By Jose Maria Giron-Sierra
This is the 3rd quantity in a trilogy on glossy sign Processing. the 3 books offer a concise exposition of sign processing subject matters, and a advisor to help person functional exploration in line with MATLAB programs.
This publication comprises MATLAB codes to demonstrate all of the major steps of the idea, supplying a self-contained advisor appropriate for autonomous examine. The code is embedded within the textual content, aiding readers to place into perform the information and techniques discussed.
The ebook basically specializes in filter out banks, wavelets, and pictures. whereas the Fourier remodel is enough for periodic signs, wavelets are greater for different circumstances, comparable to short-duration indications: bursts, spikes, tweets, lung sounds, and so forth. either Fourier and wavelet transforms decompose signs into elements. additional, either also are invertible, so the unique signs will be recovered from their parts. Compressed sensing has emerged as a promising concept. one of many meant functions is networked units or sensors, that are now changing into a fact; therefore, this subject is additionally addressed. a variety of experiments that show snapshot denoising functions also are integrated. within the curiosity of reader-friendliness, the longer courses were grouped in an appendix; additional, a moment appendix on optimization has been further to complement the content material of the final chapter.
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Additional info for Digital Signal Processing with Matlab Examples, Volume 3 Model-Based Actions and Sparse Representation
The body falls vertically. The radar is placed a distance L from the body vertical. The radar measures the distance y from the radar to the body. Body state variables are chosen such that x1 is altitude, x2 is velocity, and x3 is the ballistic coefficient. 148) Fig. 22 Falling body example g y x1 L 44 1 Kalman Filter, Particle Filter and Other Bayesian Filters where ρ is air density and k is a constant. 81 m/s2 is gravity acceleration. 150) Notice the two nonlinearities of the example: the drag, and the square root.
99) This last expression could be interpreted as a white noise generator, departing from the sequence y(n). In this case, it is a whitening filter. 4 Some Connections The Kalman filter is connected with other topics, mainly because it is a recursive procedure to minimize a quadratic criterion. 101) The equations above are a particular case of the Gauss-Markov model for A = I , B = 0, C = d(n)T , w(n) = 0. 104) Notice that the equations above are the same already obtained for least squares recursive parameter identification (see the section on parameter identification in Chap.
Then there are not matrix inversions, only scalar operations. This is called sequential processing. See  for details of numerical aspects of Kalman filtering. Several chapters of  are devoted to different mechanizations of the Kalman filter. 6 Information Filter Some difficulties could appear with the initialization of variables in the Kalman filter. For instance, having no knowledge of state error covariance could lead to suppose large or infinite values as starting point. The consequence could be an undetermined value of K, (∞/∞).
Digital Signal Processing with Matlab Examples, Volume 3 Model-Based Actions and Sparse Representation by Jose Maria Giron-Sierra