The integro differential method is one of the older aliasing limiting technique. It's stunning that they published that as new stuff.

Anyway it works specifically like a charm with x/sqrt(x^2+1) as its integrand is simply sqrt(x^2+1).

I've implemented this scheme on the Axoloti and it is very efficient. On the little ARM STM32F4, the 1/x and sqrt float run in parallel with integer operations. Thus interleaving fixed point calculation leads to something efficient.

Code: Select all

```
int32_t outGain = param_OutGain<<3;
const int32_t *pIn = inlet_in;
int32_t *pOut = outlet_out - 1;
while(pOut < outlet_out + BUFSIZE - 1){
float r;
float y1 = y0;
y0 = arm::vsqrtf(arm::q_to_float(nextSq1, 22));
nextX0 = ___SMMUL(param_InGain, *pIn)<<7; //execs in parallel
nextSq1 = ___SMMLA(nextX0, nextX0, 1<<22);
int32_t x1_x0 = x1 - x0; // we avoid division by small values
if(abs(x1_x0) > (1<<17)){ //the divider is not too small
r = y1 - y0; // go diff !
r /= arm::q_to_float(x1_x0, 27);
} else { // it's too small use the direct value
r = arm::q_to_float(x0, 27) / y0;
}
x1 = x0;
x0 = nextX0;
pIn++;
pOut++;
*pOut = ___SMMUL(outGain, arm::float_to_q(r, 30));
}
```