Frequency domain reconstruction of stochastically sampled signals based on compressive sensing
The field of compressed sensing (CS) has recently been gaining traction as a viable workaround to the Nyquist-Shannon sampling theorem (NSST). This allows highly accurate signal recovery from incomplete frequency information. In this paper, we investigate the ability of compressive sampling to recover the higher harmonics of a recorded guitar signal. Sampling is done in the temporal domain, and the reconstruction is performed in the frequency domain. It is shown that even when taking a small number of random samples corresponding to some underlying sub-Nyquist rate, the base frequency, including up to fifth-order harmonics, can be recovered. The performance of three algorithms, namely least absolute shrinkage and selection operator (LASSO), orthogonal matching pursuit (OMP), and smoothed ℓ0 norm (SL0) algorithm in terms of computation time and reconstruction error (cosine similarity) were investigated.