Written using clear and accessible language, this text provides detailed coverage of the core mathematical concepts underpinning signal processing. All the core areas of mathematics are covered, including generalized inverses, singular value decomposition, function representation, and optimization, with detailed explanations of how basic concepts in these areas underpin the methods used to perform signal processing tasks. A particular emphasis is placed on the practical applications of signal processing, with numerous in-text practice questions and real-world examples illustrating key concepts, and MATLAB programs with accompanying graphical representations providing all the necessary computational background. This is an ideal text for graduate students taking courses in signal processing and mathematical methods, or those who want to establish a firm foundation in these areas before progressing to more advanced study.

If you understand basic mathematics and know how to program with Python, you’re ready to dive into signal processing. While most resources start with theory to teach this complex subject, this practical book introduces techniques by showing you how they’re applied in the real world. In the first chapter alone, you’ll be able to decompose a sound into its harmonics, modify the harmonics, and generate new sounds. Author Allen Downey explains techniques such as spectral decomposition, filtering, convolution, and the Fast Fourier Transform. This book also provides exercises and code examples to help you understand the material. You’ll explore: Periodic signals and their spectrums Harmonic structure of simple waveforms Chirps and other sounds whose spectrum changes over time Noise signals and natural sources of noise The autocorrelation function for estimating pitch The discrete cosine transform (DCT) for compression The Fast Fourier Transform for spectral analysis Relating operations in time to filters in the frequency domain Linear time-invariant (LTI) system theory Amplitude modulation (AM) used in radio Other books in this series include Think Stats and Think Bayes, also by Allen Downey.

Digital Signal Processing 101: Everything You Need to Know to Get Started provides a basic tutorial on digital signal processing (DSP). Beginning with discussions of numerical representation and complex numbers and exponentials, it goes on to explain difficult concepts such as sampling, aliasing, imaginary numbers, and frequency response. It does so using easy-to-understand examples and a minimum of mathematics. In addition, there is an overview of the DSP functions and implementation used in several DSP-intensive fields or applications, from error correction to CDMA mobile communication to airborne radar systems. This book is intended for those who have absolutely no previous experience with DSP, but are comfortable with high-school-level math skills. It is also for those who work in or provide components for industries that are made possible by DSP. Sample industries include wireless mobile phone and infrastructure equipment, broadcast and cable video, DSL modems, satellite communications, medical imaging, audio, radar, sonar, surveillance, and electrical motor control. - Dismayed when presented with a mass of equations as an explanation of DSP? This is the book for you! - Clear examples and a non-mathematical approach gets you up to speed with DSP - Includes an overview of the DSP functions and implementation used in typical DSP-intensive applications, including error correction, CDMA mobile communication, and radar systems

The summer school held in Portovenere followed a tutorial format with the purpose of familiarizing postdoctoral or postgraduate students in the basic theories and up-to-date applications of present knowledge. Although, from a teaching point of view, a certain areount of overlapping is always useful, in order to avoid excessive duplication direct contact between lecturers expert in the same subject was encouraged during the preparation phase. In recent years computer facilities and theoretical implementa tion have considerably increased the possibility of solving problems relating to signal detection in noise. Any type of communication may take advantage of signal processing principles, including any type of physical measurement that can be considered as a non-semantic and/or quasi-semantic communication. Since signal processing techniques are common to many branches of science (telecommunications, radar, sonar, seismology, geophysics, nuclear research, space research and others), the advanced and sophisticated levels reached singularly in anyone of them could be used to the advantage of the others. In particular, underwater acoustics is a discipline which, to some extent, represents a practical general model that has permitted the development of signal processing techniques suitable to meet data reduction and interpretation needs of other branches of science. This ASI consequently underlined the inter-disciplinarity of signal proces sing in order that the principles of outstanding methods developed in one field may be adapted to others.

This comprehensive and engaging textbook introduces the basic principles and techniques of signal processing, from the fundamental ideas of signals and systems theory to real-world applications. Students are introduced to the powerful foundations of modern signal processing, including the basic geometry of Hilbert space, the mathematics of Fourier transforms, and essentials of sampling, interpolation, approximation and compression The authors discuss real-world issues and hurdles to using these tools, and ways of adapting them to overcome problems of finiteness and localization, the limitations of uncertainty, and computational costs. It includes over 160 homework problems and over 220 worked examples, specifically designed to test and expand students' understanding of the fundamentals of signal processing, and is accompanied by extensive online materials designed to aid learning, including Mathematica® resources and interactive demonstrations.

Signal Processing for Neuroscientists introduces analysis techniques primarily aimed at neuroscientists and biomedical engineering students with a reasonable but modest background in mathematics, physics, and computer programming. The focus of this text is on what can be considered the 'golden trio' in the signal processing field: averaging, Fourier analysis, and filtering. Techniques such as convolution, correlation, coherence, and wavelet analysis are considered in the context of time and frequency domain analysis. The whole spectrum of signal analysis is covered, ranging from data acquisition to data processing; and from the mathematical background of the analysis to the practical application of processing algorithms. Overall, the approach to the mathematics is informal with a focus on basic understanding of the methods and their interrelationships rather than detailed proofs or derivations. One of the principle goals is to provide the reader with the background required to understand the principles of commercially available analyses software, and to allow him/her to construct his/her own analysis tools in an environment such as MATLAB®. - Multiple color illustrations are integrated in the text - Includes an introduction to biomedical signals, noise characteristics, and recording techniques - Basics and background for more advanced topics can be found in extensive notes and appendices - A Companion Website hosts the MATLAB scripts and several data files: http://www.elsevierdirect.com/companion.jsp?ISBN=9780123708670

Develops mathematical and probabilistic tools needed to give rigorous derivations and applications of fundamental results in signal processing theory.