Digital filter models for media having linear with frequency loss characteristics

Linear with frequency acoustic loss characteristics have been observed for soft biological tissue when probed with diagnostic ultrasound and for Plexiglas when used for underwater applications. Two digital filter models are described that exhibit this linear characteristic. The first filter model, designed using a frequency sampling technique, produces a symmetric unit sample response and a linear with frequency phase characteristic. Several features of this linear phase model, however, are found to be incompatible with the physical mechanisms producing the loss. Upon resolving these incompatibilities, a second filter model is obtained which has a minimum phase transfer function. Experimental verification, using Plexiglas as an acoustic propagation medium, demonstrates the superiority of the minimum phase model for describing the physical mechanisms which produce a linear with frequency loss characteristic.