A Fast Linear Separability Test by Projection of Positive Points on Subspaces

A geometric and non parametric procedure for testing if two finite set of points are linearly separable is proposed. The Linear Separability Test is equivalent to a test that determines if a strictly positive point h > 0 exists in the range of a matrix A (related to the points in the two finite sets). The algorithm proposed in the paper iteratively checks if a strictly positive point exists in a subspace by projecting a strictly positive vector with equal co-ordinates (p), on the subspace. At the end of each iteration, the subspace is reduced to a lower dimensional subspace. The test is completed within r ≤ min(n, d + 1) steps, for both linearly separable and non separable problems (r is the rank of A, n is the number of points and d is the dimension of the space containing the points). The worst case time complexity of the algorithm is O(nr3) and space complexity of the algorithm is O(nd). A small review of some of the prominent algorithms and their time complexities is included. The worst case computational complexity of our algorithm is lower than the worst case computational complexity of Simplex, Perceptron, Support Vector Machine and Convex Hull Algorithms, if d

Analog/RF Built-in-Self-Test Subsystem for a Mobile Broadcast Video Receiver in 65-nm CMOS

A built-in-self-test (BIST) subsystem embedded in a 65-nm mobile broadcast video receiver is described. The subsystem is designed to perform analog and RF measurements at multiple internal nodes of the receiver. It uses a distributed network of CMOS sensors and a low bandwidth, 12-bit A/D converter to perform the measurements with a serial bus interface enabling a digital transfer of measured data to automatic test equipment (ATE). A perturbation/correlation based BIST method is described, which makes pass/fail determination on parts, resulting in significant test time and cost reduction.