Gesture Signal Processing

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(Filtering)
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We can approximate integration and differentiation by using digital filters.  Let '''q''' be the input signal and '''p''' be the output signal. 
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Simple integrator:
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Here is a simple approximation of an integrator.  We see that with each time step, '''p<sub>intgr</sub>''' is updated to be nearly the same as the previous '''p<sub>intgr</sub>''', but it is affected by the input '''q'''.
<pre>
<pre>
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y[n] = 0.1*x[n] + 0.9*y[n-1]
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p<sub>intgr</sub> = 0.1*q + 0.9*p<sub>intgr</sub>;
</pre>
</pre>
example of lp filter
example of lp filter
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Simple differentiator:
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Next we show how to approximate a differentiator.  The extra variable '''r''' is introduced to represent the previous input value.
<pre>
<pre>
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y[n] = x[n] - x[n-1]
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p<sub>diff</sub>[n] = q[n] - q[n-1]
</pre>
</pre>
example of hp filter
example of hp filter
[http://ccrma.stanford.edu/~jos/filters/ book on simple filter design]
[http://ccrma.stanford.edu/~jos/filters/ book on simple filter design]
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== Thresholding ==
== Thresholding ==

Revision as of 17:38, 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

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, pintgr is updated to be nearly the same as the previous pintgr, 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

Thresholding

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