[sdiy] BLIT/BLEP virtual analogue synthesis

[Tom Wiltshire]

On 4 Aug 2010, at 15:18, Olivier Gillet wrote:

>> However, for the BLEP, I need to know the sub-sample position of the ramp discontinuity. If the sub-sample position is designated "a", then the accumulator value after a wraparound is (1-a) * increment. I can detect the wraparound and divide the accumulator value by the increment to find the sub-sample position, but this is a division by (probably) a 32-bit number.
>> 
>> Is there a way to do it that avoids the big ugly division?
> 
> I assume you're working on an architecture where divisions are done in
> software. I haven't thought much about it but I think you could use
> prior knowledge about the number of bits in the result to unroll the
> loop of the binary division algorithm. You know that the result will
> be between 0 and 1, the compiler does not.
> 
> Let's say you use a 16 bits phase counter positioned at 64000, with a
> phase increment of 2400. The phase parameter of the blep will depend
> on ((6400 + 2400) % 65536) / 2400 = 1536 / 2400. That's the division
> you're talking about, right?
> 
> You won't use the number 1536/2400 anyway since you're working with
> integers... You'll probably want to compute something which is more
> like 256 * 1536 / 2400. So the division you really have to do is
> 393216 / 2400. Now there's a bit of knowledge you know and the
> standard software implementation of / generated by your compiler
> doesn't know: the result will always be 8 bits, all the upper bits
> will be 0. So you can unroll the 8 iterations of the binary division
> loop to compute each of the bit, instead of going with a loop through
> the 32 iterations of the standard software division.

Good point. Perhaps you can't *avoid* the division, but you might be able to simplify it.

>> With reference to my earlier email, I wasn't really suggesting listing to 8KHz square waves (bandlimited or not) - it's just that I couldn't really grasp how such an algorithm would manage to degrade correctly and only generate a couple of harmonics in an extreme case.
> 
> Trust the maths :)

Antti said something similar. I think you're both right, but I still make too many basic errors to really trust *my* maths!

> At high frequency, the ratio between the "period"
> of the BLEP ripples and the oscillator frequency will get close to 1.
> The 8kHz band limited square wave will be a sine because the ripples
> of the BLEPs will overlap each other exactly.

Ok, I see. This is clearer to me now.

>> I thought Olivier's suggestion of using BLEP for low frequencies and something else for highs was insightful. BLIT/BLEP algorithms have a computational cost that increases with frequency. This would make it a good match for something like additive synthesis, which has a computation cost that *decreases* with frequency. So use each for the the part of the spectrum it's best at - it's an interesting idea. Of course, there's extra complications in using two algorithms, and perhaps that outweighs the benefits on specific hardware.
> 
> Sadly, you can't do real sync or PWM with additive synthesis.

Another good point. I'll worry about it once I get BLEP working.

Thanks,
Tom