7. Application examples

Finally, we present four examples of the use of time-frequency representations, in the fields of industrial research for the first two, military research for the third and geophysics for the last.

• In non-destructive ultrasonic testing of diffusive media, such as grained materials (cast irons...), fibrous materials (composites...)..., a frequently encountered problem is to distinguish between signals that may come from a reflection on an interface (of large dimensions compared with the wavelength of the ultrasound used), from diffusion by inclusions (of small dimensions compared with the wavelength of the ultrasound used), or from a crack (constituting a harmful defect). A special case is the detection of a crack emerging at the interface between two steels and perpendicular to it: in normal inspection, the crack head echo is confused with...