Signal processing is the discipline of extracting information from collections of measurements. To be effective, the measurements
must be organized and then filtered, detected, or transformed to expose the desired information. Distortions caused by uncertainty,
noise, and clutter degrade the performance of practical signal processing systems.In aggressively uncertain situations, the
full truth about an underlying signal cannot be known. This book develops the theory and practice of signal processing systems
for these situations that extract useful, qualitative information using the mathematics of topology -- the study of spaces
under continuous transformations. Since the collection of continuous transformations is large and varied, tools which are
topologically-motivated are automatically insensitive to substantial distortion. The target audience comprises practitioners
as well as researchers, but the book may also be beneficial for graduate students.