This book can be used as a textbook for undergraduate courses in Fourier analysis or applied mathematics, which covers Fourier series and orthogonal functions, Fourier and Laplace transforms and an introduction to complex variables. These topics are tied together through the application of the spectral analysis of analog and discrete signals. Its emphasis on applications makes it suitable for courses with students from different backgrounds. The textbook has been extensively class-tested over the past 10 years.