This authored monograph presents key aspects of signal processing analysis in the biomedical arena. Unlike wireless communication systems, biological entities produce signals with underlying nonlinear, chaotic nature that elude classification using the standard signal processing techniques, which have been developed over the past several decades for dealing primarily with standard communication systems. This book separates what is random from that which appears to be random, and yet is truly deterministic with random appearance. At its core, this work gives the reader a perspective on biomedical signals and the means to classify and process such signals. In particular, a review of random processes along with means to assess the behavior of random signals is also provided. The book also includes a general discussion of biological signals in order to demonstrate the inefficacy of the well-known techniques to correctly extract meaningful information from such signals. Finally, a thorough discussion of recently proposed signal processing tools and methods for addressing biological signals is included. The target audience primarily comprises researchers and expert practitioners but the book may also be beneficial for graduate students.