Time-scale approach for chirp detection. II. (English) Zbl 1185.41027
Summary: A new approach for joint detection and estimation of signals embedded in stationary random noise is considered and compared to previously studied methods, for the subclass of amplitude and frequency modulated signals. The method is a “reassigned” version of the Hough-wavelet transform and it is compared to the matched filter approach and the Hough-wavelet transform itself. Extensions to previous results obtained with these two methods are also presented. As target application, the problem of gravitational waves at interferometric detectors is considered. Our main conclusion is that there is no gain in introducing the reassignment operation.
[Part I, cf. M. Morvidone and B. Torresani, Int. J. Wavelets Multiresolut. Inf. Process. 1, No. 1, 19–49 (2003; Zbl 1044.94514).]
[Part I, cf. M. Morvidone and B. Torresani, Int. J. Wavelets Multiresolut. Inf. Process. 1, No. 1, 19–49 (2003; Zbl 1044.94514).]
MSC:
| 41A60 | Asymptotic approximations, asymptotic expansions (steepest descent, etc.) |
| 26E70 | Real analysis on time scales or measure chains |
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
| 60G35 | Signal detection and filtering (aspects of stochastic processes) |
| 94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |
| 62P35 | Applications of statistics to physics |
Citations:
Zbl 1044.94514References:
| [1] | Auger F., IEEE Trans. Signal Process. 40 pp 1068– |
| [2] | DOI: 10.1103/PhysRevD.51.5360 · doi:10.1103/PhysRevD.51.5360 |
| [3] | DOI: 10.1088/0264-9381/13/4/002 · Zbl 0875.53011 · doi:10.1088/0264-9381/13/4/002 |
| [4] | DOI: 10.1016/j.acha.2007.04.003 · Zbl 1144.94003 · doi:10.1016/j.acha.2007.04.003 |
| [5] | Carmona R., Practical Time-Frequency Analysis. Gabor and Wavelet Transforms with an Implementation in S (1998) · Zbl 1039.42504 |
| [6] | DOI: 10.1006/acha.1998.0254 · Zbl 0934.94002 · doi:10.1006/acha.1998.0254 |
| [7] | DOI: 10.1137/1.9781611970104 · Zbl 0776.42018 · doi:10.1137/1.9781611970104 |
| [8] | DOI: 10.1109/18.119728 · Zbl 0743.42010 · doi:10.1109/18.119728 |
| [9] | Flandrin P., Traité des Nouvelles Technologies, série Traitement du Signal, in: Temps-Fréquence (1993) |
| [10] | DOI: 10.1137/0515056 · Zbl 0578.42007 · doi:10.1137/0515056 |
| [11] | Harthong J., Etudes sur la mécanique quantique (1984) · Zbl 0589.35002 |
| [12] | DOI: 10.1006/acha.1996.0204 · Zbl 0864.94010 · doi:10.1006/acha.1996.0204 |
| [13] | DOI: 10.1109/TSP.2002.805489 · Zbl 1369.94168 · doi:10.1109/TSP.2002.805489 |
| [14] | DOI: 10.1109/TASSP.1978.1163047 · doi:10.1109/TASSP.1978.1163047 |
| [15] | Koopmans L. H., Probability and Mathematical Statistics 22, in: The Spectral Analysis of Time Series (1995) |
| [16] | DOI: 10.1007/978-1-4684-9358-0 · doi:10.1007/978-1-4684-9358-0 |
| [17] | Mallat S., A Wavelet Tour of Signal Processing (1998) · Zbl 1125.94306 |
| [18] | DOI: 10.1142/S0219691303000037 · Zbl 1044.94514 · doi:10.1142/S0219691303000037 |
| [19] | Picinbono B., Annales des Télécommunications 38 pp 179– |
| [20] | Tchamitchian Ph., Wavelets and Their Applications (1991) |
| [21] | DOI: 10.1088/1742-6596/110/6/062025 · doi:10.1088/1742-6596/110/6/062025 |
| [22] | Van-Trees H., Detection, Estimation, and Modulation Theory. Part I (1968) · Zbl 0202.18002 |
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