Nonuniform sequential sampling for signal analysis

New electronic technologies for signal analysis raise the possibility of sampling very rapidly, with a time-varying density, and determining empirically both the sampling rate and the window width as the signal evolves in time. These opportunities also point to the possibility of sequentially sampling in a time-varying way in more traditional problems. Motivated by these ideas, we establish a sampling formula, valid in cases where both sampling rate and window width may be varied. The formula states that, in terms of the ways in which these quantities should alter with time, optimal performance is achieved when the window width is inversely proportional to squared sampling rate, and sampling rate is directly proportional to squared bias.