Electroencephalogram (EEG) spectral analysis quantifies the amount of rhythmic (or oscillatory) activity of different frequency in EEGs. Based on numerous studies that reported significant relationship between the EEG spectrum and human behavior, cognitive state, or mental illnesses, EEG spectral analysis is now accepted as one of the principal analysis methods in the field of neuroscience. Despite the tremendous amount of research related to its usefulness, EEG spectral analysis still exhibits inconsistent results among studies. This might be partly because of the various methodological decisions the researchers have to make during EEG spectral analysis. Indeed, there is no standardized analysis procedure. In this chapter, we cover some background principles of spectral analysis and introduce important issues that researchers must consider during EEG spectral analysis.

EEG Spectral Analysis

CORDIC-based VLSI architecture for real time implementation of flat top window

Two different window function families, namely, the first-order Bessel (I/sub 1/-cosh) family and raised-cosine family, which have variable parameters and hence make them flexible in digital spectrum analysis applications, are considered. Closed-form expressions are obtained which facilitate the tradeoffs between record length, spectral resolution, leakage suppression, bandwidth, etc. Simple expressions relating to mainlobe width and maximum sidelobe level are given for the two families considered. The results are compared to those obtained by J.F. Kaiser and R.W. Schafer (1980) in the case of zeroth-order Bessel (I/sub 0/-sinh) family. >

Variable parameter window families for digital spectral analysis

Images of an object embedded in an inhomogeneous medium are shown to contain speckle artefacts. The efficacy of a speckle processing technique called 'shift-and-add' for removing these artefacts is investigated. Shift-and-add is known to be applicable to any object which is dominated by a bright isolated point scatterer. This scatterer is called the 'reference'. Evidence that certain naturally occurring biological structures are capable of acting as a reference is presented. It is shown that an idealised version of shift-and-add, in conjunction with Fourier imaging, provides an approximate method for imaging an arbitrary object. Experimental results are reported which show that under most circumstances shift-and-add is able to reduce artefacts caused by multiple scattering. When the object is not dominated by point scatterers the shift-and-add image contains a significant 'ghosting' artefact. A theoretical model which accounts for this artefact is proposed and verified by simulation. Several extensions of shift-and-add are reported which allow the artefacts to be reduced and so allow an appreciably larger class of objects to be imaged. In particular, most objects dominated by several bright point scatterers can be reconstructed. This is verified experimentally for a simple object embedded in animal tissue. Additionally, a wide class of piecewise-constant extended objects can be reconstructed. One dimensional simUlations are presented to support this conclusion. A generalised shift-and-add prinCiple, which in theory allows arbitrary objects to be reconstructed, is proposed. It is shown that, in practice, the class of objects which can be reconstructed by the extensions to shift-and-add introduced in this thesis is considerably wider than that which can be successfully imaged by previously reported versions of shift-and-add.

Imaging in a Distorting Medium

Ternary sequences have been searched earlier with good merit factor or alternatively good discrimination as the search criterion. When one of these measures is a search criterion, the other measure takes generally a poor value. As both of them are quantifications of the abstract notion of a sequence with peaky autocorrelation, it is better to look for sequences with good values of merit factor and discrimination simultaneously, without optimizing either measure. This is called Simonization. Simonized ternary sequences are listed.

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Simonization for signal design

A set of windows, whose normalised main lobe widths fall between those of Hamming and the sum-cosine window, are developed. The windows are compared with Kaiser's near optimum zeroth-order Bessel windows. The results show that the new windows yield 4 to 9 dB improvement in the first sidelobe gain, and the improvement in maximum sidelobe gain varies from 2.8 to -0.85 dB, compared with that of Kaiser windows. The energy in the main lobe of Kaiser windows is at most 0.005% larger than that of the new windows. The distinct advantage of the windows is their very simple form, similar to that of a Hamming window.

Synthesis of windows from raised-cosine pulse

The parameters of various windows have been determined and the performance of the truncated Taylor family, the raisedcosine family, Kaiser's modified zeroth-order Bessel family, sum-cosine and Blackman windows have been compared.

V.U. Reddy

Papers

Synthesis of windows from raised-cosine pulse

Performance comparison of data windows