Finding islands of zeros in a sequence

Question

Imagine you have a very long sequence. What is the most efficient way of finding the intervals where the sequence is all zeros (or more precisely the sequence drops to near-

Answer 1

These are the steps I would take to solve your problem in a vectorized way, starting with a given vector sig:

• First, threshold the vector to get a vector tsig of zeros and ones (zeroes where the absolute value of the signal drops close enough to zero, ones elsewhere):

  tsig = (abs(sig) >= eps);  %# Using eps as the threshold
  

• Next, find the starting indices, ending indices, and duration of each string of zeroes using the functions DIFF and FIND:

  dsig = diff([1 tsig 1]);
  startIndex = find(dsig < 0);
  endIndex = find(dsig > 0)-1;
  duration = endIndex-startIndex+1;
  

• Then, find the strings of zeroes with a duration greater than or equal to some value (such as 3, from your example):

  stringIndex = (duration >= 3);
  startIndex = startIndex(stringIndex);
  endIndex = endIndex(stringIndex);
  

• Finally, use the method from my answer to the linked question to generate your final set of indices:

  indices = zeros(1,max(endIndex)+1);
  indices(startIndex) = 1;
  indices(endIndex+1) = indices(endIndex+1)-1;
  indices = find(cumsum(indices));