Gesture Signal Processing

Filtering

While studying sensors, we discovered that often a particular sensor will measure the position x, velocity v, or acceleration a of an object. However, we might like to use a different variable to control the way we synthesize sound. Ideally, integration and differentiation can be applied to convert between variables.

We can approximate integration and differentiation by using digital filters. Let q be the input signal and p be the output signal.

Here is a simple approximation of an integrator. We see that with each time step, p_intgr is updated to be nearly the same as the previous p_intgr, but it is affected by the input q.

p<sub>intgr</sub> = 0.1*q + 0.9*p<sub>intgr</sub>;

example of lp filter

Next we show how to approximate a differentiator. The extra variable r is introduced to represent the previous input value.

p<sub>diff</sub>[n] = q[n] - q[n-1]

example of hp filter

book on simple filter design