FILTERING

An unfiltered input of the IR sensor is given below. A button was pressed when the user intended to flex.

MOVING AVERAGE

Initially, we used a moving average filter - a DSP tool given to us in class. The intended purpose was to keep the flexing inputs while smoothing out the noise. Since we want to detect flexing ‘online’ or real time, the moving average filter also had to be a causal system. Therefore, the average only took values at or before index n.

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The moving average equation was of the following form:

MOVING AVERAGE EFFECTS

Below shows the original signal filtered by different moving averages, which vary in their span - how many data points they average together.
It interested us to to find that the moving average acts very similarly to a low pass filter.

DISADVANTAGES OF MOVING AVERAGE

Some disadvantages with this type of moving avg filter is as follows: The more indices you use for the average filter the smoother the signal, but also the more attenuated the flexing signal is. Since we don’t want to reduce the desired signal, this is not ideal, because it reduces the signal when we are trying to reduce the noise.

Also, a negative effect as you can see is that the filtered signal is delayed from the original signal. Including more past indices makes the filtered output more delayed. This is an effect of using a causal system.

EXPONENTIAL MOVING AVERAGE

The next method we tested for filtering was the Exponential moving average. One benefit of using this type of filtering is it uses a recursive formula, which is faster computation wise on the microcontroller. As you can see in the formula below, the filtered output (denoted by x bar) only depends on the previous filtered output and the current input. The weights associated with each can be adjusted with the forgetting factor - or lambda - to fine tune the effect of the filter. Another benefit of this filter is it can better preserve the features we want to keep in the signal. In our case, we used a lambda of .5 - which corresponds to the graph in the middle. We found it gets rid of some of the low level noise without affecting the main dips too much.

With the first Weight W = 1;

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In Matlab we can use the function:   dsp.MovingAverage('Method','Exponential weighting','ForgettingFactor',value); to create an Exponentially weighted moving average.

The Exponential Weighting filter has many benefits: Since it is a recursive definition and only depends on the current input and last weighted input, there is less processing that needs to take place within the controller. Along with that, the weighted nature of the algorithm will allow us to adjust the impact of the old data vs new incoming data and therefore try to not attenuate the signal we desire to keep.

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Below, we have filtered outputs with two different forgetting factors of .5 and .85 respectively, along with the original signal to compare to. 

As you can see, as the forgetting factor increases, the more attenuated the noise is. At a forgetting factor of .5, the Exponential weighting method is good about keeping the flexing dips in the signal while still smoothing out the data

We can use the filter(b,a,x) function in Matlab, with a = [1], b = [1/k]/sum(1/k) for integers 1<k<5  in to apply the LCCDE as a filter and get the following result:

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        OUR CHOICE OF FILTER

Weighted sum seems to not do as good of a job as Exponential Weighting to keep the flexing dips, but does a better job of removing noise than the standard moving average.

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Looking at all the options, it looks like exponential weighting at a forgetting factor of .5 is the best method to use. It will be nearly impossible to get rid of all the noise, but it does a good job of smoothing out the curve and keeping the flexing dips that we desire.

To incorporate the exponential weighting filter into arduino or another multicontroller, it is fairly simple.