Fullband and subband implementations of FastICA algorithm for blind source separation

In signal processing, blind source separation is a very important problem encountered in many real-time applications. The uniqueness of the blind source separation problem is that it requires the recovery of independent signals from a set of observed mixed signals with no prior information available about the original signals. The radio waves emitted by mobile phones, the speech signals of people in the same room, and the electrical signals coming from different brain cells are some examples of the original signals and the sources generating them. When such signals are captured by microphones, sensors or other receivers they are mixed using different weights by each receiver. These observed mixed signals are our only available information for separation. The observed mixed signals appear completely noisy while the underlying independent signals are highly structured. The term "blind" signifies that there is very little information available to us about the original signals in the separation process.;The blind source separation problem can be addressed by various linear transformation techniques. All these methods require the observed data to be centered: i.e., of zero mean. The classical methods of finding a linear transformation of a random variable can be categorized into second order methods like Principal Component Analysis (PCA) and factor analysis and higher-order methods like projection pursuit, redundancy reduction and blind deconvolution. Independent component analysis is a recently developed and a very efficient linear transformation method for solving the blind source separation problem compared to other classical methods.;In this thesis, the concepts related to independent component analysis and its advantages over other classical linear transformation techniques are discussed. The objective of this thesis is to implement the Independent Component Analysis (ICA) algorithm of fast convergence (namely, FastICA) using the subband and the fullband approaches. This thesis also focuses on the real-time scenario of acoustic microphone path: i.e., the multipath representations of fullband and subband FastICA algorithms are implemented.;In the fullband FastICA, the observed mixed signals are directly fed to the FastICA algorithm to obtain the separated components. In the subband approach, the observed mixed signals are divided into four, eight and sixteen subbands using polyphase filtering and decimation. From the obtained subband mixed signals, a single subband each of the mixed signals are fed to the FastICA algorithm for separation of one subband each of the independent components. The processing required to obtain the fullband independent components from these separated subbands is determined. A comparison is made between the independent components blind separated using the fullband and the subband approaches of the FastICA algorithm.;The multipath representation involves a convolutive mixing process of the individual signals to obtain the observed mixed signals which are fed to the FastICA algorithm. Hence, this is a natural and a real-time process as seen in most applications. The multipath implementation of fullband and subband FastICA is performed as mentioned above and similar comparison is made.;The computational complexity of FastICA using the subband signals is much less than that of the FastICA using the fullband signals. The subband version of FastICA converges faster than the fullband FastICA. Simulation results show that the efficiency of the FastICA algorithm in terms of separation of independent components increases with the increasing number of subbands.;The various applications of independent component analysis methods to solve blind source separation problems observed in various fields are discussed.