tb_spectrogram — 2D `typed` op

• Data kinds: signal → image

• Call: fullseye.apply(img, "tb_spectrogram", a=0.5, b=0.5) (the 2-D model is one image plus two scalar knobs a,b∈[0,1])

*No figure: this op takes signal as input. A Studio program starting from an image cannot reach that type — see the runnable examples below for how it is used.*

Usage

STFT magnitude spectrogram -> `(freqs, times, S) with S shape (n_freqs, n_frames). Hann-windowed; *hop* defaults to win//2`.

**Same raw convention as :func:spectrum, but a different divisor.** Each

column is the unnormalised `|rfft(frame * hann(win))|`, so it is not an

amplitude either — and dividing by `2/win` is *wrong* here, because the

Hann window has already thrown away part of the signal. The correct one-sided

amplitude conversion divides by the window's coherent gain::

w = np.hanning(win)

amp = S * (2.0 / w.sum()) # bins 1 .. win/2-1; DC / Nyquist: 1/w.sum()

Measured on a unit sine at a bin centre (`rate = 16000` Hz, 1000 Hz,

amplitude exactly 1.0, `win = 256`): the raw column peak is

`63.7497786196906; * 2/win gives 0.49804514546633283` (too small by

exactly the Hann coherent gain `sum(w)/win = 0.498046875`), while

`* 2/sum(w) gives 0.9999965273676957`. Only the second one is the

amplitude that was actually in the signal.

Peak *positions*, frame-to-frame ratios and any dB *difference* are unaffected

by either factor. This function returns magnitudes only — the phase is

discarded, so it cannot be inverted; use `acoustics.stft / acoustics.istft`

for a round-trip.

Typed bridge of the 1d op `spectrogram into the 2-D evolution registry: the same implementation, called under the op(v, a, b) convention. a drives rate (default 1) and b drives win` (default 256).

References (sample data, literature)

• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).

• Operator provenance and references — the sources of the research/methods this op family came from.

Runnable examples (verified samples that actually call this op)

• (none yet)

Ops the type connects to (they accept `image` as input)

identity · gaussian · mean_box · bilateral · unsharp · median · min_filter · max_filter

Same category (`typed`)

tb_points_to_voxel · tb_estimate_point_normals · tb_iss_keypoints · tb_angle_3points · tb_project_points · tb_render_point_depth · tb_statistical_outlier_removal · tb_radius_outlier_removal

*Provenance: ops.py — 2D operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*

tb_spectrogram — 2D typed op