Though we have mainly discussed the use of wavetables to produce sinusoidal signals, in fact, wavetable techniques can be used to produce much more complex, periodic signals.
Wavetable techniques must be used with care to avoid aliasing, particularly if the phase incrment is greater than one. To do this, it is necessary to know the highest frequency component in the table and avoid using values of the phase increment that will cause that component to alias. For example, if a table has a single period of a sinusoid added with another sinusoid that has 4 complete periods, then the phase increment must remain at or below , where is the table size, to avoid aliasing (you need at least two samples per period of the highest frequency component in the table).
One technique that is used in practice is to use additive techniques to generate multiple sawtooth wavetables an octave apart containing bandlimited harmonics. During synthesis, the necessary wavetables to produce a full, though bandlimited, spectrum are mixed together with appropriate weightings.
Finally, an impulse train can be generated by differentiating the sawtooth, and a square wave can be produced by adding a sawtooth to another inverted, delayed sawtooth.