 Spectral envelope

A spectral envelope is a smooth description of the broad shape of a frequency spectrum, separating slowly varying magnitude structure from fine spectral peaks. It is an estimated representation, not a uniquely defined extra part of the Fourier transform. Smoothing scale, whether one smooths linear magnitude or log magnitude, and the estimation method all matter.^[ref]

For a periodic signal passed through a linear time-invariant system, the harmonic line at $k{f}_0$ has amplitude proportional to $|X_{k}H(k{f}_0)|$. The excitation sets the line spacing $f_0$, while the filter's frequency response shapes their broad heights. Changing the fundamental frequency can therefore move the lines without moving the filter's resonant peaks. A spectral envelope aims to capture that broad shape; overly aggressive smoothing can erase meaningful resonances, while insufficient smoothing retains the individual harmonics.