Stochastic Signal Processing vs Polynomial Regression

Speech, music, seismic vibrations, oil prices, and climate measurements are all examples of stochastic (random) signals. In this textbook—intended for individuals with prior training in introductory signal processing and introductory probability theory—we develop techniques to process such signals to extract useful information. We present case studies ranging from music to photographic images to oil prices to climate data to the motion of individual biomolecules. This textbook, as an interactive textbook ("iBook"), makes use of your device's ability to display dynamic information through films and animations and to hear the results of the techniques applied to music. At the end of every chapter there are homework problems ranging from easy to "olympic". We make use of your device's interactive capabilities to offer 59 laboratory experiments in signal processing. The experiments use the camera, the microphone, the speakers, and the graphical user interface. These experiments are not simulations; they are examples of real digital processing of signals in your device. In this time of at-home and online learning, this is the way to learn signal processing through study and experimentation.

Polynomial Regression is your calculator and, more importantly, learning tool. You will be able to: * Construct polynomials of up to 20 degrees from either real or complex roots. * Interpolate polynomials from points by Lagrange, Newton or Vandermonde methods and Quadratic or Cubic splines. * Perform Least Squares approximation by orthogonal projection, with or without QR factorization, or partial derivatives. * Learn about each of the algorithms with derivations, proofs, step by step demonstrations, and visual tools. * Have an option to enter data by either typing or tapping on XY plane, and save data sets between program runs.