Abstract: Higher-order Statistics (HOS), also known as
cumulants, cross moments and their frequency domain counterparts,
known as poly spectra have emerged as a powerful signal processing
tool for the synthesis and analysis of signals and systems. Algorithms
used for the computation of cross moments are computationally
intensive and require high computational speed for real-time
applications. For efficiency and high speed, it is often advantageous
to realize computation intensive algorithms in hardware. A promising
solution that combines high flexibility together with the speed of a
traditional hardware is Field Programmable Gate Array (FPGA). In
this paper, we present FPGA-based parallel architecture for the
computation of third-order cross moments. The proposed design is
coded in Very High Speed Integrated Circuit (VHSIC) Hardware
Description Language (VHDL) and functionally verified by
implementing it on Xilinx Spartan-3 XC3S2000FG900-4 FPGA.
Implementation results are presented and it shows that the proposed
design can operate at a maximum frequency of 86.618 MHz.
Abstract: This paper deals with the localization of the wideband sources. We develop a new approach for estimating the wide band sources parameters. This method is based on the high order statistics of the recorded data in order to eliminate the Gaussian components from the signals received on the various hydrophones.In fact the noise of sea bottom is regarded as being Gaussian. Thanks to the coherent signal subspace algorithm based on the cumulant matrix of the received data instead of the cross-spectral matrix the wideband correlated sources are perfectly located in the very noisy environment. We demonstrate the performance of the proposed algorithm on the real data recorded during an underwater acoustics experiments.
Abstract: In this paper we present a technique to speed up
ICA based on the idea of reducing the dimensionality of the data
set preserving the quality of the results. In particular we refer to
FastICA algorithm which uses the Kurtosis as statistical property
to be maximized. By performing a particular Johnson-Lindenstrauss
like projection of the data set, we find the minimum dimensionality
reduction rate ¤ü, defined as the ratio between the size k of the reduced
space and the original one d, which guarantees a narrow confidence
interval of such estimator with high confidence level. The derived
dimensionality reduction rate depends on a system control parameter
β easily computed a priori on the basis of the observations only.
Extensive simulations have been done on different sets of real world
signals. They show that actually the dimensionality reduction is very
high, it preserves the quality of the decomposition and impressively
speeds up FastICA. On the other hand, a set of signals, on which the
estimated reduction rate is greater than 1, exhibits bad decomposition
results if reduced, thus validating the reliability of the parameter β.
We are confident that our method will lead to a better approach to
real time applications.