Analysis of MUSIC and ESPRIT frequency estimates for sinusoidal signals with lowpass envelopes

In this correspondence, the MUSIC and ESPRIT frequency estimates of sinusoidal signals with lowpass envelopes are analyzed. To achieve computational simplicity, the frequency estimation is conducted as if the signal had a constant amplitude. The aim of the correspondence is to analyze the degradation of performance induced by the aforementioned mismodeling. Unified expressions for the bias and variances of the MUSIC and ESPRIT frequency estimators are derived under the hypothesis of small bandwidth of the signal envelope. Numerical simulations illustrate the agreement between theoretical and empirical results and study the influence of the envelope bandwidth on the frequency estimation performance.