# 3.11 Changing the decision level

Again, using the interactive in Section 3.9 you will now look at changing the decision level.

The decision level is represented by the right-hand vertical edge of the grey area on the histogram display. Use the Decision level (V) slider to set the decision level midway between 0 and 1. You will have to judge its position by eye. Click on Apply to implement the decision level and look at the statistics.

## Activity 10

Allow about 5 minutes

1. Why are there are false detections?
2. Why are the detection rates (correct and false) practically the same for 0 and 1?

### Answer

1. The effect of noise is to take the signal occasionally over the decision level, so that a 0 is detected as a 1 and vice versa.
2. The percentages of correct and false detections are virtually the same for 0s and 1s because of the symmetry of the situation. The noise affects the 0s and 1s equally, and the decision level is symmetrically placed between 0 and 1.

The symmetrical arrangement that you have used so far, with the decision level halfway between the two binary symbols, is typical of much practical implementation of binary signal detection, but looking at an asymmetrical arrangement is instructive.

Use the Decision level (V) slider to place the decision level asymmetrically between 0 and 1 (that is, much closer to 1 than to 0, or vice versa), then click on Apply.

## Activity 11

Allow about 10 minutes

Explain, in general terms, the correct and false detection statistics that have resulted from your asymmetrical placement. You will not be able to give a precise account, but you might be able to explain the relative sizes of the statistics.

### Answer

You may have got something similar to Figure 34, with the decision level fairly close to 1.

Figure 34 Asymmetrical decision level

Because the decision level is so close to 1, noise-affected 0 signals very rarely go beyond the decision level. This is why false detections of 1 are at 0%, as this statistic reflects 0s that are wrongly detected as 1s. As there are no false detections of 0s, all detections of 0 must be correct, which is why correct detections of 0 are shown at 50%.

With the decision level close to 1, noise-affected 1s quite often drop below the decision level and are detected as 0s. This is why the false detection rate for 0 is relatively high, at almost 14%. Correspondingly, the correct detection rate for 1 is relatively low, at just above 36%. These two statistics add to approximately 50%.

Now you have explored how adding noise and changing the decision level affects the data signal, to end this course you will apply the FIR filter.

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