Phase unwrapping

Question

I am facing a problem in unwrapping a phase. I have a data set presented by $a_i$, where $i$ varies from $1$ to $N$. I need it as follows:

• If $\mathrm{abs}(a_{i+1} - a_i) > 3$, add $6 k \,$ to $a_{i+1}$, otherwise return $a_{i+1}$. If $a_{i+1} > a_i$ for the first time, $k = -1$, otherwise $k = 1$.

• For every time $\mathrm{abs}(a_{i+1} - a_i) > 3$ and $a_{i+1} > a_i$, $k \to k + 1$ otherwise $k \to k - 1$.

  For example, the first time $\mathrm{abs}(a_{i+1} - a_i) > 3$, add $6$ if $a_{i+1} > a_i$. For the second time $\mathrm{abs}(a_{i+1} - a_i) > 3$, add $12$ if $a_{i+1} > a_i$. And for third time, if $a_{i+1} < a_i$, add $6$ not $18$.

So, can anyone please help me to write the code in Mathematica for the above logic. I am getting stuck. And thank you in adv. for the help.

Answer 1

a = {1.1, 1.3, 7.5, 1.4, 13.2};

FoldList[Plus, a[[1]], Mod[Differences[a], 6, -3]]

(*    {1.1, 1.3, 1.5, 1.4, 1.2}    *)

If and For are not ideal; better do list processing.