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This step is an extension of SAR Processing (Brute Force, Single Range Bin). In extending from a single range bin to a single range line, one must consider that the shape of the hyperbola changes as we go out in range:
As an example, suppose we wish to form a continuous two-dimensional image using a beamwidth of 1000 successive looks (1000 radar PRIs) over an range extent of 1000 pixels deep at a radar PRF of 200 PPI. The following two steps are then necessary:
STEP 1 --Compute one range pixel by rotating and summing 1000 vectors along the appropriate range-azimuth hyperbola:
A + jB = (x1 + j y1) (cos1 + j sin1) + (x2 + j y2) (cos2 + j sin2) ... + (x1000+ j y1000) (cos1000 + j sin1000)
STEP 2 -- Compute one 1000-point range line by repeating Step 1 1000 times
TOTAL OPERATIONS PER SECOND
(1000 points) x (PRF of 200) x (8 operations per vector rotate) = 1.6 million operations/second
where an operation is either a multiply or add, independent of memory accesses.
For information on using interpolation to select points intermediate to those obtained from an evenly sampled data set, see Synthetic Aperture Radar (SAR) Processing Overview.
For information on extending the Brute Force Method to more than one range line, see SAR Processing (Brute Force, Multiple Range and Azimuth Bins).