Gesture Signal Processing

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Next we show how to approximate a differentiator, so now '''x''' represents a measured position, and '''v''' represents velocity (although the result is scaled by a constant).  The extra variable '''r''' is introduced to represent the previous position measurement.  Hence, the estimated velocity is the difference between the current position and the previous position.  This filter is an example of a high-pass filter because it passes mainly high frequencies.
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Next we show how to approximate a differentiator, so now '''x''' represents a measured position, and '''v''' represents velocity (although the result is scaled by a constant).  The extra variable '''r''' is introduced to represent the previous position measurement.  This is an example of a high-pass filter because it passes mainly high frequencies.
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<pre>
<pre>
v = x - r;
v = x - r;

Revision as of 16:45, 10 October 2008

Interpolation

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.

Image:variables.png


Here is a simple approximation of an integrator. In this case, we integrate an acceleration measurement in order to obtain velocity. We see that with each time step, v is updated to be nearly the same as the previous v, but it is affected by the input a. This is an example of a low-pass filter because the filter passes mainly low frequencies.

v = 0.1*a + 0.9*v;


Next we show how to approximate a differentiator, so now x represents a measured position, and v represents velocity (although the result is scaled by a constant). The extra variable r is introduced to represent the previous position measurement. Hence, the estimated velocity is the difference between the current position and the previous position. This filter is an example of a high-pass filter because it passes mainly high frequencies.

v = x - r;
r = x;

Filter design is an important part of the field of signal processing. For more details, see Julius Smith's book on simple filter design.

Thresholding

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