1. A signal processing method, comprising: sampling an analog signal, which has a spectral density defining one or more bands, to produce a digitized signal; expressing a spectral transform of the digitized signal as a matrix multiplied by a vector, wherein the vector comprises multiple elements that represent the spectral density of the analog signal as a function of frequency within respective spectral slices; determining indices of a subset of the elements of the vector in which the spectral density is concentrated; and reconstructing the analog signal from the digitized signal using the subset of the elements of the vector and a corresponding subset of columns of the matrix having the indices.