Many measurement tasks such as speaker polar pattern measurement, or PA coverage, require a large number of measurements to achieve accuracy due to the need to sample the measurement above the Nyquist/Shannon limit of two times the highest frequency. Sparse and Compressive Sampling allows one to sample the signal at apparently less than the Nyquist/Shannon limit of two times the highest frequency, this without losing any signal fidelity or even lower with some loss of accuracy! How can this be, is it black magic, or is it a beautiful science based method for achieving high accuracy with a few limited measurements?
The purpose of this presentation is to give a non-mathematical introduction to Sparse/Compressive Sampling and measurement. We will examine the difference between “Sparse” and “Dense” signals. We will 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 sampled at much lower rates. We will then show how some of these methods are already used in audio, and suggest other areas of application, in particular audio and acoustic measurements. Finally we will finish off by showing how a commonly used audio system can be considered to be a form of compressive sensing.