Space/time/frequency methods in adaptive radar - New Jersey ...

14The collected data comprise a set of reflectivity measurements in two dimensions.The dimensions of the data format is referred to as slant range and cross range.A data record will extend in slant range over the range swath and continuouslyin cross range along the flight path over which the data are collected as shown inFigure 2.4(b). Before processing, the data set does not resemble a map or image andechos from individual point targets are dispersed in both range and azimuth. Datacollected from the slant-range and cross-range space are processed to achieve rangeand azimuth compression.2.3 Why are Time-frequency Representations Needed ?A one-to-one relation exists between a signal in the time domain, s(t), and thespectrum in the frequency domain, S(f). This relation is shown using the Fouriertransform. For a one-dimensional signal, s(t), the Fourier transform is given byThe inverse Fourier transform isis shown in Figure 2.5.While the Fourier transform allows a signal to be transformed back and forthbetween the time and frequency domains, it does not allow for a combination of thetwo domains. The time localization of the spectral components is contained in thephase of the spectrum but it may not be easy to interpret.