Spectral analysis of waves on the ocean surface using high resolution time frequency representations

The use of equivalent time-frequency representations for image spectral analysis purpose is shown in this paper. The term equivalent time-frequency representation (ETFR) is proposed for time-frequency representation (TFR) generalized to images, in order to distinguish them from the TFR of the 1D signals. The generalizations of some well known tips (Hilbert transform and interpolation) used when dealing with 1D signals are reminded. Problems that occur due to the bidimensional nature of images are pointed out. The way of deriving ETFR from TFR is explained through the generalization of the kernel. That point is thoroughly described and justified. The way of getting High-Resolution TFRs or ETFRs is indicated. Applications on SAR images of the ocean surface are presented. The authors show how ETFR can be used for image spectral analysis purposes, namely estimation of the swell or of internal waves in their case