Dual frames for causal induction: the normative and the heuristic

2017 ◽  
Vol 23 (3) ◽  
pp. 292-317 ◽  
Author(s):  
Ikuko Hattori ◽  
Masasi Hattori ◽  
David E. Over ◽  
Tatsuji Takahashi ◽  
Jean Baratgin
Keyword(s):  
Dual Frames ◽  
Causal Induction

scholarly journals GENERAL FRAMEWORK FOR CONSISTENT SAMPLING IN HILBERT SPACES

2005 ◽  
Vol 03 (04) ◽  
pp. 497-509 ◽  
Author(s):  
YONINA C. ELDAR ◽  
TOBIAS WERTHER
Keyword(s):  
Hilbert Spaces ◽  
General Framework ◽  
Inner Product ◽  
Riesz Bases ◽  
Oblique Projection ◽  
Dual Frames ◽  
Infinite Dimensional ◽  
Reconstruction Scheme ◽  
Linear Reconstruction ◽  
Oblique Dual

We introduce a general framework for consistent linear reconstruction in infinite-dimensional Hilbert spaces. We study stable reconstructions in terms of Riesz bases and frames, and generalize the notion of oblique dual frames to infinite-dimensional frames. As we show, the linear reconstruction scheme coincides with the so-called oblique projection, which turns into an ordinary orthogonal projection when adapting the inner product. The inner product of interest is, in general, not unique. We characterize the inner products and corresponding positive operators for which the new geometrical interpretation applies.

A Z-Axis Decoupled Micromachined Gyroscope with Dual Frames

2011 ◽  
Vol 483 ◽  
pp. 169-173
Author(s):  
Hai Lin Tang ◽  
Xian Xue Liu ◽  
Hao Zhou
Keyword(s):  
Quality Factor ◽  
Test Results ◽  
Dual Frames ◽  
Fabrication Errors ◽  
Micromachined Gyroscope

A z-axis decoupled micromachined gyroscope with dual frames is designed, fabricated and tested. The robust structure considering fabrication errors is obtained by the use of optimal robustness of design and process compensation. The gyroscope is packaged in vacuum, and test results show that quality factor of driving and sensing modes are 2000 and 800, respectively. In the range of 0~2400 deg/sec, sensitivity and linearity of the fabricated gyroscope are 1 deg/sec and 0.3%, respectively.

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