1. A method for extracting information from data representing a signal, comprising: receiving, by a processing device, a set of data from a sensor, the set of data comprising a plurality of measurements of the signal generated at a first sampling rate; randomly selecting, by the processing device, a subset of the plurality of measurements, the subset having fewer members than the set of data; determining a value for each of a plurality of amplitude variables, each amplitude variable corresponding to a particular frequency component in a set of frequency components, the set of frequency components having a greater number of members than the subset of the plurality of measurements, by: deriving an underdetermined system of equations based on: a selected basis function; the subset of the plurality of measurements; and the plurality of amplitude variables and corresponding frequency components; solving the underdetermined system of equations to determine the value for each amplitude variable using a non-linear optimization technique to minimize an L 1 norm of the set of frequency components, wherein the value of each amplitude variable identifies an amplitude of the corresponding frequency component in the signal; and storing frequency component information including the value of at least some of the amplitude variables and corresponding frequency components in a storage medium.