Browsing by Author "Duarte, Isabel M. P."
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- Accurate Spectral Estimation of Non-periodic Signals Based on Compressive SensingPublication . Duarte, Isabel M. P.; Vieira, José M. N.; Ferreira, Paulo J S G; Albuquerque, DanielIn this work we propose a method based on compressive sensing (CS) for estimating the spectrum of a signal written as a linear combination of a small number of sinusoids. In practice one deals with signals with finite-length and so the Fourier coefficients are not exactly sparse. Due to the leakage effect in the case where the frequency is not a multiple of the fundamental frequency of the DFT, the success of the traditional CS algorithms is limited. To overcome this problem our algorithm transform the DFT basis into a frame with a larger number of vectors, by inserting a small number of columns between some of the initial ones. The algorithm takes advantage of the compactness of the interpolation function that results from the ‘1 norm minimization of the Basis Pursuit (BP) and is based on the compressive sensing theory that allows us to acquire and represent sparse and compressible signals, using a much lower sampling rate than the Nyquist rate. Our method allow us to estimate the sinusoids amplitude, phase and frequency.
- Iterative Algorithm for High Resolution Frequency EstimationPublication . Duarte, Isabel M. P.; Vieira, José M. N.; Ferreira, Paulo J S G; Albuquerque, DanielCompressed sensing (CS) is a theory that allows us to recover sparse or compressible signals from a much smaller number of samples or measurements than with traditional methods. The problem of detection and estimation of the frequency of a signal is more difficult when the frequencies of the signal are not present on the DFT basis. The Fourier coefficients are not exactly sparse due to the leakage effect if the frequency is not a multiple of the fundamental frequency. In this work we present a high frequency resolution spectrum estimation algorithm that explores the CS, for this type of nonperiodic signal from finite number of samples. It takes advantage of the sparsity of the signal in the frequency domain. The algorithm transforms the DFT basis into a frame with a large number of vectors by inserting columns between some of the existing ones. The proposed algorithm can estimate the amplitudes and frequencies even when the frequencies are too close together, a particularly difficult situation which are not covered by most of the known algorithms. Simulation results show good convergence and a high resolution when compared with other algorithms