I'm guessing this somehow scratches at the surface of what I've read
about no signal being properly band limited unless it's infinit.

You're talking about Sinc filtering (ideal low pass filter), which is essentially an IIR filter that needs infinite past and future samples. In practice, a very steep filter is used to attenuate the signal above the Nyquist frequency to almost nothing. A Lanczos (windowed Sinc) filter will be close to ideal.

For synthesis of non-sinusoidal test waveforms, a BLIT (Band-Limited Impulse Train) oscillator will give you a perfectly band limited signal.

Thor


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