| dc.description.abstract | In system identification scenario, the linear approximation of the system modelled by its impulse response, is estimated in real time by gradient type Least Mean Square (LMS) or Recursive Least Squares (RLS) algorithms. In recent applications like acoustic echo cancellation, the order of the impulse response to be estimated is very high, and these traditional approaches are inefficient and real time implementation becomes difficult. Alternatively, the system is modelled by a set of shorter adaptive filters operating in parallel on subsampled signals. This approach, referred to as subband adaptive filtering, is expected to reduce not only the computational complexity but also to improve the convergence rate of the adaptive algorithm. But in practice, different subband adaptive algorithms have to be used to enhance the performance with respect to complexity, convergence rate and processing delay. A single subband adaptive filtering algorithm which outperforms the full band scheme in all applications is yet to be realized.
This thesis is intended to study the subband adaptive filtering techniques and explore the possibilities of better algorithms for performance improvement. Three different subband adaptive algorithms have been proposed and their performance have been verified through simulations. These algorithms have been applied to acoustic echo cancellation and EEG artefact minimization problems.
Details of the work
To start with, the fast FIR filtering scheme introduced by Mou and Duhamel has been generalized. The Perfect Reconstruction Filter Bank (PRFB) is used to model the linear FIR system. The structure offers efficient implementation with reduced arithmetic complexity. By using a PRFB with non adjacent filters non overlapping, many channel filters can be eliminated from the structure. This helps in reducing the complexity of the structure further, but introduces approximation in the model. The modelling error depends on the stop band attenuation of the filters of the PRFB. The error introduced due to approximation is tolerable
for applications like acoustic echo cancellation.
The filtered output of the modified generalized fast filtering structure is given by
(formula)
where, Pk(z) is the main channel output, Pk,, k+1 (z) is the output of auxiliary channel filters at the reduced rate, Gk (z) is the kth synthesis filter and M the number of channels in the PRFB. An adaptation scheme is developed for adapting the main channel filters. Auxiliary channel filters are derived from main channel filters.
Secondly, the aliasing problem of the classical structure is reduced without using the cross filters. Aliasing components in the estimated signal results in very poor steady state performance in the classical structure. Attempts to eliminate the aliasing have reduced the computation gain margin and the convergence rate. Any attempt to estimate the subband reference signals from the aliased subband input signals results in aliasing. The analysis filter Hk(z) having the following antialiasing property
(formula)
can avoid aliasing in the input subband signal. The asymmetry of the frequency response prevents the use of real analysis filters. In the investigation presented in this thesis, complex analysis filters and real'synthesis filters are used in the classical structure, to reduce the aliasing errors and to achieve superior convergence rate.
PRFB is traditionally used in implementing Interpolated FIR (IFIR) structure. These filters may not be ideal for processing an input signal for an adaptive algorithm. As third contribution, the IFIR structure is modified using discrete finite frames. The model of an FIR filter s is given by Fc, with c = Hs. The columns of the matrix F forms a frame with rows of H as its dual frame. The matrix elements can be arbitrary except that the transformation should be implementable as a filter bank. This freedom is used to optimize the filter bank, with the knowledge of the input statistics, for initial convergence rate enhancement .
Next, the proposed subband adaptive algorithms are applied to acoustic echo cancellation problem with realistic parameters. Speech input and sufficiently long Room Impulse Response (RIR) are used in the simulations. The Echo Return Loss Enhancement (ERLE)and the steady state error spectrum are used as performance measures to compare these algorithms with the full band scheme and other representative subband implementations.
Finally, Subband adaptive algorithm is used in minimization of EOG (Electrooculogram) artefacts from measured EEG (Electroencephalogram) signal. An IIR filterbank providing sufficient isolation between the frequency bands is used in the modified IFIR structure and this structure has been employed in the artefact minimization scheme. The estimation error in the high frequency range has been reduced and the output signal to noise ratio has been increased by a couple of dB over that of the fullband scheme.
Conclusions
Efforts to find elegant Subband adaptive filtering algorithms will continue in the future. However, in this thesis, the generalized filtering algorithm could offer gain in filtering complexity of the order of M/2 and reduced misadjustment . The complex classical scheme offered improved convergence rate, reduced misadjustment and computational gains of the order of M/4 . The modifications of the IFIR structure using discrete finite frames made it possible to eliminate the processing delay and enhance the convergence rate. Typical performance of the complex classical case for speech input in a realistic scenario (8 channel case), offers ERLE of more than 45dB. The subband approach to EOG artefact minimization in EEG signal was found to be superior to their fullband counterpart.
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