A flexible and computationally efficient method for spectral analysis of sinusoidal signals using the Basis Pursuit De-Noising (BPDN) is proposed. This method estimates a slotted Auto-Correlation Function (ACF) and computes the spectrum as the sparse representation of the ACF in a dictionary of cosine functions. Simulation results illustrate flexibility and effectiveness of the proposed method.

Let V(φ) be a shift invariant subspace of L2(R) with a Riesz or frame generator φ(t). We take φ(t) suitably so that the regular sampling expansion : f(t) = f(n)S(t-n) holds on V(φ). We then find conditions on the generator φ(t) and various bounds of the perturbation {δ n }n∈Z under which an irregular sampling expansion: f(t) = f(n+ δn)Sn(t) holds on V(φ). Some illustrating examples are also provided.

The paper obtains an algorithm to estimate the irregular sampling in wavelet subspaces. Compared to our former work on the problem, the new estimate is relaxed for some wavelet subspaces.