Band Limited Impulse Train Synthesis
the main idea behind BLIT is that these analog synth waveforms that we are trying to generate digitally can be thought of as the integral (over $t$) of impulse trains.

a sawtooth can be thought of as the integral of the sum of a little bit of DC and an impulse train.  a square wave is the integral of impulses of alternating signs.  the  triangle wave is the integral of the square wave.

so, to create bandlimited waveforms of the above, the impulse trains are bandlimited which means that each impulse $\delta(t-t_n)$ is replaced by a $\operatorname{sinc}(t-t_n)$ function, which is that impulse bandlimited through a Nyquist brick-wall LPF.  that sequence of bandlimited impulses is a BLIT.

then, since integration is a filter with s-plane transfer function of $H(s)=\frac{1}{s}$ and is LTI (Linear, Time-Invariant), integrating the BLITs will introduce no new frequency components.  if your BLITs are bandlimited, so are the other waveforms that are derived from filtering the BLITs.