Add FFT pulse-spectrum analyzer (closes #12)

[Oishi1029]

Closes #12

What

• pulse_spectrum(pulse; n_samples=1000) in src/post_process.jl: samples any
  Piccolo.AbstractPulse via Piccolo.sample, computes the one-sided power spectrum of each
  drive channel with FFTW (rfft along the time axis), and returns
  (freqs_GHz, power::Matrix) with one row per drive channel. Durations are in ns, so
  rfftfreq(n, 1/dt) yields GHz directly.
• plot_pulse_spectrum(pulse; kwargs...): new StrettoMakieExt package extension (Makie as
  a weak dependency, following the PiccoloMakieExt pattern — docstring on a stub in src,
  method added in the extension). Plots all drive channels on a shared axis, frequency in
  GHz vs. power on a log y-axis; extra kwargs forward to the Axis.
• FFTW added to [deps], Makie to [weakdeps], both with compat entries.

Why these choices

• rfft/rfftfreq give the one-sided spectrum directly for real-valued controls (no manual
  slicing of a two-sided FFT) — the spec's fftfreq snippet, one-sided.
• Power is the unnormalized FFTW |X|² (documented in the docstring and pinned by a test).
• Plotted power is clamped at floatmin(Float64) only inside the plot so an identically-zero
  drive channel can't crash the log axis; returned data is untouched.
• Per the issue's out-of-scope list: no filtering, no automatic wiring into
  default_post_process, no CompilationReport changes.

Tests

Two new @testitems in src/post_process.jl:

• a two-channel ZeroOrderPulse with sines at 0.05 GHz and 0.20 GHz produces per-channel
  spectral peaks within one frequency bin of the true frequencies (also pins the return-shape
  contract: n÷2+1 non-negative freqs, (n_drives, n_freqs) power matrix);
• a constant pulse is pure DC with power (amplitude·n)², pinning the normalization.

Full suite passes locally (Julia 1.12, macOS):

Test Summary: | Pass  Total   Time
Package       |  116    116  47.6s
     Testing Stretto tests passed

Makie extension smoke-tested locally with CairoMakie — peaks land at 0.04995 GHz and
0.1998 GHz for input sines at 0.05 and 0.20 GHz (within one frequency bin). Demo plot attached below.

Disclosure

I used Claude (Anthropic) to help draft the implementation and tests, which I then reviewed,
manually verified, and tested locally.

[jack-champagne]

Hi @Oishi1029, thanks for your submission to #12 for unitaryHACK! 👋 We've done an initial read-through and it looks like a real, well-formed contribution. We're pulling it down to run the test suite locally tonight and will follow up with detailed feedback in the morning. Appreciate your patience!

[Oishi1029]

Thanks @jack-champagne ! Happy to answer any questions on the design choices. Looking forward to your feedback.

[codecov]

Codecov Report

❌ Patch coverage is 40.00000% with 9 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
ext/StrettoMakieExt.jl	0.00%	9 Missing ⚠️

📢 Thoughts on this report? Let us know!