Chivapreecha, Sorawat
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Chivapreecha, Sorawat
Alternative Name
Chivapreecha, S.
Chivapreecha, Sorwat
Main Affiliation
Email
sorawat.ch@kmitl.ac.th
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Item type:Publication, Generalized Pascal matrices, inverses, computations and properties using one-to-one rational polynomial s-z transformations(2008-01-01); Dejhan, KobchaiThis paper proposes a one-to-one mapping between the coefficients of continuous-time (s-domain) and discrete-time (z-domain) IIR transfer functions such that the s-domain numerator/denominator coefficients can be uniquely mapped to the z-domain numerator/denominator coefficients. The one-to-one mapping provides a firm basis for proving the inverses of the so-called generalized Pascal matrices from various first-order s-z transformations. We also derive recurrence formulas for recursively determining the inner elements of the generalized Pascal matrices from their boundary ones. Consequently, all the elements of the whole generalized Pascal matrix can be easily generated through utilizing their neighbourhood, which can be exploited for further simplifying the Pascal matrix generations. Finally, we reveal and prove some interesting properties of the generalized Pascal matrices. © 2008 IEEE. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Unified Pascal matrix for first-order s-z domain transformations(2009-06-16); Dejhan, KobchaiThe so-called generalized Pascal matrix is used for transforming a continuous-time (CT) linear system (filter) into a discrete-time (DT) one. This paper derives an explicit expression for a new generalized Pascal matrix called unified Pascal matrixfrom a unified first-order s-z transformation model and rigorously proves the inverses for various first-order s-z transformations. After deriving a recurrence formula for recursively generating the inner elements of the unified Pascal matrix from its boundary elements, we also show that the recurrence formula leads to computationally unstable solutions for high-order systems due to the so-called catastrophic cancellation in numerical computation, but the unstable problem can be solved through partitioning the whole unified Pascal matrix into several small matrices (submatrices) and then using the recurrence formula to compute the submatrices individually from their boundary elements. This operation almost retains the same computational complexity while guarantees numerically stable solutions. Moreover, an interesting property of the unified Pascal matrix is proved. © 2009 IEEE.