22 October 1996 Directional spatial frequency distribution of two-dimensional signals
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The time-frequency analysis techniques developed for 1D time series are extended to determine the spatial frequencies at a specific point on a 2D surface or image. The 2D surface/image is sampled along a number of evenly angularly- spaced axes passing through the point of interest. The time- frequency analysis techniques are then applied to each of the 1D data sets. When taken together, the results from the Directional Spatial Frequency Distribution (DSFD), a 2D plot of spectral energy as a function of spatial frequency and the direction. When the 2D data consists of planar waves, a spatial correlation masking process can be used on the DSFD to produce a localized estimate of spatial frequency and direction of measurement called the Equivalent Planar Wave Sinusoidal Decomposition (EPWSD). The DSFD and EPWSD are calculated for simulated 2D data consisting of sinusoids and chirp signals from single and multiple directions as well as ocean wave measurements made by an airborne scanning radar altimeter and compared to a standard 2D Fourier transform. It is shown that the EPWSD technique provides a very localized estimate of frequency and direction of arrival even if the frequency is changing rapidly with position.
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David E. Hollinberger, David E. Hollinberger, P. G. Madhavan, P. G. Madhavan, "Directional spatial frequency distribution of two-dimensional signals", Proc. SPIE 2846, Advanced Signal Processing Algorithms, Architectures, and Implementations VI, (22 October 1996); doi: 10.1117/12.255440; https://doi.org/10.1117/12.255440

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