Search results for: inverse stereographic projection

Authors: Khald Anisse, Amina Radgui, Mohammed Rziza

Abstract:

Tracking objects on video sequences is a very challenging task in many works in computer vision applications. However, there is no article that treats this topic in catadioptric vision. This paper is an attempt that tries to describe a new approach of omnidirectional images processing based on inverse stereographic projection in the half-sphere. We used the spherical model proposed by Gayer and al. For object tracking, our work is based on snake method, with optimization using the Greedy algorithm, by adapting its different operators. The algorithm will respect the deformed geometries of omnidirectional images such as spherical neighborhood, spherical gradient and reformulation of optimization algorithm on the spherical domain. This tracking method that we call "spherical snake" permitted to know the change of the shape and the size of object in different replacements in the spherical image.

Keywords: computer vision, spherical snake, omnidirectional image, object tracking, inverse stereographic projection

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Authors: Yiwei Huang, Chunyu Zhao, Jingjing Ding

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Electrical Resistivity Tomography has been widely used in the medicine and the geology, such as the imaging of the lung impedance and the analysis of the soil impedance, etc. Linear Back Projection is the core algorithm of Electrical Resistivity Tomography, but the traditional Linear Back Projection can not make full use of the information of the electric field. In this paper, an imaging method of Parallel Electrode Linear Back Projection for Electrical Resistivity Tomography is proposed, which generates the electric field distribution that is not linearly related to the traditional Linear Back Projection, captures the new information and improves the imaging accuracy without increasing the number of electrodes by changing the connection mode of the electrodes. The simulation results show that the accuracy of the image obtained by the inverse operation obtained by the Parallel Electrode Linear Back Projection can be improved by about 20%.

Keywords: electrical resistivity tomography, finite element simulation, image optimization, parallel electrode linear back projection

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Authors: Gayus Pratama Polunggu, Pamela Felita Adibrata, Hafidh Fathur Riza

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Opak Fault is a large fault that extends from the northeast to the southwest of Yogyakarta Special Region. Opak Fault allegedly re-active after the 2006 Yogyakarta earthquake, about eleven years ago. Opak Fault is a big fault, therefore the activation will bring up the microstructure around the Opak River. This microstructure will reveal a different direction of force from the Opak Fault because the trigger for the emergence of the microstructure is the reactivation of the Opak Fault. In other words, this microstructure is a potentially severe weak area during a tectonic disaster. This research was conducted to find out the impact from the reactivation of Opak Fault that triggered the emergence of microstructure around Opak River which is very useful for disaster mitigation information around research area. This research used the approach from literature study in the form of the journal of structural geology and field study. The method used is a laboratory analysis in the form of stereographic analysis.

Keywords: Opak fault, reactivation, microstructure, stereographic

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Authors: Adel Mohsen

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A direct method based on the good Broyden's updates for evaluating the inverse of a nonsingular square matrix of full rank and solving related system of linear algebraic equations is studied. For a matrix A of order n whose LU-decomposition is A = LU, the multiplication count is O (n3). This includes the evaluation of the LU-decompositions of the inverse, the lower triangular decomposition of A as well as a “reduced matrix inverse”. If an explicit value of the inverse is not needed the order reduces to O (n3/2) to compute to compute inv(U) and the reduced inverse. For a symmetric matrix only O (n3/3) operations are required to compute inv(L) and the reduced inverse. An example is presented to demonstrate the capability of using the reduced matrix inverse in treating ill-conditioned systems. Besides the simplicity of Broyden's update, the method provides a mean to exploit the possible sparsity in the matrix and to derive a suitable preconditioner.

Keywords: Broyden's updates, matrix inverse, inverse factorization, solution of linear algebraic equations, ill-conditioned matrices, preconditioning

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Authors: Bolatbek Rysbaiuly, Aliya S. Azhibekova

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Problems concerning the interpretation of the well testing results belong to the class of inverse problems of subsurface hydromechanics. The distinctive feature of such problems is that additional information is depending on the capabilities of oilfield experiments. Another factor that should not be overlooked is the existence of errors in the test data. To determine reservoir properties, some inverse problems for parabolic equations were investigated. An approach to solving the inverse problems based on the method of regularization is proposed.

