eCall AutoCorellate Sketch - Figure 14: Autocorrelation properties of pulse sequence of Figure 10 

ref: ts_126267v120000p.pdf
3GPP TS 26.267 version 12.0.0 Release 12 2 ETSI TS 126 267 V12.0.0 (2014-10)
5.1.6 Synchronization signal and frame format

The synchronization frame consists of the direct concatenation of:
  1) the synchronization tone st (n) ; and
  2) the synchronization preamble s p (n) .
Note that the synchronization preamble is not only used in the synchronization frame,
but fragments thereof are also inserted into the MSD data frame for the purpose of synchronization tracking.

The synchronization tone st (n) consists of a sampled sinusoidal tone of frequency 500 Hz or 800 Hz, and of 64 ms duration.

A frequency of 500 Hz is chosen to indicate that the fast modulator mode is to be applied
and a frequency of 800 Hz indicates that the robust modulator mode is used for the subsequent MSD frames.
This page is a sketch to calculate the auto correlation of the red sequence to the green sequence to produce the blue Autocorrelation and plots it.

The red sequence is slid past the green sequence, sample by sample and the sum of the products is calculated using the function below.

For eCall the green sequence has the 5 copies of the red sequence, but the first and last are inverted. When the red sequence is found in the green sequence we see a blue spike. We should see 5 blue spikes.

The blue trace is: "Figure 14: Autocorrelation properties of pulse sequence of Figure 10"

function autoCorrelate( n ){
  var sum = 0;
  for ( var i = 0; i <  sync2A.length ; i++ ){
    sum += sync2A[ i ]*1 * longSync3A[ i+n ]*1
  }
  return ""+sum
}
When the red sequence is found in the green sequence there is a big blue spike!

Auto Corellation of Preamble. 

Result:
----+-+--++-++++-+-++--+---++++-+-++--+---++++-+-++--+----+-+--++-+++
0,0,0,0,1,2,3,2,1,2,-1,2,-1,0,-1,-2,-1,0,-15,-1,-1,-3,1,-3,-1,1,1,3,1,-1,15,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,15,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,15,1,1,3,-1,3,1,-1,-1,-3,-1,1,-15,0,-1,-2,-1,0,-1,2,-1,2,1,2,3,2,1,0,0,