fix: real-domain spectrum renders as +-fc conjugate-symmetric Euler pairs

[striderZA]

Summary

Fixes #39. In the "real" (analog) signal domain — everywhere upstream of the ADC's DDC — the spectrum display now correctly honors Euler's formula: a real cosine at fc is physically 0.5*(exp(j*2*pi*fc*t) + exp(-j*2*pi*fc*t)), i.e. equal-power content at both +fc and -fc. The spectrum-analyzer render path previously collapsed this to one full-power bin at +fc with no representation of the mirror.

Design

Full design doc: docs/superpowers/specs/2026-08-03-spectrum-euler-conjugate-symmetry-design.md
Implementation plan: docs/superpowers/plans/2026-08-03-spectrum-euler-conjugate-symmetry.md

• New Spectrum::is_complex_baseband flag (default false), propagated through every pass-through component exactly like fs_Hz already is.
• New conjugateSymmetricExpand() helper in common/spectrum.h: splits each non-DC tone into +fc/-fc half-power (-3.0103 dB) entries per Euler's formula. DC tones pass through unchanged.
• Interior DSP is untouched by design: the signal generator, nonlinear_model.h's harmonic/IM math, every gain/filter/S-parameter stage, and the mixer keep operating on the existing collapsed single-entry-per-tone representation — splitting there would corrupt the nonlinear model's real-power-calibrated harmonic math.
• The expansion happens at exactly one point: the spectrum-analyzer render path, only for real-domain (is_complex_baseband == false) spectra.
• AdcEngine's output now sets is_complex_baseband = true. Its DDC power/phase math (alias_frequency, NCO-shift/windowing) is unchanged — verified against the repo's own docs/resources/rf_adc_info.md, image rejection there already correctly discards the mirror, so no additional compensation is needed.

Testing

New standalone executable tests/test_signal_domain.cpp (required by this toolchain's MinGW-w64 TEST_CASE registration ceiling — see tests/AGENTS.md), 24 test cases / 46 assertions, covering:

• The is_complex_baseband flag defaulting and propagation through every component (generator, amplifier, attenuator, combiner, equalizer, ideal filter, coax, splitter, mixer, PFB channelizer, touchstone S-parameter data, ADC).
• conjugateSymmetricExpand() unit tests (real tone split, DC tone passthrough, multiple tones, empty input).
• Spectrum-analyzer render tests: a real-domain tone renders as a +/-fc half-power pair; a complex-baseband tone renders unchanged (no mirroring).
• Regression pin: the existing "ADC DDC preserves tone power and phase" test continues to pass with unchanged expected values.

Full existing suite (build/bin/tests.exe) verified unchanged throughout every commit: 217 test cases / 65522 assertions, zero regressions.

Commits

7 implementation tasks + design/plan docs + a DOX pass (updated common/AGENTS.md and tests/AGENTS.md per this repo's binding documentation contract) + one review-driven perf fix (avoid an unnecessary tone-vector copy in the common complex-baseband render path).

[striderZA]

Review: PR #40 — Real-domain spectrum Euler/conjugate-symmetry fix

Verified locally (worktree .worktrees/spectrum-euler, commit 2f0b561):

• Full build: clean (cmake --build build, no warnings from touched files).
• build/bin/tests.exe: 217 test cases / 65522 assertions, all pass — matches PR claim, no regressions.
• build/bin/test_signal_domain.exe: 24 test cases / 46 assertions, all pass — matches PR claim.

Design review:

• The core physics is correct: conjugateSymmetricExpand splits non-DC tones into ±fc pairs at P - 10*log10(2) dBm each, DC passes through unchanged. Confirmed against Euler's formula.
• Scoping decision to keep interior DSP (generator, nonlinear_model.h, mixer, gain/filter/S-param stages) on the collapsed single-entry representation is correct and well-justified — splitting there would break the amplitude-calibrated harmonic/IM math. Render-time-only expansion is the right call even though issue #39's "Expected behaviour" text nominally also asks for the representation to change; the design doc's §2 rationale for not doing that is sound.
• ADC power bookkeeping analysis (§5 of the design doc) checks out: since interior tones are never actually split before reaching the ADC, no compensation gain is needed on the DDC output — adding one would double-count and break the existing "ADC DDC preserves tone power and phase" regression test. Confirmed this test still passes unmodified.
• is_complex_baseband propagation was checked line-by-line against every update() branch in amplifier, attenuator, combiner, equalizer, ideal_filter, coax, splitter, mixer, pfb_channelizer, touchstone/s_parameter_data.cpp. Coverage is complete for every branch that assigns out.tones.
• renderCombinedSpectrum reuses the fixed integratePowerPerBin, so multi-spectrum overlay rendering picks up the fix for free — no separate gap there.
• Frequency grids for all real-domain producers span [MIN_FREQ, MAX_FREQ] = [-20GHz, +20GHz] (buildDefaultFrequencyGrid / signal generator), so the -fc mirror always has a bin to land in; no silent-drop risk from a positive-only grid.

Minor, non-blocking findings:

1. combiner_engine.cpp's two N < 2 degenerate-frequency-grid early-return branches (lines ~103 and ~198) exit before the new out.is_complex_baseband assignment runs, so the flag can go stale in that edge case. This is not a new bug — it's exact parity with the pre-existing out.fs_Hz gap in the same branches (also unset there today). Not worth blocking on; flag if fs_Hz staleness there is ever fixed, fix is_complex_baseband alongside it.
2. Merge conflict with current master: master has since merged #38 which also appends a new test executable block at the end of tests/CMakeLists.txt (test_issue37_pfb_input_removal), colliding textually with this PR's test_signal_domain block at the same insertion point. Trivial rebase (keep both add_executable/add_test blocks), but the PR needs it before merge — GitHub reports MERGEABLE: DIRTY.

Verdict: Approve pending a rebase onto current master to resolve the tests/CMakeLists.txt conflict. No functional or physics concerns.

[striderZA]

Rebased onto current master (10abe42) to resolve the tests/CMakeLists.txt conflict with #38's test_issue37_pfb_input_removal — both new test-executable blocks kept, additive change only. Rebuilt clean and reran: tests.exe 217/65522, test_signal_domain.exe 24/46, test_issue37_pfb_input_removal.exe 4/4 — all pass. Force-pushed (2f0b561 → ca3feda, same 11 commits, only the CMakeLists conflict resolved). PR is now MERGEABLE/CLEAN.