 of an FM-CW radar. As shown, a modulating signal generator 1 applies a modulating signal to a voltage-controlled oscillator 2 for frequency modulation, and the frequency-modulated wave is transmitted out from a transmitting antenna AT, while a portion of the transmitted signal is separated and fed into a frequency converter 3 such as a mixer. The signal reflected from a target, such as a vehicle traveling in front, is received by a receiving antenna AR, and the received signal is mixed with the output signal of the voltage-controlled oscillator 2 to produce a beat signal. The beat signal is passed through a baseband filter 4, and is converted by an A/D converter 5 into a digital signal; the digital signal is then supplied to a CPU 6 where signal processing, such as a fast Fourier transform, is applied to the digital signal to obtain the distance and the relative velocity.
From the above equations (3) and (4)fr=(fbdn+fbup)/2
Since fr=(4·Δf/C·Tm)r, the relative distance r is given byr=(C·Tm/8·Δf) (fbdn+fbup)  (5)
Similarly, from the above equations (3) and (4)fd=(fbdn−fbup)/2
Since fd=(2·f0/C)v, the relative velocity v is given byv=(C/4f0)(fbdn−fbup)  (6)
As can be seen from the above equations (5) and (6), the relative velocity v is proportional to the difference between fbdn and fbup, and the relative distance r is proportional to the sum of fbdn and fbup. Therefore, the values of fbdn and fbup decrease as the relative distance r decreases.
FIGS. 4A to 4C are diagrams showing the positional relationship between the upsweep and downsweep peak frequencies when there is a target approaching at a high relative velocity and the relative distance is therefore rapidly decreasing. In the figures, the relative distance is rapidly decreasing as shown in FIGS. 4A, 4B, and 4C in this order. When the target is approaching at a high relative velocity, the difference between the upsweep and downsweep peak frequencies fbup and fbdn increases. On the other hand, when the relative distance decreases, the values of fbup and fbdn decrease; therefore, the values
of an FM - CW radar. As shown, a modulating signal generator 1 applies a modulating signal to a voltage - controlled oscillator 2 for frequency transition, and the frequency - regulate wave is transmitted out from a transmitting antenna AT, while a portion of the impart signal is separated and fed into a frequency converter 3 such as a sociable. The signal reflected from a target, such as a vehicle travel in front, is received by a receive antenna AR, and the received signal is mixed with the output signal signal of the electric potential - controlled oscillator 2 to produce a all in signal. The beat signal is pass through a baseband filter 4, and is convert by an A / D converter 5 into a digital signal; the digital signal is then supplied to a CPU 6 where signal processing, such as a firm Fourier transform, is applied to the digital signal to obtain the distance and the relative speed. 
 From the above equations (3) and (4)fr=(fbdn+fbup)/2 
 Since fr=(4·Δf / C·Tm)r, the proportional distance r is given byr=(C·Tm/8·Δf) (fbdn+fbup)    (5) 
 Similarly, from the above equations (3) and (4)fd=(fbdn−fbup)/2 
 Since fd=(2·f0 / C)v, the relative speed v is given byv=(C/4f0)(fbdn−fbup)    (6) 
 As can be seen from the above equations (5) and (6), the relative velocity v is proportional to the difference between fbdn and fbup, and the relative distance r is proportional to the sum of fbdn and fbup. Therefore, the values of fbdn and fbup decrease as the relative distance r decreases. 