Keywords: iterative approach, inverse problem, parabolic equation, reservoir properties

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Authors: Noriko Hanakawa, Masaki Obana

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A simulation tool has been proposed for big-scale projection mapping events. The tool has four main functions based on Mapbox and Unity utilities. The first function is building a 3D model of real cities by MapBox. The second function is a movie projection to some buildings in real cities by Unity. The third function is a movie sending function from a PC to a virtual projector. The fourth function is mapping movies with fitting buildings. The simulation tool was adapted to a real projection mapping event that was held in 2019. The event has been finished. The event had a serious problem in the movie projection to the target building. The extra tents were set in front of the target building. The tents became the obstacles to the movie projection. The simulation tool can be reappeared the problems of the event. Therefore, if the simulation tool was developed before the 2019 projection mapping event, the problem of the tents’ obstacles could be avoided with the simulation tool. In addition, we confirmed that the simulation tool is useful to make a plan of future projection mapping events in order to avoid obstacles of various extra equipment such as utility poles, planting trees, monument towers.

Keywords: projection mapping, projector position, real 3D map, avoiding obstacles

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Authors: Faisal Yousafzai, Murad-ul-Islam Khan, Kar Ping Shum

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We introduce the concept of partially inverse AG**-groupoids which is almost parallel to the concepts of E-inversive semigroups and E-inversive E-semigroups. Some characterization problems are provided on partially inverse AG**-groupoids. We give necessary and sufficient conditions for a partially inverse AG**-subgroupoid E to be a rectangular band. Furthermore, we determine the unitary congruence η on a partially inverse AG**-groupoid and show that each partially inverse AG**-groupoid possesses an idempotent separating congruence μ. We also study anti-separative commutative image of a locally associative AG**-groupoid. Finally, we give the concept of completely N-inverse AG**-groupoid and characterize a maximum idempotent separating congruence.

Keywords: AG**-groupoids, congruences, inverses, rectangular band

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Authors: Yu Menshikov

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In this paper the influence of errors of function derivatives in initial time which have been obtained by experiment (uncontrollable inaccuracy) to the results of inverse problem solution was investigated. It was shown that these errors distort the inverse problem solution as a rule near the beginning of interval where the solution are analyzed. Several methods for remove the influence of uncontrollable inaccuracy have been suggested.

Keywords: inverse problems, filtration, uncontrollable inaccuracy

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Authors: Jakub Havlicek, Jiri Cajthaml

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The article describes the effect of the replacement of the used reference coordinate system in the georeferencing of an old map of Europe. In particular, it was the map entitled “Europe, the Map of Rivers and Mountains on a 1 : 12 000 000 Scale”, elaborated by professor D. Cipera and Dr. J. Metelka for Otto’s Geographic Atlas of 1924. The work was most likely produced using the equal-area conic (Albers) projection. The map was georeferenced into three types of projection – the equal-area conic, cylindrical Plate Carrée and cylindrical Mercator map projection. The map was georeferenced by means of the affine and the second-order polynomial transformation. The resulting georeferenced raster datasets from the Plate Carrée and Mercator projection were projected into the equal-area conic projection by means of projection equations. The output is the comparison of drawn graphics, the magnitude of standard deviations for individual projections and types of transformation.

Keywords: georeferencing, reference coordinate system, transformation, standard deviation

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Authors: Renata Masarova, Bohuslava Juhasova, Martin Juhas, Zuzana Sutova

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In dynamic system theory a mathematical model is often used to describe their properties. In order to find a transfer matrix of a dynamic system we need to calculate an inverse matrix. The paper contains the fusion of the classical theory and the procedures used in the theory of automated control for calculating the inverse matrix. The final part of the paper models the given problem by the Matlab.

Keywords: dynamic system, transfer matrix, inverse matrix, modeling

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Authors: Abdon Choque-Rivero

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The Jacobi system with the Dirichlet boundary condition is considered on a half-line lattice when the coefficients are real valued. The inverse problem of recovery of the coefficients from various data sets containing the so-called transmission eigenvalues is analyzed. The Marchenko method is utilized to solve the corresponding inverse problem.

Keywords: inverse scattering, discrete system, transmission eigenvalues, Marchenko method

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Authors: Gabriel I. Loaiza Ossa, Carlos A. Cadavid Moreno, Juan C. Arango Parra

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It is known that the Riemannian manifold determined by the family of inverse Gaussian distributions endowed with the Fisher metric has negative constant curvature κ= -1/2, as does the family of usual Gaussian distributions. In the present paper, firstly, we arrive at this result by following a different path, much simpler than the previous ones. We first put the family in exponential form, thus endowing the family with a new set of parameters, or coordinates, θ₁, θ₂; then we determine the matrix of the Fisher metric in terms of these parameters; and finally we compute this matrix in the original parameters. Secondly, we define the inverse q-Gaussian distribution family (q < 3) as the family obtained by replacing the usual exponential function with the Tsallis q-exponential function in the expression for the inverse Gaussian distribution and observe that it supports two possible geometries, the Fisher and the q-Fisher geometry. And finally, we apply our strategy to obtain results about the Fisher and q-Fisher geometry of the inverse q-Gaussian distribution family, similar to the ones obtained in the case of the inverse Gaussian distribution family.

