CAPT OF A SAAB 340 SF34 DSNDED TOO EARLY OUTSIDE THE FAF CAUSING ATC TO ADVISE OF A LOW ALT ALERT.

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ON THE FINAL VECTOR FOR THE APCH WE WERE VECTORED THROUGH THE FINAL APCH COURSE. WE NOTIFIED ATC AND THEY GAVE ANOTHER VECTOR TO INTERCEPT. WE INTERCEPTED AND RPTED ESTABLISHED; ATC THEN CLRED US FOR THE APCH AND GAVE US OUR DISTANCE TO DELFA (FAF) AS 5 MI. I THEN DSNDED TO 2200 FT MSL AND AS WE LEVELED AT 2200 FT; SET 1200 FT (60 FT ABOVE MDA) INTO OUR ALT ALERTER. WHEN WE IMPROPERLY IDENTED DELFA; AS THE 290 DEG RADIAL CTRED (BUT DME STILL READ APPROX 15 MI); I BEGAN MY TIME AND DSCNT TO MDA. I GOT JUST ABOUT 200 FT ABOVE MDA (1400 FT) WHEN ATC ADVISED US HE HAD A LOW ALT ALERT ON US. I IMMEDIATELY STARTED TO CLB BACK TO 2200 FT WHEN I CLBED ABOUT 400-500 FT. THE CTLR RADAR IDENTED DELFA AND I BEGAN A DSCNT AGAIN TO MDA. WE BROKE OUT OF THE CLOUDS AT APPROX 700 FT AGL AND GOT THE RWY IN SIGHT AND LANDED WITHOUT INCIDENT. I'M NOT SURE WHETHER WE WERE NOT GETTING ACCURATE DME DATA OR THE CTLR WAS; BUT THERE WAS DEFINITELY CONFUSION OVER OUR DISTANCE TO DELFA BECAUSE HE (ATC) INITIALLY GAVE US 5 MI TO DELFA; AT LEAST A 1.5 - 2.5 MINS HAD PASSED (SINCE HIS RPT OF 5 MI) BEFORE WE IDENTED DELFA (WITH THE XRADIAL (290 DEGS) CTRED) AND BEGAN OUR DSCNT. WHEN HE GAVE US THE LOW ALT ALERT HE TOLD US WE WERE STILL 2-3 MI FROM DELFA; WHICH GIVEN OUR AIRSPD AND WIND DIDN'T QUITE MAKE SENSE TO ME. FACTORS AFFECTING THIS MIGHT HAVE BEEN THE LACK OF CLR ATC COM AND IMPROPER PROCS TO IDENT DELFA BY US. WE SHOULD HAVE WAITED FOR THE NEEDLE TO CTR AND THE DME TO REACH 12.9 MI; BUT EVEN THE FACT THAT WE DIDN'T USE THE DME; I DON'T BELIEVE WE COULD HAVE BEEN THAT FAR OFF. WE INFORMED ATC TO CHK THE APCH TO MAKE SURE THE VOR AND DME AND RADAR WERE OPERATING PROPERLY. I THINK I STARTED MY DSCNT SLIGHTLY EARLY BUT NOT NEARLY AS MUCH AS ATC RPTED (2-3 MI FROM DELFA AFTER I HAD ALREADY DSNDED 800 FT). THE WX WAS ALSO VERY TURBULENT AND WINDY AND RAINING WHICH MAY HAVE AFFECTED THE INCIDENT.