Deconvolution by Wavelets for Extracting Impulse Response Functions

1997 ◽  
Author(s):  
Francisco José Vicente de Moraes ◽  
Hans Ingo Weber
Keyword(s):  
Impulse Response ◽  
Dynamic Systems ◽  
Impulse Response Functions ◽  
Wavelet Domain ◽  
Response Functions ◽  
Convolution Integral ◽  
Frequency Domains ◽  
Output Noise ◽  
Systems Identification ◽  
Important Input

Abstract The extraction of Impulse Response Functions (Markov parameters) is a major feature on dynamic systems identification. The convolution integral is a most important input-output relationship for linear systems. Existing methods for calculating the IRFs from the convolution integral are carried out in time or frequency domains. The orthonormal wavelet transform consists on decomposing a given signal on mutually orthogonal local basis functions. It is possible to make use of the orthogonal properties of wavelets for calculating the convolution integral. The wavelet domain preserves the temporal nature of data and, simultaneously, different frequency bands are isolated by the multiresolution analysis, without loosing the orthogonality of the wavelet terms. Algorithm matrices are well conditioned and the method is not very sensitive to output noise. Simulated and experimental analysis are performed and results presented.

Impulse-response functions and anthropogenic CO2

1995 ◽  
Vol 22 (4) ◽  
pp. 413-416 ◽  
Author(s):  
Francesco N. Tubiello ◽  
Michael Oppenheimer
Keyword(s):  
Impulse Response ◽  
Impulse Response Functions ◽  
Response Functions ◽  
Anthropogenic Co2

IMPROVING EXTRACTION OF IMPULSE RESPONSE FUNCTIONS USING STATIONARY WAVELET SHRINKAGE IN TERAHERTZ REFLECTION IMAGING

2010 ◽  
Vol 09 (04) ◽  
pp. 387-394 ◽  
Author(s):  
YANG CHEN ◽  
YIWEN SUN ◽  
EMMA PICKWELL-MACPHERSON
Keyword(s):  
Experimental Data ◽  
Impulse Response ◽  
Response Function ◽  
Impulse Response Function ◽  
Terahertz Imaging ◽  
Impulse Response Functions ◽  
Response Functions ◽  
Inverse Filtering ◽  
Wavelet Shrinkage ◽  
Gaussian Filtering

In terahertz imaging, deconvolution is often performed to extract the impulse response function of the sample of interest. The inverse filtering process amplifies the noise and in this paper we investigate how we can suppress the noise without over-smoothing and losing useful information. We propose a robust deconvolution process utilizing stationary wavelet shrinkage theory which shows significant improvement over other popular methods such as double Gaussian filtering. We demonstrate the success of our approach on experimental data of water and isopropanol.

A Comparison of Approaches to Select the Informativeness of Priors in BVARs

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Jan Prüser ◽  
Christoph Hanck
Keyword(s):  
Impulse Response ◽  
Prior Information ◽  
Hierarchical Modeling ◽  
Small Samples ◽  
Model Parameters ◽  
Impulse Response Functions ◽  
Response Functions ◽  
Vector Autoregressions ◽  
The Rich ◽  
Bayesian Vars

Abstract Vector autoregressions (VARs) are richly parameterized time series models that can capture complex dynamic interrelationships among macroeconomic variables. However, in small samples the rich parametrization of VAR models may come at the cost of overfitting the data, possibly leading to imprecise inference for key quantities of interest such as impulse response functions (IRFs). Bayesian VARs (BVARs) can use prior information to shrink the model parameters, potentially avoiding such overfitting. We provide a simulation study to compare, in terms of the frequentist properties of the estimates of the IRFs, useful strategies to select the informativeness of the prior. The study reveals that prior information may help to obtain more precise estimates of impulse response functions than classical OLS-estimated VARs and more accurate coverage rates of error bands in small samples. Strategies based on selecting the prior hyperparameters of the BVAR building on empirical or hierarchical modeling perform particularly well.

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