How to keep the same length interpolating points linearly or exponentially?

[Nowhk]

Hi guys

This is the code I have for a "function generator" signal that I'll use to modulate some params (taken inspiration from Rampage module, within VCV Rack):

Code: Select all

#include <iostream>
#include <math.h>

const double sampleRate = 44100.0;

inline float interpolate(float a, float b, float frac) { 
    return a + frac * (b - a); 
}

inline float shapeDelta(float delta, float length, float shape) {
    float mul = 1.0;
    
	float lin = copysignf(1.0f, delta) * 10.0 / length;
	float exp = mul * M_E * delta / length;

	return interpolate(lin, exp, shape * 0.90f);
}

int main() {
    float lengthInSeconds = 1e-2;
    float in = 10.0;
    
    // linear
    float out = 0.0;
    float shape = 0.0;
    int numSteps = 0;
    while (in - out > 1e-3) {
        float delta = in - out;
        float inc = shapeDelta(delta, lengthInSeconds, shape) * (1.0 / sampleRate);
        
        out += inc;
        numSteps++;
    }
    std::cout << "shape: " << shape << " | num steps: " << numSteps << " | value: " << out << std::endl;
    
    // exp
    out = 0.0;
    shape = 1.0; // changing the shape
    numSteps = 0;
    while (in - out > 1e-3) {
        float delta = in - out;
        float inc = shapeDelta(delta, lengthInSeconds, shape) * (1.0 / sampleRate);
        
        out += inc;
        numSteps++;
    }
    std::cout << "shape: " << shape << " | num steps: " << numSteps << " | value: " << out << std::endl;    
}

With shape = 0, its linear, and it takes (length) 441 samples to complete (0.01 seconds).
With shape = 1, its exponential, but it takes (length) 582 samples to complete (more than 0.01 seconds).

I'd like to keep the same (~) length, using both linear or exp (also considering to modulate/change shape in the middle of the cycle).

I guess that all I need is to change that mul factor (due to the position/delta/shape?!?!).
That's the question: how would you manage that mul?

It seems to me a nice way of easily generate CV signal, but I'd like to keep fixed the time of each cycle while changing the shape.

Thanks guys, as usual!

[sault]

The first thing I see is that you never have a fully exponential shape because of the 0.9 * shape in the shapeDelta function... but no, changing mul won't help because mul is a linear operation and we need an exponential operation.

One way to calculate things might be

decay = exp( ln(target_val)/(srate*ms) );

In other words, for you

decay = exp( ln(0.001)/(srate*0.01) );

In the case of the srate being 44100 that gives us about 0.984458 which when raised to the 441st power is right about 0.001. So you need to have that e^x thing going on in there somewhere.