Foundations of Signal Processing

Abstract

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. • Introduces students 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. • Discusses issues in real-world use of these tools such as effects of truncation and quantization, limitations on localization, and computational costs. • Includes over 160 homework problems and over 220 worked examples, specifically designed to test and expand students' understanding of the fundamentals of signal processing. • Accompanied by extensive online materials designed to aid learning, including Mathematica resources and interactive demonstrations.

How to Quantify Student’s Regularity?

“…By employing time domain [6,24] and frequency domain [21] techniques, we defined nine measures corresponding to regularity patterns on three dimensions: intra-day, intra-week and intra-course. Investigation of students' activities corresponding to low and high values of these measures illustrates their behaviour.…”

“…To use time domain methods we slice the time series into segments of the length of interest (e.g. day, week) and compare repeatability of the slices [6,24]. In particular, we use Jensen-Shannon divergence to analyse a histogram of a segmented signal [13].…”

A Comparative Study of Speech Compression using Different Transform Techniques

“…Since the speech files were of short duration, the entire signal was decomposed at once without framing, The wavelets used in this paper are Haar and Daubechies (db2, db4, db6, db8, db10) wavelets [15]. Global threshold and uniform quantization were applied the transform coefficients.…”

Multi-scale dynamics of glow discharge plasma through wavelets: Self-similar behavior to neutral turbulence and dissipation

“…A wavelet function is characterized by a translation parameter (a) and scale parameter (s) [10]. The wavelet transform of a signal decomposes it into components dependent upon both position and scale.…”

“…Being a local approach, it brings out the non-stationary nature of this dynamical system quite effectively [10]. We make use of both discrete and continuous wavelets to probe different aspects of the dynamics.…”