Spectrum estimation using frequency shifting and decimation

Abstract

Parametric spectral estimation techniques are widely used to estimate the parameters of sums of complex sinusoids corrupted by noise. In this work, we show that the numerical stability of the estimated frequencies not only depends on the size of the amplitudes associated to the real frequencies, but also to the distance among frequencies. Therefore, for closely spaced frequencies, the estimates are vulnerable to large deviate from their true values. To overcome this problem we propose a strategy to artificially increase the frequency separation by downsampling the base band equivalent of the noisy signal before applying a spectral estimation technique. This methodology significantly improves the estimation performance especially in the low signal to noise ratio regime. The performance of the technique is assessed in terms of the root mean square error and it is compared to results obtained in previous publications.