Keywords: base of changes, information geometry, inverse Gaussian distribution, inverse q-Gaussian distribution, statistical manifolds

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Authors: Benjawan Rangsikamol, Chutimet Srinilta

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This research paper deals with extraction of Thai character features using the proposed histogram projection so as to improve the recognition performance. The process starts with transformation of image files into binary files before thinning. After character thinning, the skeletons are entered into the proposed extraction using histogram projection (horizontal and vertical) to extract unique features which are inputs of the subsequent recognition step. The recognition rate with the proposed extraction technique is as high as 97 percent since the technique works very well with the idiosyncrasies of Thai characters.

Keywords: character recognition, histogram projection, multilayer perceptron, Thai character features extraction

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Authors: Mohamed Hafid, Marcel Lacroix

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This study presents a simple inverse heat transfer procedure for predicting the wall erosion and the time-varying thickness of the protective bank that covers the inside surface of the refractory brick wall of a melting furnace. The direct problem is solved by using the Finite-Volume model. The melting/solidification process is modeled using the enthalpy method. The inverse procedure rests on the Levenberg-Marquardt method combined with the Broyden method. The effect of the location of the temperature sensors and of the measurement noise on the inverse predictions is investigated. Recommendations are made concerning the location of the temperature sensor.

Keywords: melting furnace, inverse heat transfer, enthalpy method, levenberg–marquardt method

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Authors: Nabil Abaab, Dhaou Akrout, Riadh Ahmadi, Mabrouk Montacer

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The study of fluid pressure and its evolution have a critical importance as they lead to understanding the tectonic history of the region. Therefore, the present work focuses on a microtectonic study of tectonic and hydraulic fracture at the anticline structure of Zemlet El Beidha (North Chott range). The study and the analysis of several stations of tectonic and hydraulic fracture allow revealing the witnesses of a paléosurpression in the deposits of Lower Cretaceous (Bouhedma Formation). In fact, we noticed that the overpressure is directly involved in the creation of various types of fractures as evidenced by the different measures and the stereographic projections. Thus, the orientations of fibers of mineralization that fills the Beefs type fracture have the same direction as the main constraint. Furthermore, we discussed the different overpressure build-up mechanisms. The results showed that tectonics is likely, responsible for this anomaly. This is confirmed by the description of the fibers and the projection of the different measurements of Beefs. The mineralization transformation from gypsum to anhydrite is heavily involved in this stress regime especially in the presence of all necessary conditions of dehydration of gypsum.

Keywords: Zemlet El Beidha, overpressure, tectonic fracture, hydraulic fracture, gypsum beefs

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Authors: Sebastian Andersen, Peter N. Poulsen

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The use of basis projection in the structural dynamic analysis is frequently applied. The purpose of the method is to improve the computational efficiency, while maintaining a high solution accuracy, by projection the governing equations onto a small set of carefully selected basis vectors. The present work considers basis projection in kinematic nonlinear systems with a focus on two widely used basis vectors; the system mode shapes and their modal derivatives. Particularly the latter basis vectors are given special attention since only approximate modal derivatives have been used until now. In the present work the complete modal derivatives, derived from perturbation methods, are presented and compared to the previously applied approximate modal derivatives. The correctness of the complete modal derivatives is illustrated by use of an example of a harmonically loaded kinematic nonlinear structure modeled by beam elements.

Keywords: basis projection, finite element method, kinematic nonlinearities, modal derivatives

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Authors: Sharon-Yasotha Veerayah-Mcgregor, Valipuram Manoranjan

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A backward or inverse problem is known to be an ill-posed problem due to its instability that easily emerges with any slight change within the conditions of the problem. Therefore, only a limited number of numerical approaches are available to solve a backward problem. This paper considers the Nagumo equation, an equation that describes impulse propagation in nerve axons, which also models population growth with the Allee effect. A creative operator splitting numerical scheme is constructed to solve the inverse Nagumo equation. Computational simulations are used to verify that this scheme is stable, accurate, and efficient.

