Topological Signal Processing [electronic resource] / by Michael Robinson.Material type: TextLanguage: English Series: Mathematical Engineering: Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2014Description: XVI, 208 p. 134 illus. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783642361043Subject(s): Engineering | Mathematics | Computer science | Topology | Telecommunication | Engineering | Signal, Image and Speech Processing | Topology | Communications Engineering, Networks | Computational Science and Engineering | Information and Communication, CircuitsAdditional physical formats: Printed edition:: No titleDDC classification: 621.382 LOC classification: TK5102.9TA1637-1638TK7882.S65Online resources: Click here to access online
Introduction and informal discussion -- Parametrization -- Signals -- Detection -- Transforms -- Noise.
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.