A method for signal reconstruction with the use of normalized spectrum
DOI:
https://doi.org/10.3103/S0735272706020075Abstract
A new method is suggested for reconstruction of signals of unknown shape by their bispectral density. The new approach is based on application of smooth functions such as cosine and sine — instead of the discontinuous function of the “arctangent of bispectrum argument” type, traditionally accepted in phase measurements. The use of simulation permits to assess effectiveness of the suggested method of reconstruction of signals with the first genus discontinuities at different discretization intervals.References
BARTELT, H.; LOHMANN, A.W.; WIRNITZER, B. "Phase and amplitude recovery from bispectra," Appl. Optics, v.23, n.18, p.3121-3129, 1984. DOI: http://doi.org/10.1364/AO.23.003121.
SUNDARAMOORTHY, G.; RAGHUVEER, M.R.; DIANAT, S.A. "Bispectral reconstruction of signals in noise: amplitude reconstruction issues," IEEE Trans. Acoust., Speech, Signal Process., v.38, n.7, p.1297-1306, 1990. DOI: http://doi.org/10.1109/29.57558.
KANG, M.G.; LAY, K.-T.; KATSAGGELOS, A. K. "Phase estimation using the bispectrum and its application to image restoration," Opt. Eng., v.30, n.7, р.976-985, 1991. DOI: http://dx.doi.org/10.1117/12.55893.
PETROPULU, A.P.; NIKIAS, C.L. "Signal reconstruction from the phase of the bispectrum," Proc. of Int. Conf. on Acoustics, Speech, and Signal Processing, 3-6 Apr. 1990. IEEE, 1990. DOI: http://doi.org/10.1109/ICASSP.1990.115718.
ALSHEBEILI, S.; CETIN, A.E. "A phase reconstruction algorithm from bispectrum (seismic reflection data)," IEEE Trans. Geosci. Remote Sensing, v.28, n.2, p.166-170, 1990. DOI: http://doi.org/10.1109/36.46695.
PETROPULU, A.P.; POZIDIS, H. "Phase reconstruction from bispectrum slices," IEEE Trans. Signal Process., v.46, n.2, p.527-530, 1998. DOI: http://doi.org/10.1109/78.655441.
NIKIAS, C.L.; RAGHUVEER, M.R. "Bispectrum estimation: A digital signal processing framework," Proc. IEEE, v.75, n.7, p.869-891, 1987. DOI: http://doi.org/10.1109/PROC.1987.13824.