noise ratio (CNR), speckle signal-to-noise ratio, histogram pixel intensity, and lesion signal-to-noise ratio. Increases in CNR of 121%, 231%, 302%, and 391% were obtained in experiments when comparing REC-FC for the full-, half-, third-, and fourth-width cases to CP. Furthermore, smaller increases in CNR of 112%, 233%, and 309% were obtained in experiments when comparing CP-FC for the half-, third-, and fourth-width cases to CP. Improved lesion detectability was observed by using REC-FC.

From toy to tool—advanced auralization procedure in daily design work.

Since more than 20 years simulation procedures are more and more common, but the auralization procedure is considered mainly as a toy. The reason for this relates partially to the efforts needed to get real auralized sound files. In a previous paper the authors reported about a method to produce high end auralization files. This method allows to use normal head phones to get the right spatial impression without in‐head localization. The main reason not to use an auralized sound impression in the daily design work is the time‐consuming procedure to calculate true impulse responses (IR) especially in large halls. In this paper new algorithms are reported to calculate IRs in multithread mode with one computer or better via a network with a set of CPUs working in parallel. So calculations in large halls maybe be reduced from 8–10 h with one CPU to 10–20 min with multicore computers. The paper explains the way from the model to high‐end auralized files. Some examples demonstrate the quality of these derived binaural files.

A new adaptive blind channel identification algorithm

This paper addresses the blind identification of single-input multiple-output (SIMO) finite-impulse-response (FIR) systems. We first propose a new adaptive algorithm for the blind identification of SIMO FIR systems. Then, its convergence property is analyzed systematically. It is shown that under some mild conditions, the proposed algorithm is guaranteed to converge in the mean to the true channel impulse responses in both noisy and noiseless cases. Simulations are carried out to demonstrate the theoretical results.

Variable step-size multichannel frequency-domain LMS algorithm for blind identification of finite impulse response systems

The choice of step size is a critical factor in blind identification of single-input multi-output systems using adaptive multichannel frequency-domain least-mean-squares (MCFLMS) algorithm. The proper step size is dependent on the signal power and it influences the speed of convergence and the final misalignment error. Applying normalised MCFLMS (NMCFLMS) algorithm, the dependency of the step-size parameter on signal power can be eliminated; however, it is shown that even for a moderate signal-to-noise ratio, the algorithm fails to converge to the eigenvector corresponding to the minimum eigenvalue of the data correlation matrix and hence misconverges to a fictitious solution. A self-adaptive variable step-size MCFLMS (VSS-MCFLMS) algorithm that optimises the performance of the algorithm in each iteration in order to achieve minimum misalignment with the true channel impulse response is proposed. The convergence analysis of the proposed algorithm is performed and it is shown that the VSS-MCFLMS algorithm converges, both in noise-free and noisy conditions, to the eigenvector corresponding to the minimum eigenvalue and is therefore more noise robust when compared with the NMCFLMS. The algorithm also shows the optimal speed of convergence in a noise-free case and the proposed variable step size guarantees the stability of the algorithm. Simulation results are presented to demonstrate that the proposed VSS-MCFLMS algorithm gives lower final misalignment when compared with the NMCFLMS algorithm without sacrificing the speed of convergence and computational efficiency.

Local Linear Impulse Responses for a Small Open Economy

Traditional vector autoregressions derive impulse responses using iterative techniques that may compound specification errors. Local projection techniques are robust to this problem, and Monte Carlo evidence suggests they provide reliable estimates of the true impulse responses. We use local linear projections to investigate the dynamic properties of a model for a small open economy, New Zealand. We compare impulse responses from local projections to those from standard techniques, and consider the implications for monetary policy. We pay careful attention to the dimensionality of the model, and focus on effects of policy on GDP, interest rates, prices and exchange rates.

Estimation of Parameters in Shot-Noise- Driven Doubly Stochastic Poisson Processes Using the EM Algorithm

To estimate the parameters, the impulse response (IR) functions of some linear time-invariant systems generating intensity processes, in Shot-Noise-Driven Doubly Stochastic Poisson Process (SND-DSPP) in which multivariate presynaptic spike trains and postsynaptic spike trains can be assumed to be modeled by the SND-DSPPs. An explicit formula for estimating the IR functions from observations of multivariate input processes of the linear systems and the corresponding counting process (output process) is derived utilizing the expectation maximization (EM) algorithm. The validity of the estimation formula was verified through Monte Carlo simulations in which two presynaptic spike trains and one postsynaptic spike train were assumed to be observable. The IR functions estimated on the basis of the proposed identification method were close to the true IR functions. The proposed method will play an important role in identifying the input-output relationship of pre- and postsynaptic neural spike trains in practical situations.