Keywords: inverse/backward equation, operator-splitting, Nagumo equation, ill-posed, finite-difference

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Authors: Hyun-Kyu Cho, Jun-Su Kim, Choon-Geun Huh, Geon Lee Young-Chul Park

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In this study, the relationship between flow properties and fluid projection distance look into connection for shape variations of foam monitor. A numerical analysis technique for fluid analysis of a foam monitor was developed for the prediction. Shape of foam monitor the flow path of fluid flow according to the shape, The fluid losses were calculated from flow analysis result.. The modified model used the length increase model of the flow path, and straight line of the model. Inlet pressure was 7 [bar] and external was atmosphere codition. am. The results showed that the length increase model of the flow path and straight line of the model was improved in the nozzle projection distance.

Keywords: injection performance, finite element method, foam monitor, Projection distance

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Authors: Rashmi Yadawad, Disha Narayanan, Ravi Gautam

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Through Wall Radar Imaging is gaining increasing importance now a days in the field of Defense and one of the most important criteria that forms the basis for the image quality obtained is the Cross-Range resolution of the image. In this research paper, the Bilateral Back projection algorithm has been implemented for Through Wall Radar Imaging. The sole purpose is to enhance the resolution in the cross range direction of the obtained Back projection image. Synthetic Data is generated for two targets which are placed at various locations in a room of dimensions 8 m by 6m. Two algorithms namely, simple back projection and Bilateral Back projection have been implemented, images are obtained and the obtained images are compared. Numerical simulations have been coded in MATLAB and experimental results of the two algorithms have been shown. Based on the comparison between the two images, it can be clearly seen that the ringing effect and chess board effect have been heavily reduced in the bilaterally back projected image and hence promising results are obtained giving a relatively sharper image with relatively well defined edges.

Keywords: through wall radar imaging, bilateral back projection, cross range resolution, synthetic data

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Authors: Ahmad Moussavi

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In this paper, we are concerned with the Jacobson semisimple skew inverse Laurent series rings R((x−1; α, δ)) and the skew Laurent power series rings R[[x, x−1; α]], where R is an associative ring equipped with an automorphism α and an α-derivation δ. Examples to illustrate and delimit the theory are provided.

Keywords: skew polynomial rings, Laurent series, skew inverse Laurent series rings

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Authors: Tae Gwan Kim, Hyun Kyu Cho, Young Hoon Lee, Young Chul Park

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Foam monitors are devices that are installed on cargo tank decks to suppress cargo area fires in oil tankers or hazardous chemical ship cargo ships. In general, the main design parameter of the foam monitor is the distance of the projection through the foam monitor. In this study, the relationship between flow characteristics and projection distance, depending on the shape was examined. Numerical techniques for fluid analysis of foam monitors have been developed for prediction. The flow pattern of the fluid varies depending on the shape of the flow path of the foam monitor, as the flow losses affecting projection distance were calculated through numerical analysis. The basic shape of the foam monitor was an L shape designed by N Company. The modified model increased the length of the flow path and used the S shape model. The calculation result shows that the L shape, which is the basic shape, has a problem that the force is directed to one side and the vibration and noise are generated there. In order to solve the problem, S-shaped model, which is a change model, was used. As a result, the problem is solved, and the projection distance from the nozzle is improved.

Keywords: CFD, foam monitor, projection distance, moment

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Authors: Dina Kon Mushid, Sage Ngoie, Tshimbalanga Madiba, Kabutakapua Kakanda

