PHASE‐DISTORTIONLESS FILTERING

Geophysics ◽  
1965 ◽  
Vol 30 (1) ◽  
pp. 32-50 ◽  
Author(s):  
S. N. Domenico
Keyword(s):  
Impulse Response ◽  
Delay Line ◽  
Seismic Events ◽  
Time Lags ◽  
Necessary And Sufficient Condition ◽  
Unit Impulse ◽  
Point Operator ◽  
Necessary And Sufficient ◽  
Time Invariant ◽  
Unit Impulse Response

Phase‐distortionless filtering is accomplished readily in a magnetic delay‐line filter. The necessary and sufficient condition for the elimination of phase distortion is a symmetrical unit‐impulse response or operator. Three‐, six‐, nine‐, and twelve‐point operators were selected from an analytical filter for which the unit‐impulse response is symmetrical. These were applied in a delay‐line filter achieved in conventional magnetic‐tape playback equipment. Advantages of phase‐distortionless filtering demonstrated here are (1) elimination of frequency‐dependent time lags and (2) identification of time‐invariant points of seismic events on a multifiltered seismogram display. The latter should faciliate the correlation of reflections between seismometer group positions and interlocking seismograms. Filtering with each of the above four operators demonstrated that the three‐point operator performs nearly as effectively as the six‐, nine‐, and twelve‐point operators.

scholarly journals Convolution-based time-domain simulation for fluidelastic instability in tube arrays

2021 ◽  
Author(s):  
Mingjie Zhang ◽  
Ole Øiseth
Keyword(s):  
Impulse Response ◽  
Response Function ◽  
Time Domain ◽  
Impulse Response Function ◽  
Time Domain Simulation ◽  
Unit Step ◽  
Tube Arrays ◽  
Unit Impulse ◽  
The Time Domain ◽  
Unit Impulse Response

AbstractA convolution-based numerical algorithm is presented for the time-domain analysis of fluidelastic instability in tube arrays, emphasizing in detail some key numerical issues involved in the time-domain simulation. The unit-step and unit-impulse response functions, as two elementary building blocks for the time-domain analysis, are interpreted systematically. An amplitude-dependent unit-step or unit-impulse response function is introduced to capture the main features of the nonlinear fluidelastic (FE) forces. Connections of these elementary functions with conventional frequency-domain unsteady FE force coefficients are discussed to facilitate the identification of model parameters. Due to the lack of a reliable method to directly identify the unit-step or unit-impulse response function, the response function is indirectly identified based on the unsteady FE force coefficients. However, the transient feature captured by the indirectly identified response function may not be consistent with the physical fluid-memory effects. A recursive function is derived for FE force simulation to reduce the computational cost of the convolution operation. Numerical examples of two tube arrays, containing both a single flexible tube and multiple flexible tubes, are provided to validate the fidelity of the time-domain simulation. It is proven that the present time-domain simulation can achieve the same level of accuracy as the frequency-domain simulation based on the unsteady FE force coefficients. The convolution-based time-domain simulation can be used to more accurately evaluate the integrity of tube arrays by considering various nonlinear effects and non-uniform flow conditions. However, the indirectly identified unit-step or unit-impulse response function may fail to capture the underlying discontinuity in the stability curve due to the prespecified expression for fluid-memory effects.

scholarly journals Spectral Analysis of Dynamic PET Studies

1993 ◽  
Vol 13 (1) ◽  
pp. 15-23 ◽  
Author(s):  
Vincent J. Cunningham ◽  
Terry Jones
Keyword(s):  
Impulse Response ◽  
Time Course ◽  
Arterial Input Function ◽  
Impulse Response Function ◽  
Impulse Response Functions ◽  
Dynamic Pet ◽  
Computer Algorithms ◽  
Arterial Blood ◽  
Unit Impulse ◽  
Unit Impulse Response

We describe a new technique for the analysis of dynamic positron emission tomography (PET) studies in humans, where data consist of the time courses of label in tissue regions of interest and in arterial blood, following the administration of radiolabeled tracers. The technique produces a simple spectrum of the kinetic components which relate the tissue's response to the blood activity curve. From this summary of the kinetic components, the tissue's unit impulse response can be derived. The convolution of the arterial input function with the derived unit impulse response function gives the curve of best fit to the observed tissue data. The analysis makes no a priori assumptions regarding the number of compartments or components required to describe the time course of label in the tissue. Rather, it is based on a general linear model, presented here in a formulation compatible with its solution using standard computer algorithms. Its application is illustrated with reference to cerebral blood flow, glucose utilization, and ligand binding. The interpretation of the spectra, and of the tissue unit impulse response functions, are discussed in terms of vascular components, unidirectional clearance of tracer by the tissue, and reversible and irreversible phenomena. The significance of the number of components which can be identified within a given datum set is also discussed. The technique facilitates the interpretation of dynamic PET data and simplifies comparisons between regions and between subjects.

scholarly journals Sufficient Conditions for Absolute Cesàro Summable Factor

2019 ◽  
Vol 4 (3) ◽  
pp. 627-634
Author(s):  
Smita Sonker ◽  
Alka Munjal
Keyword(s):  
Impulse Response ◽  
Infinite Series ◽  
Sufficient Conditions ◽  
Absolute Summability ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Minimal Set ◽  
Bibo Stability ◽  
Necessary And Sufficient ◽  
Bounded Input

Quasi-f-power increasing sequence has been used for infinite series to establish a theorem on a minimal set of sufficient conditions for absolute Cesàro φ-|〖C,α;δ;l|〗_k summable factor. Further, a set of new and well-known arbitrary results have been obtained by using the main theorem. The presented main result has been validated by the previous result under suitable conditions. In this way, the Bounded Input Bounded Output (BIBO) stability of impulse response has been improved by finding a minimal set of sufficient conditions for absolute summability because absolute summable is the necessary and sufficient condition for BIBO stability.

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