Technical Report No. 2013-2 : Utilizing Incommensurate Sampling Rates to Layer Audio Files for Use with Variable Bandwidth (AU-CAS-MathStats)

In the study of Sampling Theory, the Nyquist-Shannon sampling theorem, proved in the first half of the 20th century, showed that a bandwidth limited signal could be exactly reconstructed when sampled at an appropriate rate. This is the basis for digital representation of audio files (CDs), since human hearing is bandwidth limited. Dr. Stephen Casey proved in his recent research that such a signal, sampled at multiple specifically chosen incommensurate rates, can also be exactly reconstructed. This research takes his theorem and applies it to a regularly sampled audio signal to construct new data sets, sampled at incommensurate rates. The signal can be reconstructed from one or more of these sets, with quality increasing as more data sets are included. Each data set can buffer individually when streamed over a broadband connection. Thus, when bandwidth changes the audio player can add or drop a data set without having to completely re-buffer.