This thesis focuses on the statistics of natural images. The first question that is to be answered is: what are natural images and why do we study them. We start with our definition, and then discuss the properties and uses of natural images. An image is a projection of an environment, and natural images are those that are taken from a natural environment, i.e., an environment that is commonly encountered by a particular organism. This means that these images represent the natural visual input (natural stimulus) of an eye. In general, images may include optical information extending over space, time (time-varying images), as well as wavelength (colour images). In this thesis, however, we restrict ourselves to images of light intensity (black and white images) that either extend exclusively over space (still images) or exclusively over time (time series). The motivation for investigating natural images is to gain a better understanding of neural processing in visual systems. Natural images and visual processing in biological systems are linked by the hypothesis that evolution has optimised visual systems to process natural stimuli. The analysis of the optimal performance of biological visual systems may inspire the building of artificial visual systems.

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1=f noise and statistically self-similar processes such as fractional Brownian motion (fBm) are vital for modeling numerous real-world phenomena, from network traffic to DNA to the stock market. Although several algorithms exist for synthesizing discrete-time samples of a 1=f process, these algorithms are inexact, meaning that the covariance of the synthesized processes can deviate significantly from that of a true 1=f process. However, the Fast Fourier Transform (FFT) can be used to exactly and efficiently synthesize such processes in O(N log N) operations for a length-N signal. Strangely enough, the key is to apply the FFT to match the target process's covariance structure, not its frequency spectrum. In this paper, we prove that this FFT-based synthesis is exact not only for 1=f processes such as fBm, but also for a wide class of long-range dependent processes. Leveraging the flexibility of the FFT approach, we develop new models for processes that exhibit one type of fBm scaling be...

The low-frequency sinusoidal oscillator (LFO) is ubiquitous in effect design. What we seek is high computational efficiency and high signal purity in an algorithmic approach to real-time sinusoid generation. This section is presented more as a cookbook than the others because for the oscillator topologies that we analyze, each has distinct advantages; that is to say, each is useful. We offer the following implementation options: 1) Direct form

A model is presented for the early (retinal) stages of temporal processing of light inputs in the visual system. The model consists of a sequence of three adaptation processes, with two instantaneous nonlinearities in between. The three adaptation processes are, in order of processing of the light input: a divisive light adaptation, a subtractive light adaptation, and a contrast gain control. Divisive light adaptation is modeled by a photopigment depletion process, followed by two further gain controls. The first of these is a fast feedback loop with square-root behavior, the second a slow feedback loop with logarithm-like behavior. This can explain several aspects of the temporal behavior of photoreceptor outputs. Subtractive light adaptation is modeled by a fractional differentiation, and can explain the attenuation of low frequencies observed in ganglion cell responses. Contrast gain control in the model is fast (Victor, 1987), and can explain the decreased detectability of test signals that are superimposed on dynamic backgrounds.

In this paper, we seek to evaluate the performance of a 60 GHz WLAN system taking into account RF circuitry imperfections and hardware requirements for various modulation techniques. A model of an RF frontend is developed, including physical imperfections of the circuitry such as power amplifier (PA) nonlinearity and voltage controlled oscillator VCO phase noise. Given the RF front-end model, several modulation techniques such as Orthogonal Frequency Division Multiplexing (OFDM) and Continuous Phase Modulation (CPM) are considered. The evaluation of the system performance in terms of bit error rate allows a better understanding of physical circuitry limitations, and optimal modulation parameters as well as circuit design recommendations can be derived. Keywords OFDM, CPM, 60 GHz, Power Amplifier, Phase noise.

Recent analyses of serial correlations in cognitive tasks have provided preliminary evidence for the presence of a particular form of long-range serial dependence known as 1/f noise. It has been argued that long-range dependence has been largely ignored by mainstream cognitive psychology even though it accounts for a substantial proportion of variability in behavior (e.g., Gilden, 1997, 2001). In this article, we discuss the defining characteristics of long-range dependence and argue that claims about its presence need to be evaluated by testing against the alternative hypothesis of short-range dependence. For the data from three experiments, we accomplish such tests with autoregressive fractionally-integrated moving average time series modeling. We find that long-range serial dependence in these experiments can be explained by any of several mechanisms, including mixtures of a small number of short-range processes. Estimation and Interpretation of 1/f α Noise 3 Estimation and Interpretation of 1/f α Noise in Human Cognition The vast majority of experiments in cognitive psychology discard any information about the order in which empirical observations are obtained. The implicit assumption of this