Add a causal half-Gaussian option to the Gaussian smoothing filter

[cboulay]

Why

FilterByDesignTransformer applies the Gaussian kernel causally via lfilter, so the acausal half of the symmetric kernel becomes pure group delay — (n_taps - 1) / 2, i.e. width * sigma samples. For a real-time BCI feature stream at 100 Hz, a 50 ms sigma costs 200 ms of lag, a large fraction of a closed-loop control budget.

What

Adds causal: bool = False to GaussianSmoothingSettings (and to gaussian_smoothing_filter_design). When True, the design is gaussian(2*K - 1, std=sigma)[K-1:] with K = int(width*sigma + 1), normalized to unit sum: the peak sits at lag 0 and the tail extends only into the past. Group delay becomes the half-Gaussian centroid, sigma * sqrt(2/pi) ≈ 0.8 * sigma.

The default of False preserves current behavior exactly.

The two modes are not interchangeable at equal sigma — halving the kernel also halves the effective averaging window. They should be compared at matched white-noise variance reduction, sum(b**2), not at matched sigma. Measured at 100 Hz:

noise gain	symmetric	causal
0.141	σ = 20 ms → 80.0 ms	σ = 38 ms → 27.3 ms
0.056	σ = 50 ms → 200.0 ms	σ = 98 ms → 75.1 ms

sigma stays in seconds and is scaled by fs in design_wrapper, unchanged. The kernel_size override and the too-small-kernel warning both apply to the causal branch, where kernel_size counts causal taps and is checked against the one-sided recommended length width * sigma + 1.

The settings docstring documents the group delay of each mode and notes that the causal kernel's stopband rolls off less steeply for a given sigma.

Tests

11 new tests (63 pass in the file, 71 with test_filter.py):

• unit sum for both modes
• causal kernel has argmax == 0, is strictly decreasing, and equals the renormalized half of the symmetric kernel of the same sigma
• measured DC group delay via scipy.signal.group_delay matches sigma * sqrt(2/pi) within a tap
• symmetric group delay is exactly (n_taps - 1) / 2
• matched-noise-gain lag comparison: the causal kernel hits the same sum(b**2) at less than half the delay
• kernel_size override and undersized/identity warnings in causal mode
• end-to-end through the transformer, confirming fs scaling still holds

Note for reviewers

Discrete truncation biases the causal group delay low relative to sigma*sqrt(2/pi) by a near-constant ~1/π tap (7.51 vs 7.82 at σ=9.8), because the n=0 tap gets full weight where the continuous centroid integral gives it half. It's in the favorable direction, but it's why the group-delay test uses abs=1.0 rather than something tighter.