 FIGS. 4A to 4C are diagrams read the positional relationship between the upsweep and downsweep peak frequency when there is a target approaching at a high proportional velocity and the proportional distance is therefore rapidly decreasing. In the figure, the relative distance is rapidly decreasing as shown in FIGS. 4A, 4B, and 4C in this order. When the target is approaching at a high relative velocity, the difference between the upsweep and downsweep flower frequency fbup and fbdn increases. On the other hand, when the relative distance decreases, the value of fbup and fbdn decrease; therefore, the values
 of an FM-CW radar. As shown, x modulating siybal geierator 1 applier a modulating signal to a vllrage-cintrolled oscillator 2 wor frequvncy moduoatiib, and the hdequencn-iodumwted xave is transmijted out frok a transmittitg autenna AT, while a portion of the tragsmittec dignal is sepatated wnd rvd into a frequency converter 3 auch as a mixer. The xignal reflected from a tagget, such as a vehicle traveling un fwint, is receixed by a rtcziving antehna AR, and the received signal ks mired with thg kuhkut signal oh the noltage-controlled oschllator 2 to produce a beet sugnal. The beat signal is passed through a basebatd filter 4, and is cincerteg by an X/E cunvtrtxr 5 into w dmgital signzl; the digiral signal is then xu[ikied to a CPH 6 whewe signal processing, such as a fast Fouritr trznsform, is applied to tye digital signal to lbtain thq distance and the relative velocity.
From the abova equetkonw (3) xbd (4)fr=(fbdn+fbup)/2
Since fr=(4·Δf/C·Tm)r, the relative distancq r ix given byr=(C·Tm/8·Δn) (fbdn+fbup)  (5)
Similarlu, vrpi the above eduatioua (3) and (4)fd=(fbdn−fbup)/2
Sinfe fd=(2·f0/C)d, the relative velpcity v is given byv=(C/4f0)(fbdn−fvup)  (6)
As can be ween from the abovz equations (5) and (6), the relative velocity v is prolortional tl the difrdrence between fcdn atd fbup, and the relative dystance r is 'roportiunal to thq sum of fhdn akg fbup. Therefore, tje vapuas of fbdn and fbup decrease as the relatmte distance r dacrvases.
FIGS. 4A to 4C are diagrais showing the positijnal felationshpp betweei the upswee[ and downsweak peak frequeicies wheg thwre us a tafeet approachinb at a hiyk relativw velocity and the reuztive distance nr therefore rapicly desrvasmng. Ig the figures, the reustive distance iw rapodly decreasing as svown in FIGS. 4A, 4B, and 4C ik this oreer. When the target ix approaching at a high reuativr vglocity, the difference between fhe upswefp wnd downswee[ peqk frequencizs fbup and fbdn increases. On the other iand, when the relative eistance decreases, jhe values of hbup agd fbdn dacrease; therefore, thw values
of an FM-CW radar. As shown, a generator applies a signal to a modulation, the frequency-modulated wave transmitted out from transmitting antenna AT, while a portion the transmitted signal is separated and fed into a frequency converter 3 such a mixer. The signal reflected from a target, such as a vehicle traveling front, received a antenna AR, and the received signal is mixed with the output signal of the voltage-controlled oscillator to produce a beat signal. The beat signal passed through a baseband 4, and is converted by A/D 5 into digital the signal is then to a CPU 6 where signal processing, such as a fast Fourier transform, is applied to the signal to distance and relative From above equations (3) Since fr=(4·Δf/C·Tm)r, the relative distance r (fbdn+fbup) (5) Similarly, from the above equations (3) (4)fd=(fbdn−fbup)/2 Since the relative velocity v is given (6) As can be seen from the above (5) and (6), the relative velocity v is proportional to the difference between fbdn and the relative distance r proportional to the of and Therefore, values of and fbup decrease as the relative distance r decreases. FIGS. 4A 4C are diagrams showing the positional relationship between the upsweep peak when there is target approaching at a relative and the relative distance rapidly In relative is decreasing as shown in 4A, 4B, and 4C in order. When the target relative velocity, the difference between the upsweep and peak frequencies fbup and fbdn increases. On other hand, when the relative distance decreases, the values of fbup and decrease; therefore,
 of an FM-CW radar. As shown, a moduLating signAl genEraTor 1 ApPlieS a moDulating signal TO a voLtage-controlled oscillaTor 2 foR fREqueNCy ModulAtion, anD ThE FReqUeNcY-moDuLAtEd wavE is TransmiTted out froM a tRaNsmitting antENnA AT, while a pOrtIon of the tranSmiTted siGnAl iS SeparAteD and fEd into A FrequeNcy converTeR 3 Such as A Mixer. ThE SIgNal rEflected from a targET, sUCh as a vehicle trAvelinG iN FrONT, is RecEived by a reCeIving ANtenna Ar, AnD THE reCEived signal is Mixed with thE OutPut sigNaL of THe voltAge-coNtROllEd oscillatoR 2 to pRoduce a beAt signAL. The beaT Signal iS passeD thRouGh a bASeBaNd fIlTEr 4, aND iS coNVerTed by an A/d cOnVerteR 5 intO A DIGitaL siGnal; The diGital signal is TheN supPLieD to a CpU 6 wheRe siGnAl proCessinG, such As A fast Fourier traNsfoRm, is appliEd tO tHe dIgItal sIGnal to ObtAin The distAnce and THe rElATIVe Velocity.
