I have a binary time series with some ASK modulated signals in different frequencies inside of it.
Let's say it's something like this: x = [0,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0, ...]
What's matter to me is having all the '1' and '0' in an interval of 4 samples or more, but sometimes the '0' and '1' change places like this: x1 = [0,0,0,1,1,1,1,1] when it had to be x2 = [0,0,0,0,1,1,1,1]
And there's also some noise as spikes as seen in n1 = [0,0,0,0,0,0,1,1,0,0,0,0,0] when it should be only zeros.
I've already tried moving average and it introduced a lag to the signal that was't good for my application.
Do you have some advices about signal processing on binary time series?