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# 3.12 Applying the FIR filter

Use the Decision level (V) slider to return the decision level to midway between 0 and 1, then click on Apply. Confirm that the statistics are as would be expected; that is, correct detections of 1s and 0s are at approximately the same percentage. The correct detection percentages do not need to be identical, but try to get them to within about 1% of each other by adjusting the detection level.

You are now going to apply the FIR filter. In the top right zone, set the FIR filter width (number of samples) slider by eye to around 30–40 samples, then click on Apply.

## Activity 12

Allow about 5 minutes

1. Compare the top right zone (histogram and statistics before filtering) to the bottom right zone (histogram and statistics after filtering). What effect has the filter had on the statistics for correct detection?
2. Explain any difference in detection statistics between those beneath the unfiltered signal and those beneath the filtered signal.

### Answer

1. The filter increases the correct detection rate.
2. The filter reduces the spread of values around the mean, which is shown by the fact that the histogram peaks are narrower than in the unfiltered histogram. The reduced spread of values reduces the probability of sample values crossing the decision level.

Some points to consider as a result of your work with the FIR filter interactive resource are as follows:

- Noise causes the actual voltages for 1s and 0s to be distributed around the intended voltage.
- The distribution of voltages can cause errors when, for example, the voltage representing a 1 is closer to 0 than to 1.
- The wider the distribution (that is, the noisier the signal), the more likely errors become.
- Filtering can reduce the width of the distribution of voltages, thereby reducing the error rate.

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