Analytic modeling of groundwater dynamics with an approximate impulse response function for areal recharge

An analytic approach is presented for the simulation of variations in the groundwater level due to temporal variations of recharge in surficial aquifers. Such variations, called groundwater dynamics, are computed through convolution of the response function due to an impulse of recharge with a measured time series of recharge. It is proposed to approximate the impulse response function with an exponential function of time which has two parameters that are functions of space only. These parameters are computed by setting the zeroth and first temporal moments of the approximate impulse response function equal to the corresponding moments of the true impulse response function. The zeroth and first moments are modeled with the analytic element method. The zeroth moment may be modeled with existing analytic elements, while new analytic elements are derived for the modeling of the first moment. Moment matching may be applied in the same fashion with other approximate impulse response functions. It is shown that the proposed approach gives accurate results for a circular island through comparison with an exact solution; both a step recharge function and a measured series of 10 years of recharge were used. The presented approach is specifically useful for modeling groundwater dynamics in aquifers with shallow groundwater tables as is demonstrated in a practical application. The analytic element method is a gridless method that allows for the precise placement of ditches and streams that regulate groundwater levels in such aquifers; heads may be computed analytically at any point and at any time. The presented approach may be extended to simulate the effect of other transient stresses (such as fluctuating surface water levels or pumping rates), and to simulate transient effects in multi-aquifer systems.

A Computer Investigation of the Performance of Virtual Reflectors: Part 1 - Development of the Method

In a companion paper [1] a technique for improving acoustic conditions in open stage auditoria by means of virtual reflectors has been proposed. Possible methods of testing the application of a virtual reflector system were discussed and it was concluded that computer simulation was the most appropriate. However, before employing a commercially available package it was necessary to devise suitable procedures. The need for both a directional loudspeaker and a directional microphone is an essential requirement for the virtual reflector system but most computer simulation packages only allow for source directivity. Hence a method of incorporating the effect of microphone directivity using the principle of reciprocity was developed. The basis of establishing the gain factor has been devised and it is proposed that the convolution of echograms rather than the convolution of true impulse responses can be employed to predict system performance. The action of the virtual reflector system has been investigated using a model of an open stage theatre. Both system microphone and system loudspeaker were selected from a catalogue of available modern commercial sound equipment. The resulting STI contours demonstrated that the effect of the virtual reflector over the audience area to the rear of a human speaker was to raise the speech intelligibility to be approximately equal to that to the front of the speaker. It has been shown that the STI at the rear of a speaker with the virtual reflector system in operation does not increase significantly with gain. This is due to the Modulation Transfer Functions which determine the STI value being determined by the convolution of two impulse responses multiplied by a gain factor and added to a third impulse response. The resulting impulse response therefore consists of many ‘reflections’ and hence the MTF's and STI values will be adversely affected if excess gain is applied.

Robustness of least-squares and subspace methods for blind channel identification/equalization with respect to effective channel undermodeling/overmodeling

The least-squares and the subspace methods are two well-known approaches for blind channel identification/equalization. When the order of the channel is known, the algorithms are able to identify the channel, under the so-called length and zero conditions. Furthermore, in the noiseless case, the channel can be perfectly equalized. Less is known about the performance of these algorithms in the practically inevitable cases in which the channel possesses long tails of "small" impulse response terms. We study the performance of the mth-order least-squares and subspace methods using a perturbation analysis approach. We partition the true impulse response into the mth-order significant part and the tails. We show that the mth-order least-squares or subspace methods estimate an impulse response that is "close" to the mth-order significant part. The closeness depends on the diversity of the mth-order significant part and the size of the tails. Furthermore, we show that if we try to model not only the "large" terms but also some "small" ones, then the quality of our estimate may degrade dramatically; thus, we should avoid modeling "small" terms. Finally, we present simulations using measured microwave radio channels, highlighting potential advantages and shortcomings of the least-squares and subspace methods.