Download Signal Processing with Fractals: A Wavelet Based Approach by Gregory Wornell PDF

By Gregory Wornell

This paintings presents a consultant to wavelet-based sign processing with fractals. assurance contains wavelet conception and modifications, statistically self-similar signs, deterministically self-similar signs, fractal modulation and linear self-similar platforms.

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Typically, our observations are incomplete. Indeed, they will generally be t i m e - h t e d and resolution-limited. More generally, the observations may contain gaps, or there may be multiple observations. ' It is important to both recogruze and accommodate such measurement noise in any algorithms for 'Actually, the coexistence of l / f and white noises in electronic and optical systems is well documented. In electronic systems, for instance, the predominant noise is l / f noise at 60 Detection and Estimationwith Fractal Processes Chap.

There are many potential problems involving signal enhancement and restoration to which the resulting smoothing algorithms can be applied. For this signal estimation problem, we use a Bayesian framework to derive algorithms that are optimal with respect to a mean-square error criterion. 2. RMS Errors in the estimates of the signal parameters as a function of the SNR of the observations. The symbols associated with each y mark the actual empirical measurements;dashed lines are provided as visual aides only.

Still more specific results will be described when U$, = 0, corresponding to the case of noise-free observations. We may also assume, where necessary, that all m E :V are positive without loss of generality. Indeed, if, for example, m1 < 0, then we could define new parameters through the invertible transformation E step: As shown in Appendix C, this step reduces to estimating the noise and signal portions of the wavelet coefficient variances at each scale m E M using current estimates of the parameters $['l, k2['],and &;['l: where 5; = a; 52 = 0 2 p m ~ - 1 3=13 for which the observations correspond to positive scales M = {l,m* - m, + 1,..

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