A computer-implemented method for characterising data, comprising sensor data, spatial signals, or time-varying measurement values, dependent on at least one variable, by sparse sampling, in terms of a family of functions φ k having a domain corresponding to said at least one variable and a codomain corresponding to said data, said family of functions sharing a common construction parameterized by at least one parameter k, wherein values φ k (ξ (j)) of said family of functions satisfy a recurrence relation that can be expressed as a generalized eigenvalue relation at a finite sequence of regularly spaced sampling points ξ (j), j = 0, 1, 2,..., 2 t - 1, the spacing being controlled by a magnifying factor r, wherein the data will be sampled; wherein the generalized eigenvalues λ 1,..., λ t of said generalized eigenvalue relation are the elements φ k ( i) evaluated at ξ when ξ = 0; the method comprising: - obtaining a finite sequence of measurements f j = f(ξ (j)), j = 0, 1, 2,..., 2 t - 1 of said data by sampling said data in said finite sequence of sampling points, said sampling being sparse sampling,, and - outputting a property which characterizes the data satisfying f j ≈ ∑ i = 1 t α i φ k i ξ j, j = 0, 1, 2,..., 2 t - 1 where the number of terms t, the support {k,...,k (t)}, and the nonzero coefficients α 1,...,α t are unknown, said outputting taking into account said finite sequence of measurements; wherein the method further comprises determining first sets of values K i, i = 1,..., t, of said at least one parameter k defining a subset of said family of functions, said determining making use of said recurrence relation satisfied in said finite sequence of sampling points by determining the generalized eigenvalues of said generalized eigenvalue relation, and wherein the method further comprises: - computing the coefficients α 1,...,α t from a linear system of equations defined by a Vandermonde matrix with said generalized eigenvalues as nodes and the measurements f j as the right-hand side; - further sampling said data in a further finite sequence of sampling points such that a location of said further finite sequence of sampling points is at least also determined by a value of an identification shift ρ, to obtain further measurements f j,ρ; - solving a linear system of equations defined by said Vandermonde matrix and the further measurements f j,ρ as the right-hand side and having as unknowns an expression involving said coefficients, values of said at least one parameter k, and said identification shift, obtained by applying said recurrence relation in said further sequence of sampling points; - using said computed coefficients α 1,..., α t to produce second sets of values K i,ρ of said at least one parameter k; and - uniquely determining said subset of said family of functions by calculating the intersections of said first sets of values K i and respective second sets of values K i,ρ corresponding to the same row index i. - obtaining a finite sequence of measurements f j = f(ξ (j)), j = 0, 1, 2,..., 2 t - 1 of said data by sampling said data in said finite sequence of sampling points, said sampling being sparse sampling,, and - outputting a property which characterizes the data satisfying f j ≈ ∑ i = 1 t α i φ k i ξ j, j = 0, 1, 2,..., 2 t - 1 where the number of terms t, the support {k,...,k (t)}, and the nonzero coefficients α 1,...,α t are unknown, said outputting taking into account said finite sequence of measurements; - computing the coefficients α 1,...,α t from a linear system of equations defined by a Vandermonde matrix with said generalized eigenvalues as nodes and the measurements f j as the right-hand side; - further sampling said data in a further finite sequence of sampling points such that a location of said further finite sequence of sampling points is at least also determined by a value of an identification shift ρ, to obtain further measurements f j,ρ; - solving a linear system of equations defined by said Vandermonde matrix and the further measurements f j,ρ as the right-hand side and having as unknowns an expression involving said coefficients, values of said at least one parameter k, and said identification shift, obtained by applying said recurrence relation in said further sequence of sampling points; - using said computed coefficients α 1,..., α t to produce second sets of values K i,ρ of said at least one parameter k; and - uniquely determining said subset of said family of functions by calculating the intersections of said first sets of values K i and respective second sets of values K i,ρ corresponding to the same row index i.