[sdiy] IIR and FIR for bandlimited waveforms (or BLEPs?)

[Tom Wiltshire]

Hi all,

Let me run a thought past you and see if I'm making any sense. This close after Xmas it's pretty unlikely. I'm not due to sober up until February.

The typical bandlimited square wave (perhaps built by additive synthesis from a harmonic series of sinewaves) has little ripples before and after each abrupt edge. There's a name for them which presently escapes me, but it doesn't matter. The point is that the ripples are symmetrical in time, before and after the edge. This is similar to a FIR lowpass filter (say, a windowed sinc pulse) which also has this same symmetrical arrangement of ripples. And lo and behold if you feed a naive square wave through the FIR filter, you get the bandlimited squarewave with symmetrical ripples.

Now, the reason this is important is because the typical analogue filter doesn't give this behaviour. If I were trying to sample a bandlimited squarewave, I could start with a non-bandlimited squarewave from the oscillators in my Pro-One, and then I could filter it using the 24dB/oct filter. This produces a bandlimited squarewave which I'd be safe to sample without aliasing, but it doesn't look like the "symmetrical ripples" version. In fact, it looks more like the result you'd get from feeding a naive squarewave through an IIR filter, rather than an FIR, which is logical enough.

Either version of the bandlimited squarewave would be suitable for sampling without any risk of aliasing. So could I use a BLEP algorithm to make a squarewave, but instead of using a FIR filter to produce the bandlimited steps, use an IIR?

Thanks,
Tom