Generation of Classic Waveforms from other Classic Waveforms

Several classic waveforms can be created from other classic waveforms.
For example, an impulse train can be generated by differentiating a sawtooth, and a square wave can be produced by adding a sawtooth to another inverted, delayed sawtooth (Matlab example).
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 (demonstrated in blitsaw.m function).
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.