Principles of Modern Radar - Volume 2 1891121537

7.11 Problems 335Fourier transforming (using the IFFT) from k u to u. FFTSHIFT to place the closestpoint of approach in the middle. (Indexing the u axis in meters may be a challenge ifthe k u sampling from problem 9 was used to generate the PSR and oversampling wasused to go from u to k u in problem 9.)12. [RDA imaging] Perform RDA imaging by matched filtering with the full PSR (viamultiplication in the frequency domain) as documented in Figure 7-44. Start with theraw, frequency-domain data generated in problem 7, as they should already have thesame RF sampling as the PSR created in problem 11. Fourier transform the syntheticdata from u to k u (using the FFT) with the appropriate amount of zero padding, if any,and FFTSHIFT to register the data with the PSR from problem 11. (If the k u domain isoversampled, there will be a linear phase modulation on the data over spatial frequencythat will cause an undesirable cross-range offset in the final RDA image. You will haveto estimate and compensate for this phase by multiplying the data by the conjugateof your estimate.) Complete the RDA processing using a two-dimensional IFFT andFFTSHIFTING in cross-range. (The point scatterer will, hopefully, be focused forboth L-band and X-band, but perhaps not at the appropriate down-range/cross-rangelocation. Accounting for image offsets due to FFT-induced linear phase modulations,especially when zero padding is involved, is notoriously challenging. Keep in mindthat erroneous shifts in (x,r) are due to uncompensated linear phase in (k u ,ω).)