Generation of Sawtooth, Square, and Triangular Waves from a BLIT

Several other classic waveforms can be created from impulse train signals.
A sawtooth waveform can be created by integrating the combination of a bandlimited impulse train minus a constant obtained by integrating over one period of the impulse train.
A “bipolar” impulse train can be created by adding a time-delayed and inverted BLIT to another BLIT, as shown in Fig. 11.
Interestingly, a “bipolar” impulse train can also be created by using an even value of in the closed-form BLIT algorithm above. In this case, the frequency of the resulting signal is 1/2 that with an odd , so a frequency scaling is necessary.

Figure 11: A bipolar BLIT created by adding a time-delayed and inverted BLIT to another BLIT.
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A square waveform can be created by integrating a bipolar BLIT.
Finally, a triangle waveform can be created by integrating the previously computed square wave.
Integration can be achieved with an IIR filter, though a “leaky” integrator should be used to avoid DC offset problems.