Signals and Systems: Theory and Applications

[From the Preface} This is a signals and systems textbook with a difference: Engineering applications of signals and systems are integrated into the presentation as equal partners with concepts and mathematical models, instead of just presenting the concepts and models and leaving the student to wonder how it all relates to engineering.\nThe first six chapters of this textbook cover the usual basic concepts of continuous-time signals and systems, including the Laplace and Fourier transforms. Chapters 7 and 8 present the discrete-time version of Chapters 1–6, emphasizing the similarities and analogies, and often using continuous-time results to derive discrete-time results. The two chapters serve to introduce the reader to the world of discrete-time signals and systems. Concepts highlighted in Chapters 1–8 include: compensator feedback configuration (Ch. 4); energy spectral density, group delay, expanded coverage of exponential Fourier series (Ch. 5); filtering of images, Hilbert transform, single-sideband (SSB), zero and first-order hold interpolation (Ch. 6); the Cooley-Tukey FFT (Ch. 7); bilateral z-transform and use for non-minimum-phase deconvolution (Ch. 8). Chapter 9 covers the usual concepts of discrete-time signal processing, including data windows, FIR and IIR filter design, multirate signal processing, and auto-correlation and crosscorrelation. It also includes some nontraditional concepts, including spectrograms, application of multirate signal processing, and the musical circle of fifths to audio signal processing, and some biomedical applications of autocorrelation and cross-correlation. Chapter 10 covers image processing, discrete-time wavelets (including the Smith-Barnwell condition and the Haar and Daubechies discrete-time wavelet expansions), and an introduction to compressed sensing. This is the first sophomore-junior level textbook the authors are aware of that allows students to apply compressed sensing concepts. Applications include: image denoising using 2-D filtering; image denoising using thresholding and shrinkage of image wavelet transforms; image deconvolution using Wiener filters; “valid” image deconvolution using ISTA; image inpainting; tomography and the projection-slice theorem, and image reconstruction from partial knowledge of 2-D DFT values. Problems allow students to apply these techniques to actual images and learn by doing, not by only reading.