Multiplying huge integers of n digits can be done in time O(n log(n)) using Fast Fourier Transforms (FFT), instead of the O(n) time complexity normally required. In this paper we present this technique from the viewpoint of polynomial multiplication, explaining a recursive divide-and-conquer approach to FFT multiplication. We have compared both methods of multiplication quantitatively and prese...

Pointwise products and quotients, defined in terms of barycentric and trilinear coordinates, are extended to products P ·Γ and quotients Γ/P, where P is a point and Γ is a curve. In trilinears, for example, if Γ0 denotes the circumcircle, then P ·Γ0 is a parabola if and only if P lies on the Steiner inscribed ellipse. Barycentric division by the triangle center X110 carries Γ0 onto the Kiepert ...

SUMMARY This paper presents a standard cell-based frequency synthesizer with dynamic frequency counting (DFC) for multiplying input reference frequency by N times. The dynamic frequency counting loop uses variable time period to estimate and tune the frequency of digitally-controlled oscillator (DCO) which enhances frequency detection's resolution and loop stability. Two ripple counters serve a...

OF THE DISSERTATION On Circuit Complexity Classes and Iterated Matrix Multiplication by Fengming Wang Dissertation Director: Eric Allender In this thesis, we study small, yet important, circuit complexity classes within NC, such as ACC and TC. We also investigate the power of a closely related problem called Iterated Matrix Multiplication and its implications in low levels of algebraic complexi...

As the pixel counts of digital imagers increase, the challenge of maintaining high yields and ensuring reliability over an imager’s lifetime increases. A fault tolerant active pixel sensor (APS) has been designed to meet this need by splitting an APS in half and operating both halves in parallel. The fault tolerant APS will perform normally in the no defect case and will produce approximately h...

0740-7475/01/$10.00 © 2001 IEEE January–February 2001 AFTER AN INTEGRATED CIRCUIT (IC) design is complete, but before first silicon arrives from the manufacturing facility, the design team prepares a set of test patterns to isolate defective parts. Applying this test pattern set to every manufactured part reduces the fraction of defective parts erroneously sold to customers as defect-free parts...

a reliability analysis of suspension bridges against buffeting failure due to gustiness of wind velocity is carried out using the concept of pra (probabilistic risk analysis) procedure. for this purpose, the bending stresses at the critical nodes of the bridge deck are obtained for buffeting forces using a spectral analysis technique and a finite element approach. for the purpose of reliability...

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