Weitere Kapitel dieses Buchs durch Wischen aufrufen
Signals are in general nonstationary. A complete representation of nonstationary signals requires frequency analysis that is local in time, resulting in the time-frequency analysis of signals. The Fourier transform analysis has long been recognized as the great tool for the study of stationary signals and processes where the properties are statistically invariant over time. However, it cannot be used for the frequency analysis that is local in time because it requires all previous as well as future information about the signal to evaluate its spectral density at a single frequency ω. Although time-frequency analysis of signals had its origin almost 60 years ago, there has been major development of the time-frequency distributions approach in the last three decades. The basic idea of the method is to develop a joint function of time and frequency, known as a time-frequency distribution, that can describe the energy density of a signal simultaneously in both time and frequency. In principle, the time-frequency distributions characterize phenomena in a two-dimensional time-frequency plane. Basically, there are two kinds of time-frequency representations. One is the quadratic method covering the time-frequency distributions, and the other is the linear approach including the Gabor transform, the Zak transform, the linear canonical transform, and the wavelet transform analysis. So, the time-frequency signal analysis deals with time-frequency representations of signals and with problems related to their definition, estimation, and interpretation, and it has evolved into a widely recognized applied discipline of signal processing.
Bitte loggen Sie sich ein, um Zugang zu diesem Inhalt zu erhalten
Sie möchten Zugang zu diesem Inhalt erhalten? Dann informieren Sie sich jetzt über unsere Produkte:
Abe, S., & Sheridan, J. T. (1994a). Generalization of the fractional Fourier transformation to an arbitrary linear lossless transformation: An operator approach, Journal of Physics A, 27, 4179–4187.
Abe, S., & Sheridan, J. T. (1994b). Optical operations on wave functions as the Abelian subgroups of the special affine Fourier transformation. Optics Letters, 19, 1801–1803.
Bastiaans, M. J. (1979). Wigner distribution function and its application to first-order optics. Journal of the Optical Society of America A, 69, 1710–1716 (1979). CrossRef
Bernardo, L. M. (1996). ABCD matrix formalism of fractional Fourier optics. Optical Engineering, 35, 732–740. CrossRef
Debnath, L., & Shah, F. A. (2015). Wavelet transforms and their applications (2nd ed.). Boston: Birkhäuser. MATH
Gabor, D. (1946). Theory of communications. Journal of Institute of Electrical and Electronic Engineers London, 93, 429–457.
Gelfand, I. M. (1950). Eigen function expansions for an equation with periodic coefficients. Doklady Akademii Nauk SSSR, 76, 1117–1120.
James, D. F., & Agarwal, G. S. (1996). The generalized Fresnel transform and its applications to optics. Optics Communication, 126, 207–212. CrossRef
Kou, K. I., & Xu, R. H. (2012). Windowed linear canonical transform and its applications. Signal Processing, 92, 179–188. CrossRef
Moshinsky, M., & Quesne, C. (1971a). Linear canonical transformations and their unitary representations. Journal of Mathematical Physics, 12(8), 1772–1780.
Moshinsky, M., & Quesne, C. (1971b). Linear canonical transformations and matrix elements. Journal of Mathematical Physics, 12(8), 1780–1783.
Shi, J., Liu, X., & Zhang, N. (2014). Generalized convolution and product theorems associated with linear canonical transform. SIViP, 8, 967–974. CrossRef
Siegman, A. E. (1986). Lasers. Mill Valley, CA: University Science Books.
Zak, J. (1967). Finite translation in solid state physics. Physical Review Letters, 19, 1385–1397. CrossRef
Zak, J. (1968). Dynamics of electrons in solids in external fields. Physical Review, 168, 686–695. CrossRef
- The Time-Frequency Analysis
Firdous A. Shah
Neuer Inhalt/© ITandMEDIA