3 CORDIC FP GA 2 L FM x ( t) = exp ( j2 f 0 t + j t 2 ) + ( t), f 0,, ( t) I ( t) Q( t), x ( t) ( t) : ( t) = arcta, x ( t) f ( t) : Q( t) I ( t) f (

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1 : (2007) CORDIC FP GA ( ) FP GA CORDIC ( Coordiate Rotatio Digital Comp uter) CORDIC,FP GA CORDIC,XIL INX CORDIC IPCore FP GA, CORDIC :CORDIC ; ; FP GA ; : TP :A A Method of Digital Frequecy Discrimiatio Based o CORD IC Algorithm ad Its Implemetatio i FPGA Yu Jiayu, L uo Digli, Cheg Mao ( X i a Elect roic Egi eeri g Research I stit ute, X i a ) Abstract : This paper preset s a met hod of digital f requecy discrimiatio based o CORDIC (Coordi2 ate Rotatio Digital Comp uter) algorit hm which is suitable to be implemeted i FP GA. The priciple of digital p hase discrimiatio ad first - order differetial digital frequecy discrimiatio usig CORDIC al2 gorithm is discussed, ad t he pipelie struct ure ad iteratio struct ure for applicatio of CORDIC algo2 rit hm i FP GA are give out. Compariso of it wit h source usage by CORDIC IPCore provided i XIL IN X ad FP GA simulatios show t hat digital f requercy discrimiatio usig iteratio struct ure ad first - order differetial based o CORD IC algorit hm is efficiet ad feasible. Keywords :CORDIC algorit hm ; digital f requecy discrimiatio ; FP GA ; istataeous frequecy 1,,,,, I Q, Wiger - Ville FP GA, 3 :

2 3 CORDIC FP GA 2 L FM x ( t) = exp ( j2 f 0 t + j t 2 ) + ( t), f 0,, ( t) I ( t) Q( t), x ( t) ( t) : ( t) = arcta, x ( t) f ( t) : Q( t) I ( t) f ( t) = 1 d ( t) 2dt ( t),i Q 1, :,ROM CORDIC,, CORDIC 3 CORDIC CORDIC J. Volder 1959,, CORDIC CORDIC i, : = - 3 i, V i di i di { - 1,1} = [ xi, yi ] T, V i = ri i = 90,= 1, : Y2 X2 = r1 si ( 1 + d1 90 ) = d1 X = r1 cos ( 1 + d1 90 ) = - d1 Y1,, : i = tg ( i- 2) i > 1, :, Y i Y i+1 = ( i- 2) ri si ( i + di i ) = Y i + di X i2 X i+1 = ( i- 2) ri cos ( i + di i ) = X i - di Y i2 = ri si i, X i - ( i- 2) - ( i- 2) = ri cos i, di i,: di = 1 Y i < 0-1 Y i 0 3 i Y i < 0,, Y i 0,, Y 0 ( ), Zi+1 i (i ), : Zi+1 = Zi + di i, Y 0,Z = + di i = 0, = arcta Y1 X1 = - di i, 37

3 V 1 CORDIC i, ( ) CORDIC -,CORDIC,,, 4 f ( ) ( ) : f ( ) = ( ) - ( - 1) TS TS, CORDIC,CORDIC, 4 ( - 1) = 5 / 6, ( ) = - 5 / 6, ( ) - ( - 1) = - 5 / 3, - 5 / 3 + 2= / 3 5 ( - 1) = / 6, ( ) = - / 6, ( ) - ( - 1) = - / 3, - / 3 + 2= 5 / ,, ( t), : ( t) = KFM t f ( 0 ) d KFM, f ( t), : ( ) = KFM ( f [ ( i - 1) TS ] TS ) TS,: ( ) - ( - 1) = KFM f [ ( - 1) TS ] TS TS,f [ ( - 1) TS ] TS,TS,, TS, ( ) - ( - 1), 47,: ( ) - ( - 1) + 2 ( - 1) > 0, ( ) - ( - 1) < - ( ) = ( ) - ( - 1) - 2 ( - 1) < 0, ( ) - ( - 1) > ( ) - ( - 1) else : x ( ) = exp [ - j( T S ) 2 ], TS = 1 f S = Hz, = B T

4 3 CORDIC FP GA Hz = s,( - T 2 T 2 ) 6, ( b) f ( ) 6 MA TL AB 5 CORDIC FP GA CORDIC 7 8, - 1,,,, x1 y1 16, 22,32 ( 2 28 ) 9 10 XIL IN XVirtex4 FP GA 7 7 1,3, 6,8 7 CORDIC, 7 7, , XIL INX CORDIC IPCore 11,,, 57

5 CORDIC , CORDIC 67

6 3 CORDIC FP GA 11 XIL IN X CORDIC IPCore CORDIC IPCore Slice Flip Flop s iput L U Ts Total equivalet gate , 12, 12 Aldec 6 FP GA,CORDIC, XIL INX CORDIC IPCore, CORDIC,, (100 ) 77

7 ,T1 T2,, V4 V5,TVS, 3,,,,, : [1 ],,[ M ]. :,1985. [2 ],[ C].,2004. [ 3 ] Walter F. J. Crewso etal. Solid2State 2kV,250k Hz Grid Modulator for Travelig2Wave Tubes[ C]. IEEE Co f. Record,2000. [4 ],[J ].,2005, (3). [5 ] P T KWR [ M ]. IFI,2003. (77 ) : [1 ] Volder,J. The CORDIC Trigoometric Comp utig Techique [J ]. IRE Tras. Electroic Comp u2 tig, 1959,EC - 8 : [ 2 ] Ray Adraka. A survey of CORDIC algorit hms for FP GA based comp uters[ C]. Adraka Cosultig Group, Ic [3 ] (),. FP GA [ M ]. :,2002. [4 ]. CORDIC [J ].,2003,19 (1) : [5 ]. [J ].,2003, (23). 001