Change SAR backprojection range-bin center convention

[tbensonatl]

Update sar_bp to follow the fftshift convention, placing zero differential range at floor(N/2) instead of the geometric midpoint (N-1)/2. For cases with an odd number of range bins, the two conventions already matched. For cases with an even number of range bins, the midpoint now matches the bin that held zero frequency from the perspective of the ifft.

Add even and odd-length unit test coverage for the complex zero differential range response.

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[greptile-apps]

Greptile Summary

The PR changes SAR backprojection to place zero differential range at floor(N/2), matching the FFT-shift convention, and updates the SARBP converter to serialize the physical frequency shifted into transform DC.

• Aligns direct and phase-LUT backprojection paths on the new range-bin center.
• Separates signal-center frequency from the range-profile phase-reference frequency.
• Documents the convention and adds even/odd zero-range coverage.

Confidence Score: 5/5

The PR appears safe to merge, with the kernel, converter, documentation, and tests consistently implementing the FFT-shift range-bin convention.

The direct and phase-LUT paths use the same integer center, interpolation remains bounds-checked, and the converter’s transform direction and frequency-sign handling cancel correctly for both SGN conventions.

Important Files Changed

Filename	Overview
include/matx/kernels/sar_bp.cuh	Direct sampling and phase-LUT generation consistently adopt floor(N/2), with existing interpolation bounds preserved.
examples/sarbp/cphd_to_sarbp_input.py	The converter distinguishes signal-center and phase-reference frequencies and derives range spacing from the raw FX sample grid; no concrete failure was established.
include/matx/operators/sar_bp.h	Public parameter and range-profile documentation now states the FFT-shift and phase-reference contracts.
test/00_transform/SarBp.cu	Tests cover even and odd profile lengths across direct and phase-LUT execution and update synthesized targets to the new convention.
docs_input/api/signalimage/radar/sar_bp.rst	API documentation accurately describes zero differential range at floor(N/2).

Flowchart

%%{init: {'theme': 'neutral'}}%%
flowchart LR
  FX["Raw FX samples"] --> SHIFT["Shift raw bin floor(N/2) to transform DC"]
  SHIFT --> FFT{"CPHD SGN"}
  FFT -->|"-1"| IFFT["IFFT"]
  FFT -->|"+1"| FWD["FFT"]
  IFFT --> PROFILE["FFT-shifted range profile<br/>zero differential range at floor(N/2)"]
  FWD --> PROFILE
  REF["SC0 + floor(N/2) × SCSS"] --> HEADER["SARBP phase-reference frequency"]
  HEADER --> BP["SAR backprojection phase correction"]
  PROFILE --> BP

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[tbensonatl]

/build

[coveralls]

Coverage is 93.332% — tbenson/sarbp-adjust-bin-offset-convention into main. No base build found for main.