Design of three-dimensional IIR digital filters with complex coefficients using spectral transformations

1990 ◽  
Vol 73 (8) ◽  
pp. 92-103 ◽  
Author(s):  
Takashi Sekiguchi ◽  
Shin-Ichi Takahashi
Keyword(s):  
Digital Filters ◽  
Three Dimensional ◽  
Spectral Transformations ◽  
Iir Digital Filters ◽  
Complex Coefficients

scholarly journals Spectral Transformations and Associated Linear Functionals of the First Kind

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 107
Author(s):  
Juan Carlos García-Ardila ◽  
Francisco Marcellán
Keyword(s):  
Orthogonal Polynomials ◽  
Linear Space ◽  
Linear Functional ◽  
Linear Functionals ◽  
Spectral Transformations ◽  
Christoffel Transformation ◽  
Complex Coefficients

Given a quasi-definite linear functional u in the linear space of polynomials with complex coefficients, let us consider the corresponding sequence of monic orthogonal polynomials (SMOP in short) (Pn)n≥0. For a canonical Christoffel transformation u˜=(x−c)u with SMOP (P˜n)n≥0, we are interested to study the relation between u˜ and u(1)˜, where u(1) is the linear functional for the associated orthogonal polynomials of the first kind (Pn(1))n≥0, and u(1)˜=(x−c)u(1) is its Christoffel transformation. This problem is also studied for canonical Geronimus transformations.

Efficient implementations of pipelined CORDIC-based IIR digital filters using fast orthonormal μ-rotations

1998 ◽  
Author(s):  
Jun Ma ◽  
Keshab K. Parhi ◽  
Gerben J. Hekstra ◽  
Ed F. A. Deprettere
Keyword(s):  
Digital Filters ◽  
Iir Digital Filters
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