Envelope

Envelope extracts the slowly varying amplitude contour of a signal, discarding the fast carrier while retaining the outline of its magnitude. It offers three algorithms selected by method: peak (an asymmetric attack/release follower), rms (a sliding root-mean-square window), and hilbert (the true analytic-signal envelope). The output is a Signal of the same length and same physical unit as the input, since an amplitude envelope is dimensionally identical to the quantity it tracks.

The peak follower is a one-pole tracker with independent time constants: it rises toward the rectified input with attack_time and decays with release_time. Fast attack and slow release produce the classic dynamics-processor envelope. The rms method computes $\sqrt{⟨x^2⟩}$ over a sliding window of window_size samples, giving a smooth energy-weighted amplitude. The hilbert method forms the analytic signal $x_a=x+i\mathcal{H}\{x\}$ and returns its instantaneous magnitude $|x_a|$, the mathematically exact envelope for narrowband signals.

The node is stateless: each evaluation processes the full input buffer with parameters interpreted against the buffer's sample rate; no state carries between runs. Attack and release times are given in seconds and are converted to per-sample coefficients using the signal's sample rate. Uncertainty ($\sigma$) propagates through the underlying arithmetic, though the nonlinearity of rectification, squaring, and magnitude means the reported $\sigma$ is a first-order approximation near amplitude zero-crossings.