Application Of Linear Filters Research Articles

Monitoring the direction of the short-term trend of economic indicators

Socioeconomic indicators have long been used by official statistical agencies to analyze and assess the current stage at which the economy stands via the application of linear filters used in conjunction with seasonal adjustment procedures. In this study, we propose a new set of symmetric and asymmetric weights that offer substantial gains in real-time by providing timely and more accurate information for detecting short-term trends with respect to filters commonly applied by statistical agencies. We compare the new filters to the classical ones through application to indicators of the US economy, which remains the linchpin of the global economic system. To assess the superiority of the proposed filters, we develop and evaluate explicit tests of the null hypothesis of no difference in revision accuracy of two competing filters. Furthermore, asymptotic and exact finite-sample tests are proposed and illustrated to assess if two compared filters have equal probabilities of failing to detect turning points at different time horizons after their occurrence.

AVA Christmas Meeting, London, UK 18 December 2012

Cohen (IEEE Trans. Signal Processing, 41, 3275-3292, 1993) suggested that a signal’s scale can beregarded as a ‘physical attribute’ that decouples the size of a phenomenon from its shape. His idea, incombination with invariant signal representations, has clear ramifications for the phenomenon of sizeconstancy in vision science. In the visual system, it is hoped that size constancy might be derived fromthe collected responses of a distribution of isotropic spatial filters whose underlying spatial extentare systematically varied from coarse to fine scales according to a diffusion model of image blur: theso-called scale-space representation (eg Koenderink, Biol. Cyb. 50, 363-370, 1984). We demonstratethat this ‘blurring’ approach is flawed. The reason is because scaling and blurring are fundamentallydifferent image operations – application of linear filters whose degrees of blur are different beforeattempting to extract scale information can seriously impair one’s ability to extract the physical attributeof scale. We show that local scale (and position) invariant signal representations can be derived byfinding unknown coefficients that allow one to predict the image intensity signal from a power seriesexpansion. We further show that the inverse of this power series is a Taylor expansion of discretelocal image derivatives whose coefficients are invariant of position and scale. The expansion retainsthe benefit of efficiency when representing 2D shape. Finally, we show how our ideas link scaling,fractional orders of differentiation and pyramid sampling as a means for determining the scale of a 2Dshape. We suggest that similar computations underpin position and scale invariant computations in the visual system.

Segmentation of linear structures from medical images

Abstract In this paper, an algorithm for the extraction of linear structures from medical images is implemented. Blood vessels in angiographic images have linear patterns. Hence, these features can be extracted easily using morphological operations. Blood vessels can be separated out as they have a specific Gaussian-like profile whose curvature varies smoothly along the vessel. In order to differentiate vessels from analogous background patterns, edge detection is performed and the application of linear filters like top-hat transformations can eliminate the background noise, thereby segmenting the entire blood vessels in the angiographic image. Such vessel extraction could help physicians in the computation of parameters related to blood flow.

Non-linear filter, using the wavelet transform, applied to seismological records

As any process in Nature, seismic recordsare affected by noise that the analystwould want to eliminate. One of the mostcommon techniques used to minimise thisnoise effect is the application of linearfilters, which reduce the bandwidth of thesignal. This method is based on the FourierTransform, and therefore any perturbationon the coefficients affects the entirerecord.We have developed a non-linear filter basedon the multiresolution analysis of theDiscrete Time Wavelet Transform (DTWT). Themain idea is to use the time-frequencylocalisation properties of the waveletdecomposition. Each coefficient isassociated to a window on thetime-frequency plane, so any perturbationwould only affect the time and frequencyrange of the correspondent window.The procedure we propose has three stages:periodic noise elimination, spikesreduction and, finally, the non-linearfiltering. The non-linear filter acts bythresholding the wavelet coefficients. Thethresholding estimator will depend on thesignal-noise ratio (SNR) in each of thefrequency bands associated to the waveletdecomposition.We have compared the proposed method to thecoherent structures method (Mallat, 1998)and to two 4th order linear filterbanks (Butterworth and Elliptic filters),applying all of them to a syntheticdatabase, and a real earthquake databaserecorded by the Short Period ROA Network.The proposed method improves the SNR in the87% of the tested events, being therelative rms error less than three, and themaximum amplitude relative error less than10% in the 90% of the synthetic database.

On the automatic interpretation of direct current resistivity soundings

A method for the automatic inversion of resistivity soundings is presented. The procedure consists of two main stages. First, application of linear filters which transforms the apparent resistivity curve into the kernel function, and vice versa. In the second stage the first and second derivatives of the kernel function are calculated and used in a second-order modified Newton-Raphson iterative fitting procedure. The model obtained is optimal in the least squares sense. The method has been tried on some field examples and produced resistivity models which show a good agreement with the geological well logs.

A Method to Compute Optimal Gains in Recursive Linear Filtering Applications

Sequence estimation in the presence of additive Gaussian noise and intersymbol interference can be performed by means of discrete Kalman filters. In adaptive receivers for data transmission, the optimal Kalman gains must be computed on-line. A recursive algorithm is presented for this purpose and its performance, i.e., accuracy and computational requirements, is discussed briefly.