FFT-ESPRIT: a kernel-based subspace estimator for frequency
super-resolution at quasi-linear time complexity
Abstract
We introduce two FFT-based ESPRIT algorithms for line spectral
estimation which have lower time complexities than the original ESPRIT
algorithm’s O(N^3). The preferred method, named FFT-ESPRIT, can be
characterized as being a kernel-based subspace estimator that achieves
super-resolution at O(N log N) for frequency estimates. First, we
demonstrate two estimations of the signal subspace via an integral
transformation on the row space of the data matrix and the data matrix
itself. The subspace-based methods are approximate in nature, and yet
perturbation bounds reveal a noise regime in which FFT-ESPRIT exceeds
ESPRIT’s performance. We demonstrate the behavior of the algorithm
across different SNR regimes and show that the estimated signal subspace
is statistically efficient. Numerical simulations show that FFT-ESPRIT
is more robust than the ESPRIT algorithm at the very low SNRs, and has a
nearly identical performance as ESPRIT at higher SNRs.