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Slope stability assessment is still the biggest challenge in mining activities and civil engineering structures. The slope in an opencast mine frequently reaches multiple weak layers that lead to the instability of the pit. Faults and soft layers throughout the rock would increase weathering and erosion rates. Therefore, it is essential to investigate the stability of the complex strata to figure out how stable they are. In the Dikuluwe-Mashamba (DIMA) area, the lithology of the stratum is a set of metamorphic rocks whose parent rocks are sedimentary rocks with a low degree of metamorphism. Thus, due to the composition and metamorphism of the parent rock, the rock formation is different in hardness and softness, which means that when the content of dolomitic and siliceous is high, the rock is hard. It is softer when the content of argillaceous and sandy is high. Therefore, from the vertical direction, it appears as a weak and hard layer, and from the horizontal direction, it seems like a smooth and hard layer in the same rock layer. From the structural point of view, the main structures in the mining area are the Dikuluwe dipping syncline and the Mashamba dipping anticline, and the occurrence of rock formations varies greatly. During the folding process of the rock formation, the stress will concentrate on the soft layer, causing the weak layer to be broken. At the same time, the phenomenon of interlayer dislocation occurs. This article aimed to evaluate the stability of metasedimentary rocks of the Dikuluwe-Mashamba (DIMA) open-pit mine using limit equilibrium and stereographic methods Based on the presence of statistical structural planes, the stereographic projection was used to study the slope's stability and examine the discontinuity orientation data to identify failure zones along the mine. The results revealed that the slope angle is too steep, and it is easy to induce landslides. The numerical method's sensitivity analysis showed that the slope angle and groundwater significantly impact the slope safety factor. The increase in the groundwater level substantially reduces the stability of the slope. Among the factors affecting the variation in the rate of the safety factor, the bulk density of soil is greater than that of rock mass, the cohesion of soil mass is smaller than that of rock mass, and the friction angle in the rock mass is much larger than that in the soil mass. The analysis showed that the rock mass structure types are mostly scattered and fragmented; the stratum changes considerably, and the variation of rock and soil mechanics parameters is significant.

Keywords: slope stability, weak layer, safety factor, limit equilibrium method, stereography method

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Authors: Mohamed Hafid, Marcel Lacroix

Abstract:

This study aimed at developing an inverse heat transfer approach for predicting the time-varying freezing front and the temperature distribution of tumors during cryosurgery. Using a temperature probe pressed against the layer of tumor, the inverse approach is able to predict simultaneously the metabolic heat generation and the blood perfusion rate of the tumor. Once these parameters are predicted, the temperature-field and time-varying freezing fronts are determined with the direct model. The direct model rests on one-dimensional Pennes bioheat equation. The phase change problem is handled with the enthalpy method. The Levenberg-Marquardt Method (LMM) combined to the Broyden Method (BM) is used to solve the inverse model. The effect (a) of the thermal properties of the diseased tissues; (b) of the initial guesses for the unknown thermal properties; (c) of the data capture frequency; and (d) of the noise on the recorded temperatures is examined. It is shown that the proposed inverse approach remains accurate for all the cases investigated.

Keywords: cryosurgery, inverse heat transfer, Levenberg-Marquardt method, thermal properties, Pennes model, enthalpy method

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Authors: Qiang Yang, Ping-An Du

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Group decision making with multiple attribute has attracted intensive concern in the decision analysis area. This paper assumes that the contributions of all the decision makers (DMs) are not equal to the decision process based on different knowledge and experience in group setting. The aim of this paper is to develop a novel approach to determine weights of DMs in the group decision making problems. In this paper, the weights of DMs are determined in the group decision environment via angle cosine and projection method. First of all, the average decision of all individual decisions is defined as the ideal decision. After that, we define the weight of each decision maker (DM) by aggregating the angle cosine and projection between individual decision and ideal decision with associated direction indicator μ. By using the weights of DMs, all individual decisions are aggregated into a collective decision. Further, the preference order of alternatives is ranked in accordance with the overall row value of collective decision. Finally, an example in a chemical company is provided to illustrate the developed approach.

Keywords: angel cosine, ideal decision, projection method, weights of decision makers

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Authors: Jianhua Zhou, Yuwen Zhang

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A two-step multigrid approach is proposed to solve the inverse heat conduction problem in a 3-D object under laser irradiation. In the first step, the location of the laser center is estimated using a coarse and uniform grid system. In the second step, the front-surface temperature is recovered in good accuracy using a multiple grid system in which fine mesh is used at laser spot center to capture the drastic temperature rise in this region but coarse mesh is employed in the peripheral region to reduce the total number of sensors required. The effectiveness of the two-step approach and the multiple grid system are demonstrated by the illustrative inverse solutions. If the measurement data for the temperature and heat flux on the back surface do not contain random error, the proposed multigrid approach can yield more accurate inverse solutions. When the back-surface measurement data contain random noise, accurate inverse solutions cannot be obtained if both temperature and heat flux are measured on the back surface.

Keywords: conduction, inverse problems, conjugated gradient method, laser

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Authors: Mohamed Hafid, Marcel Lacroix

Abstract:

This study presents an inverse analysis for predicting the thermal conductivities and the heat flux of a high-temperature metallurgical reactor simultaneously. Once these thermal parameters are predicted, the time-varying thickness of the protective phase-change bank that covers the inside surface of the brick walls of a metallurgical reactor can be calculated. The enthalpy method is used to solve the melting/solidification process of the protective bank. The inverse model rests on the Levenberg-Marquardt Method (LMM) combined with the Broyden method (BM). A statistical analysis for the thermal parameter estimation is carried out. The effect of the position of the temperature sensors, total number of measurements and measurement noise on the accuracy of inverse predictions is investigated. Recommendations are made concerning the location of temperature sensors.

