state transitions
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Estimating state transitions

Some sounds are changing slowly and some are changing rapidly. One standard way of estimating stationary is to compare the sound to its self (e.g., using autocorrelation matrix) and see how quickly the self similarity (100% at the diagonal by definition) dies as we move off the diagonal. 

SAP2 offers a similar procedure, but based on similarity across features. For each time point in a sound, we calculated how long the self-similarity holds. For example, starting from a  time point i, we move forward to time point i+1... until the similarity to i decrease to a certain threshold. Then the same procedure is repeated, but moving backward to time point  i-1...

We use MAD (median absolute deviation) as a yardstick for similarity across four features: pitch, FM, Wiener entropy and Goodness of pitch. The second parameter is how many time similarity should decrease below threshold before we say that the state has changed (namely, that the sound is no longer similar to its origin).

Note: one way of doing this procedure is by keeping the segmentation threshold so low that the entire sound is a "single syllable". If you do this, the estimates will include silences as a "state", namely, how long a silence last will be treated the same as how long a note self-similarity lasts. If you do segment the sound (as you probably do by default) then silences will not count and will be marked as zeros (you should then treat those zeros as undefined).

How to:

Start SAP2 in "Explore & Score" and open a sound in Sound 1. Go to "segmented comparisons" and observe the "period of repetition" control:

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The parameter "state transition threshold" determines the difference between sound time windows in units of MADs that indicates a state transition. The "# mismatches to reject" is by default 5 mismatches (in each direction). Click Calc Durations and SAP2 will show you the results in the "note duration" window.

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Each number is the duration of a state, and the numbers are 1ms apart by default, or as determined by the "advance window" parameter of the spectral analysis.

Now select all the numbers and cut them (ctrl-c) and paste them to Excel (ctrl-v). plotting the graph might look like this for a zebra finch song.
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And here is a bengalese finch song example:

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