Consider now that we have a channel which is discrete, and in fact, binary - i.e. the value at each time frame is either T (true) or F (false); for example, the Blues and Reds domain as shown in table 4.2. Also assume that we know from our background knowledge that most of the time, the value is likely to be false - and that times when the value is true are very important. For example, this may be an indication of the failure of some sensor. So the types of events we may be interested in is events where the value goes from F to T.
In this case, the parameters would be:
In this case, it is easy to define our finding function
(Note the above is a little simplified and does not take into account the possibility of the sequence starting with a T or ending with a T).
So, for example, consider channel c from Stream 2 from table
4.2. Applying the function f to the channel will
give us the set
.
These examples should serve to illustrate the general concepts of PEPs. It is also important to note that we need not, in a given domain, restrict ourselves to a single PEP, or analyse a channel with one PEP alone. In addition to the above, we could use other means as well. For example, we could apply a wavelet transform and pick the most significant coefficients of the wavelet transform and express them in terms of parameters. We could have a local maximum PEP as well, which is parametrised as the time of the maximum, the value of the maximum and the values and times of the nearest minima either side of the maximum. In fact we could have all of these simultaneously.