SAR is not compensating for the doppler of moving targets. It only compensates for the doppler shift of stationary targets
as it assumes that all targets are stationary on Earth.
SAR has side lobes because of which when those capture doppler, they might not suffice Nyquist criterion.

## GMTI using Symmetric Defocusing

### Abstract
Two filters,which differ only in the signs of the phase responses, are used to defocus the complex image respectively.
In the two defocused images,each stationary target is blurred to the same extent,but each moving target is blurred to different extents.
Therefore, moving targets can be indicated by patch-by-patch sharpness comparison of the two defocused images.
The results of the simulated and real data show that this algorithm is effective and efficient.


### Step-By-Step

1. We have an azimuth signal
2. We take an FFT of it and we focus it with a H(f) filter.
3. With Filter 1 , defocusing is done on Step2 output, we obtain S1(f)
4. With Filter 2 , defocusing is done on Step2 output, we obtain S2(f)
5. Inverse FFT of S1(f) gives s1(t)
6. Inverse FFT of S2(f) gives s2(t)
   * If Stationary targets, then both filters will have same Time Period thus blurring of same extent
   * If Moving targets, then both filters will have different Time Periods thus blurring to different extent
7. We use contrast to find absolute difference between the two images.
8. The contrast of these two patches are calculated patch-by-patch.
9. We use Constant False Alarm Method to find a probability density function of the Contrast difference.



### Typical Range-Doppler Algorithm

1. SAR Raw Data is given.
2. FFT in range
3. Range Compression
4. FFT in Azimuth
5. RCMC
6. Azimuth Compression
7. 2D FFT