Novel discrete orthogonal transforms are introduced in this paper, namely the unified complex Hadamard transforms. These transforms have elements confined to four elementary complex integer numbers which are generated based on the Walsh-Hadamard transform, using a single unifying mathematical formula. The generation of higher dimension transformation matrices is discussed in detail.

Family of unified complex Hadamard transforms

The pinned sine transform (PST) coder described is a practical approximation to the pinned KLT coder. The image is partitioned into two fields: a boundary field, which depends only on the coded block boundaries, and a pinned field, which vanishes at the boundaries and is subsequently sine transformed and compressed. The reconstructed image is continuous across the block boundaries and "blocking effects" are hardly visible. Simulation results are given for fixed and adaptive compression schemes with fair image quality at low bit rates down to 0.3 bits/pel.

A Pinned Sine Transform Image Coder

Publisher Summary This chapter focuses on fast discrete transforms. It discusses the theoretical bases of the various transforms, their basic properties, performance criteria, and various fast algorithmic implementations so that sufficient objective information is available for the user to make an informed choice. It reviews the theoretical aspects of unitary transforms. Unitary transforms have a preeminent position in the realm of discrete transforms, because they are easy to invert and they preserve energy. A discrete transform is not necessarily a unitary transform. The chapter concentrates only on unitary transforms and reviews the optimal Karhunen–Loeve transform (KLT). Some advantages of KLT are that it completely decorrelates the signal in the transform domain, minimizes the mean-square error (MSE) in bandwidth reduction or data compression, packs the most energy in the fewest number of transform coefficients, and minimizes the total representation entropy of the sequence that is linked to the rate-distortion criterion of transform performance. The chapter highlights the disadvantages of KLT as well. The suboptimal transforms are grouped into sinusoidal and nonsinusoidal transforms. The chapter reviews these transforms. The sinusoidal discrete transforms are suboptimal in terms of decorrelating the signal. They are, however, asymptotically equivalent to the KLT under some constraints of signal statistics. The chapter also discusses various performance criteria that form a basis for selecting a particular transform and the computational complexities of the various algorithms.

Fast Discrete Transforms

This work aims to analyze the EEG signals produced by facial gestures and eye movements called artifacts. Although these signals are considered contaminants in EEG signals used for medical diagnosis, these are observed in order to consider the possibility of using them as inputs for certain applications. As such, the project aims to observe distinct signal patterns in the EEG signals acquired for certain facial gestures as a preliminary work to facial gesture detection. Using the Emotiv Epoc Neuroheadset, the cross correlation between pairs of 14 channels for six facial gestures and their frequency response are compared. These facial gestures are blink, left wink, right wink, raise brow, smile, and clench. Particular channel pairs are found to be highly correlated for certain facial gestures and can be used as possible means of detecting these gestures. In the frequency domain, only the gestures smile and clench registered a distinctive frequency response among the other gestures. Moreover, the Emotiv Epoc neuroheadset paired with the Arduino Duemilanove board was found to be an effective tool as a controller for household appliances. Also, the neuroheadset was useful in developing an extended communication platform. As such not only does it prove to be a viable device for developing systems in aiding the physically-challenged, but also provides a glimpse of the potential advances in the field of Brain-Computer Interfaces.

A study on ocular and facial muscle artifacts in EEG signals for BCI applications

The applicability of the recursive Walsh-Hadamard transformation to FIR and IIR (finite- and infinite-impulse-response) filtering is investigated. It is shown that using a common structure for recursive transforms recently introduced by G. Peceli (1986), the usual frequency-domain FIR filtering problem can be easily converted into a Walsh sequency-domain filtering problem. It is also shown that a simple modification of this structure results in a possible alternative for IIR filter implementations. >

Digital filters based on recursive Walsh-Hadamard transformation

The purpose of this correspondence is to point out a number of significant references, in the area of Walsh-Fourier transform conversion, that were missed in a recent paper [1].

R. Kitai

Papers

Discrete Fourier transform via Walsh transform