A Fast Algorithm to Solve Nonhomogeneous Cauchy–Riemann Equations in the Complex Plane

1992 ◽  
Vol 13 (6) ◽  
pp. 1418-1432 ◽  
Author(s):  
Prabir Daripa
Keyword(s):  
Complex Plane ◽  
Fast Algorithm ◽  
Cauchy Riemann

Robust multiscale analytic sampling approximation to periodic function and fast algorithm

2017 ◽  
Vol 15 (01) ◽  
pp. 1750006
Author(s):  
Youfa Li ◽  
Jing Shang ◽  
Gengrong Zhang ◽  
Pei Dang
Keyword(s):  
Hardy Space ◽  
Periodic Function ◽  
Complex Plane ◽  
Time Domain ◽  
Fast Algorithm ◽  
Unit Disc ◽  
Numerical Experiments ◽  
Approximation Error ◽  
Hankel Matrix ◽  
Sample Error

By applying the multiscale method to the Möbius transformation function, we construct the multiscale analytic sampling approximation (MASA) to any function in the Hardy space [Formula: see text]. The approximation error is estimated, and it is proved that the MASA is robust to sample error. We prove that the MASA can be expressed by a Hankel matrix, making use of which, a fast algorithm is established to compute the MASA. Since what we acquire in practice may well be the samples on time domain instead of the analytic ones on the unit disc of the complex plane, we establish a fast algorithm for acquiring analytic samples. Numerical experiments are carried out to demonstrate the efficiency of the MASA.

Optimization of Perfect Reconstruction Cosine-Modulated Filter Banks: Fast Algorithm

2001 ◽  
Vol 56 (12) ◽  
pp. 8 ◽  
Author(s):  
Oscar G. Ibarra-Manzano ◽  
Yuriy V. Shkvarko ◽  
Rene Jaime-Rivas ◽  
Jose A. Andrade-Lucio ◽  
Gordana Jovanovic-Dolecek
Keyword(s):  
Fast Algorithm ◽  
Filter Banks ◽  
Perfect Reconstruction
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