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Although they do not belong to a very well defined class of signals, transient signals are found in many practical fields (from biological signals to signals used in telecommunication systems), so the development of robust and efficient tools for their analysis is an important objective in signal processing. In particular, this work is focused mainly on solving some signal analysis problems raised by the ultrasonic investigation of water in pipes. However, this applicative context is used only as a basis for developing generic tools that can find their usefulness in various other applications. The book addresses the issue of (transient) signal analysis from the perspective of the phase space recurrence concept, borrowed from dynamical systems theory. It shows that recurrence plot analysis brings into the field of signal processing two important concepts: vector samples, and recurrence. The use of these concepts allowed us to generalize and extend well-known signal processing tools, as well as to build signal representations that proved to be useful in various tasks related to transient signal detection and characterization.