Waves vs Stochastic Signal Processing

Waves is an interactive environment for exploring graphical solutions to partial differential equations. Waves currently consists of three activities that explore Fourier series as well as series solutions to the heat and wave equations. Fourier is a tool for plotting a Fourier series that best approximates a periodic function. Diffusion plots solutions to the one-dimensional heat equation in space and animates the time evolution. Waves plots solutions to the one-dimensional wave equation in space and allows. In each of these activities you can specify the appropriate boundary and/or initial conditions. The app contains built-in examples as well as the option to save your work for future analysis. You can use Waves for homework, in-class activities or a new research project.

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.