Abstract— Compressed 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.
Index Terms— Compressed sensing, redundant frames, signal reconstruction, sparse representations, spectral estimation.
Isabel M. P. Duarte and Daniel F. Albuquerque are with the School of Technology and Management of Viseu, Polytechnic Institute of Viseu, CI&DETS, Portugal (e-mail: isabelduarte@estv.ipv.pt, dfa@estv.ipv.pt).
José M. N. Vieira and Paulo J. S. G. Ferreira are with Signal Processing Lab., IEETA/DETI, University of Aveiro, Portugal.
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Cite: Isabel M. P. Duarte, José M. N. Vieira, Paulo J. S. G. Ferreira, and Daniel F. Albuquerque, " Iterative Algorithm for High Resolution Frequency Estimation," International Journal of Information and Electronics Engineering vol. 4, no. 6, pp. 413-417, 2014.
