Time delay estimate and sampling frequency
A colleague of mine has investigated time delay estimation using compressed sensing in this paper: http://vbn.aau.dk/en/publications/compressive-parameter-estimation-for-sparse-translationinvariant-signals-using-polar-interpolation(56d35506-d4ae-4296-9a36-7ec95b1160c7).html
You can find the accompanying Matlab code here: http://www.sparsesampling.com/cpe/