I am in uncertain territory when it comes to republishing other peoples work... so I would refer questions about the Modified Optimum Elliptic Filter itself to John Ehlers own published works... I listed the source I originally used in the header of the indicator code.

The formula is:

Modified Optimum Elliptic Filter and Detrender
{Ehlers TASC Jul 00, p. 29}
P1:=(H+L)/2;
V1:=P1 + 0.088*Ref(PREV,-5);
V2:=ROC(V1,6,$) + 1.2*Ref(PREV,-5) - 0.7*Ref(PREV,-11);
D1:=Ref(V2,-12) - (2*Ref(V2,-6))+V2;

S1:=0.13785*(2*D1-Ref(D1,-1))+0.0007*(2*Ref(D1,-1)-
Ref(D1,-2))+0.13785*(2*Ref(D1,-2)-
Ref(D1,-3))+(1.2103*PREV)-(0.4867*Ref(PREV,-1));

S2:=0.13785*(2*S1-Ref(S1,-1))+0.0007*(2*Ref(S1,-1)-
Ref(S1,-2))+0.13785*(2*Ref(S1,-2)-
Ref(S1,-3))+1.2103*PREV-0.4867*Ref(PREV,-1);
S1;
S2

An article particularly directed to explaining the formulas used in the Eliptical filter would be "THE JOY OF DETRENDING III" By John Ehlers which is available on the internet... just google it, and you can instantly have a personal copy in MS Word format which includes formulas, chart photos... everything you could possibly need to understand John's fine work.

As to the question about EMA or SMA... moving averages per se, are not used... it is more of a mathematical smoothing technique, and fully explained by John himself... I just try to code things.

Yes, this is a short period that this indicator produces... I am only phase shifting to obtain a crossing, useful for an EA, or as source for an alert.

I have found this indicator to be useful, much like Ehler's Instantaneous Trendline... it is something very fast, reliable, and holds a trend better than a moving average... less whipsawing. This indicator does not hold the trend as long as Ehler's Instantaneous trendline does... and there can be differing reasons for either holding or not holding on to a potential trend... the longer you try to, the more likely prices can reverse. That is why I like this indicator... it holds a minimal trend, has the direction right, and is very stable. To the extent the market flatten's out on it, it provides good trend till it goes flat, and the flat price action is easily filtered out. That is why I think it is probably most useful as an input for an EA, but could also on longer timeframes be coupled with an alert for manual trading input.

Anyway, it is a pleasure to contribute anything helpful. Thanks for kind replies.