Applications 
1) Raw signal : 
Since the raw baseband SAR signal can be expressed as a convolution 
integral, S(X) - o(X) * h9(X), the autocorrelation of this signal equals[ 3 ]: 
E(se) 56 «5)]«. E[sto. s] x h, (©) x k, C1) 
and È | s) ; s(e vx) ] = hat) x h. (-T) 
This last result provides a way to estimate the SAR response h(t) 
(specifically, the self-convolution of this response). Then the basic processing 
parameters, the Doppler center frequency and frequency rate, can be estimated 
from the Fourier transform of this self-convolution. These parameters are 
essential in range migration correction, in look extraction and in azimuth 
compression. Moreover, the ultimate SAR resolution (in the case of perfect 
matched filtering), can be directly measured in this response. 
2) Processed image : 
Since the processed SAR image (before detection) can be expressed as a 
convolution integral T(X) = S(X) * h (X), where h, (X) is the processor response, 
the autocorrelation of the complex image signal equals [3 ]: 
ABC z £st). ste«v) X 11} x ht) 
and E | Te) (eT) Eh (Ta ht » h tt) x h, (-T) 
Therefore, the computation of the autocorrelation of the complex image 
signal enables the checking of the overall (SAR and Pre-processor) transfer 
function : resolution, matching of the processor, measurement of the residual 
offset in focussing. 
458