In audio for virtual and augmented reality systems it is often necessary to measure very large data sets. For example, HRTFs from different spatial angles, or spatial impulse responses in a room as function of angle or position, or even training sets for neural networks. This can result in a large number of measurements being required to collect the dataset with adequate fidelity. Even then compromises are often necessary to make the data set manageable. Sparse sampling is a technique that can overcome these limitations. Sparse Sampling allows one to sample the signal at apparently less than the Nyquist/Shannon limit of two times the highest frequency, without losing any signal fidelity. If some loss of fidelity is allowed the signal can be sampled at an even lower average rate. How can this be? The answer is that the effective information rate is actually lower than the highest frequency. The purpose of this tutorial is to give a (mostly) non-mathematical introduction to Sparse Sampling, and its application to audio for virtual and augmented reality systems. We will examine the difference between “Sparse” and “Dense” signals and define what is meant by “rate of innovation” and see how it relates to sample rate. We will then go on to see how we can create sparse signals either via transforms or filters to provide signals that can be sample at much lower rates. We will then show how some of these methods are already used in audio, and suggest other areas of application, such as measurements in audio for virtual and augmented reality systems, and parameter sets for neural networks. The tutorial will be accessible to everyone, you will not have to be an electronic engineer to understand the principles behind this alternative approach to sampling for audio for virtual and augmented reality systems.
