FLC OF A GULFSTREAM G4 FAILED TO FOLLOW ATC CLRNC AFTER HAVING TROUBLE HEARING THE EXACT CLRNC FIXES DUE TO POOR XMISSION AND PHRASEOLOGY BY ATC. ATC INTERVENED AND NOTED THAT THEY WERE OFF COURSE; BUT CHANGED THE CLRNC TO COINCIDE WITH WHAT THE RPTR BELIEVED TO BE THE CLRNC.

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WHILE FLYING THE ROKIT ONE (ROKIT.ROKIT1) ARR INTO HOU WE WERE ISSUED A CLRNC THAT WE WERE UNABLE TO UNDERSTAND DUE TO THE POOR AUDIO AND XMISSION QUALITY OF THE CTLR. WE ASKED FOR A REPEAT OF THE CLRNC AND AGAIN FOUND IT TOUGH TO DECIPHER WHAT WAS BEING SAID -- WE THOUGHT HE HAD CLRED US DIRECT DRXLR INTXN AND THEN A 300 DEG HDG FOR VECTORS. WE ASKED A THIRD TIME FOR THE CLRNC TO BE REPEATED AND THE RESPONSE WAS 'DRXLR -- LIKE THE BASKETBALL PLAYER -- THEN A 300 DEG HDG.' WE READ BACK 'DIRECT DRXLR THEN 300 DEGS FOR VECTORS.' AFTER WE BEGAN TOWARDS DRXLR THE CTLR CAME BACK AND ADVISED WE WERE S OF COURSE. I ADVISED THAT WE WERE PROCEEDING DIRECT TO DRXLR AND THAT OUR UNDERSTANDING WAS THAT WE WERE CLRED DIRECT DRXLR; THEN 300 DEGS FOR VECTORS. WE WERE ADVISED THAT THE CLRNC WAS MRPHY THEN DRXLR AND THAT 'THAT'S ALL RIGHT; CONTINUE.' THERE WERE 3 PLTS IN THE COCKPIT -- WE ALL 3 FELT THAT THE CLRNC WAS DIRECT TO DRXLR FOLLOWED BY A 300 DEG HDG. WE ASKED 3 TIMES FOR CLARIFICATION OF THE CLRNC AND FELT WE HAD IT CORRECTLY BEFORE PROCEEDING DIRECT TO DRXLR. FOR WHATEVER REASON THE CTLR WAS HARD TO UNDERSTAND -- POOR AUDIO; POOR ANNUNCIATION; FAST PACE; ACCENT; NON STANDARD PHRASEOLOGY MAY HAVE CONTRIBUTED; I DON'T KNOW. WE HAVE BEEN TAUGHT TO ALWAYS GET CLARIFICATION IF UNSURE OF ANY CLRNC -- WE FELT THAT WE HAD SATISFIED THIS REQUIREMENT AND WERE NOT QUESTIONED AS TO OUR READBACK. WE CONTINUED WITHOUT FURTHER COMMENT FROM THE APCH CTLR.