Orthogonal filters

Electrical Engineering, Mathematics and Computer ScieneElectrical Engineering, Mathematics and Computer Scienc

Efficient Partitioning of Algorithms for Long Convolutions and their Mapping onto Architectures

We present an efficient approach for the partitioning of algorithms implementing long convolutions. The dependence graph (DG) of a convolution algorithm is locally sequential globally parallel (LSGP) partitioned into smaller, less complex convolution algorithms. The LSGP partitioned DG is mapped onto a signal flow graph (SFG), in which each processor element (PE) performs a small convolution algorithm. The key is then to reduce the complexity of the SFG in two steps: 1. local reduction of complexity: the short Fast Fourier Transform (FFT) is used to perform the small convolution within the PE, 2. global reduction of complexity: the short FFTs within the PEs are relocated to the global level, where redundant short FFT operations are eliminated. The remaining operation within the PEs is now a simple element-wise multiply-add. After a graph transform, the structure of the SFG kernel is recognized as a set of parallel small convolutions. If we use the short FFT to perform these short convolutions, we come to our final realization of the long convolution algorithm. The computational complexity of this realization is close to the optimum for convolutions, that is, script O sign (N log N). Our approach is thus achieving this N log N - low without having to implement large-size FFTs. We use, instead, small FFT blocks. The advantage is that small FFT transforms are commercially available, and that they can even be implemented in single-chip VLSI architectures. Our final SFG is three dimensional and can be mapped efficiently onto prototype architectures or dedicated VLSI processors. We demonstrate the procedure in the paper by a design example: the implementation of a prototype convolution architecture that we designed for a real-time radar imaging system

Factored orthogonal matrix-vector multiplication with applications to parallel and adaptive eigenfiltering and SVD

A novel algorithm is presented for adaptive eigenfiltering and for updating the singular value decomposition (SVD). It is an improvement upon an earlier developed Jacobi-type SVD updating algorithm, where now the exact orthogonality of the matrix of singular vectors/eigenvectors is guaranteed by storing a minimal factorization. This orthogonality property is known to be crucial for the numerical stability of the overall algorithm. The factored approach leads to a triangular array of rotation cells, implementing an orthogonal matrix - vector multiplication, and a novel array for SVD updating. Both arrays can be built up of CORDIC processors since the algorithms make exclusive use of orthogonal plan..

Deprettere, “Azimuth and elevation computation in high resolution DOA estimation

ABSTRACT In this paper, we discuss a number of high-resolution direction finding methods for determining the two-dimensional directions of arrival of a number of plane waves, impinging on a sensor array. The array consists of triplets of sensors that are identical, as an extension of the 1D ESPRIT scenario to two dimensions. New algorithms are devised that yield the correct parameter pairs while avoiding an extensive search over the two separate one-dimensional parameter sets