How to find the period of two overlapping series of pulses ?

I have two series of pulses of the same amplitude but one has a period of 3 seconds and the other a period of 4 seconds.

As a result of have the pulses at the following times:

0, 3, 4, 6, 8, 9, 12, 15, 16, 18, 20, 21 etc

Is there a way to get Matlab to determine the two periods i.e. 3 seconds and 4 seconds ? I used Matlab a long, long time ago (over 20 years, sheesh !) and I'll looking to use if for a personal project. I've got the DSP and Signal Processing toolboxes.

And is the method scalable so that it can more series (possibly up to 10) ?

Thanks in advance

Answer 1

[Samatha Aleti]

Hi,

As per my understanding you are trying to find at what different increments(least possible) the sequence is generated. You can find this by taking a range of numbers and checking if the sequence contains all its multiples according to the sequence length. Here is a sample code:

x = [0, 3, 4, 6, 8, 9, 12, 15, 16, 18, 20, 21]; 
Range = [1:10]'; % Range 
period = zeros(length(Range),1); % Initialize output value
startSeq = 0; % Starting number of sequence
for i = 1:length(Range) 
    % Check if this number is already included or counted in other series
   if ~any((mod(Range(i), period(period>0)) == 0))
     series = x(rem(x, Range(i)) == 0); % All multiples present in the sequence
     l = length(series); 
     if l > 1 
        mul = Range(i) * [startSeq:l-1];  
        if all(ismember(mul,series)) % Check if all multiples are present in the sequence
          period(i) = Range(i); 
        end 
     end  
   end
end 
period = period(period>0) 

Also, following are some similar functions that you can refer:

“seqperiod” to find the period of repeating sequence

“pulseperiod” to find period of bilevel pulse