Keywords: inverse heat transfer, phase change, metallurgical reactor, Levenberg–Marquardt method, Broyden method, bank thickness

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Authors: S. Gómez, G. Sánchez, J. Zarama, M. Castañeda Ramos, J. Escoto Alcántar, J. Torres, A. Núñez, S. Santana, F. Nájera, J. A. Lopez

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This paper shows in detail the mathematical model of direct and inverse kinematics for a robot manipulator (welding type) with four degrees of freedom. Using the D-H parameters, screw theory, numerical, geometric and interpolation methods, the theoretical and practical values of the position of robot were determined using an optimized algorithm for inverse kinematics obtaining the values of the particular joints in order to determine the virtual paths in a relatively short time.

Keywords: kinematics, degree of freedom, optimization, robot manipulator

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Authors: Apirak Sombat, Teerapol Saleewong, Poom Kumam, Parin Chaipunya, Wiyada Kumam, Anantachai Padcharoen, Yeol Je Cho, Thana Sutthibutpong

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This research is aimed to study a two-step iteration process defined over a finite family of σ-asymptotically quasi-nonexpansive nonself-mappings. The strong convergence is guaranteed under the framework of Banach spaces with some additional structural properties including strict and uniform convexity, reflexivity, and smoothness assumptions. With similar projection technique for nonself-mapping in Hilbert spaces, we hereby use the generalized projection to construct a point within the corresponding domain. Moreover, we have to introduce the use of duality mapping and its inverse to overcome the unavailability of duality representation that is exploit by Hilbert space theorists. We then apply our results for σ-asymptotically quasi-nonexpansive nonself-mappings to solve for ideal efficiency of vector optimization problems composed of finitely many objective functions. We also showed that the obtained solution from our process is the closest to the origin. Moreover, we also give an illustrative numerical example to support our results.

Keywords: asymptotically quasi-nonexpansive nonself-mapping, strong convergence, fixed point, uniformly convex and uniformly smooth Banach space

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Authors: Y. T. Tsai, Jin H. Huang

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The sound pressure level (SPL) of the moving-coil loudspeaker (MCL) is often simulated and analyzed using the lumped parameter model. However, the SPL of a MCL cannot be simulated precisely in the high frequency region, because the value of cone effective area is changed due to the geometry variation in different mode shapes, it is also related to affect the acoustic radiation mass and resistance. Herein, the paper presents the inverse method which has a high ability to measure the value of cone effective area in various frequency points, also can estimate the MCL electroacoustic parameters simultaneously. The proposed inverse method comprises the direct problem, adjoint problem, and sensitivity problem in collaboration with nonlinear conjugate gradient method. Estimated values from the inverse method are validated experimentally which compared with the measured SPL curve result. Results presented in this paper not only improve the accuracy of lumped parameter model but also provide the valuable information on loudspeaker cone design.

Keywords: inverse problem, cone effective area, loudspeaker, nonlinear conjugate gradient method

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Authors: Phuoc Si Nguyen

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Infinite impulse response (IIR) filters can be designed from an analogue low pass prototype by using frequency transformation in the s-domain and bilinear z-transformation with pre-warping frequency; this method is known as frequency transformation from the s-domain to the z-domain. This paper will introduce a new method to transform an IIR digital filter to another type of IIR digital filter (low pass, high pass, band pass, band stop or narrow band) using a technique based on inverse bilinear z-transformation and inverse matrices. First, a matrix equation is derived from inverse bilinear z-transformation and Pascal’s triangle. This Low Pass Digital to Digital Filter Pascal Matrix Equation is used to transform a low pass digital filter to other digital filter types. From this equation and the inverse matrix, a Digital to Digital Filter Pascal Matrix Equation can be derived that is able to transform any IIR digital filter. This paper will also introduce some specific matrices to replace the inverse matrix, which is difficult to determine due to the larger size of the matrix in the current method. This will make computing and hand calculation easier when transforming from one IIR digital filter to another in the digital domain.

Keywords: bilinear z-transformation, frequency transformation, inverse bilinear z-transformation, IIR digital filters

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