My first job as a graduate assistant in linguistics in 1965-66 was in Ilse Lehiste's acoustic phonetics lab at Ohio State, and for a time, I spent many hours running a Kay Sonagraph, making sonagrams (spectrograms) from taped informant sessions. I don't know how the variable bandpass filter was implemented, but you could see what was happening. The Sonagraph recorded a short sample of speech -- just a few seconds -- then replayed that over and over as the bandpass filter moved its band little by little.
A strip of special coated paper was strapped on a rotating drum, and an electrode burnt a line of varying darkness, depending on the output of the bandpass filter. The electrode moved upward on the drum (or downward, I can't remember), so you would be left at the end with a time vs. frequency analysis of the sample, with dark areas on the paper corresponding to the formants. At least for men's voices, you could also see the vertical striations for individual vocal cord vibrations, and count them to estimate the voice pitch.
At the time, Lehiste was investigating the acoustics of the overlong consonants of Estonian, and the rearticulations partway through the articulations of the consonants were clear on the Sonagrams as small bursts of energy (quite inaudible).