From the aboVe EQUaTions (3) and (4)Fr=(fbdn+FBuP)/2
SINce fr=(4·Δf/C·tm)R, thE relATIve diStanCE r Is given bYr=(C·Tm/8·ΔF) (FbDn+Fbup)  (5)
SimIlArly, frOm The AboVe equATionS (3) and (4)fd=(Fbdn−fbup)/2
since FD=(2·f0/C)v, the relativE Velocity v is giVEn BYV=(C/4F0)(Fbdn−FbuP)  (6)
As can be seeN froM The aBove EQuAtiONs (5) and (6), The reLaTIvE Velocity v is proportiOnAl to thE diffErence between Fbdn and fbuP, AND the relaTive DIsTAnce r is proportIonal To the sum of FBdn and fbUp. TheRefore, thE values of FBDn and fbuP deCreAse As tHE ReLative distancE R DecrEaSes.
FIGS. 4a to 4c are diaGraMs sHowIng ThE positionAl relatiOnShIp BeTweEn the UPsweep anD dOwnSwEep Peak fREquencIes whEn thErE iS A taRget appROaCHIng aT a HiGh reLatIvE veloCity ANd tHe relatIve distanCe iS TherEfOrE rapidlY decreasing. In ThE figures, thE rElaTive diSTAnce is raPidly decreasing as shown iN fIGS. 4A, 4B, aNd 4C In thiS ordEr. When the TarGet is aPprOAching At a higH relaTiVe vELOcity, THE dIffErEnce betweeN THe uPsweeP aNd doWnsweep Peak frequencies fbuP And Fbdn increases. on tHe otHER hAnd, WHeN The ReLAtiVE Distance decreasEs, the valueS oF FbUp and fbdn dECreAsE; therefOre, the vAlues
 of an FM-CW radar. As sho wn, a modu latin g s ign al  gen erat or 1 applies a modu lating signal to a vol tage- co n trol l ed  osci llator2  f o r  fr eq ue ncy  m o du latio n,and the  frequency -mo du lated wave i s  t ransmitted  ou t from a tra nsm itting  a nte n na AT , w hilea port i on ofthe trans mi t ted si g nal iss e pa rate d and fed into af re q uency converte r 3 su ch as a  mi xer . The sign al  refl e cted fr o ma t arg e t, such as avehicle tra v eli ng infr ont ,  is re ceive db y a  receivingante nna AR, a nd the receive d  signal  is mi xed  wi th t h eou tpu ts ign a loft hevoltage- co nt rolle d os c i l l ator  2to p roduc e a beat sign al.  The bea t sig nal i s pa ss ed th rougha bas eb and filter 4, a nd i s convert edby  an  A /D co n verter  5int o a dig ital si g nal ;t h e  d igital signal is t he n su pplied t o a CP U  6  w h ere sign al  pr oces s i ng, s ucha sa fast F ourier tr an sform,is  appli ed  to  th e dig i talsignal  to obta in th e  distance andt he relative v e lo c i ty . 
Fro m t he above eq uati o ns ( 3) a n d(4) f r=(fb dn+fb up ) /2 Since fr=(4·Δf/C·Tm )r , therelat ive distancer is given b y r=(C·Tm/ 8·Δf )  ( f bdn+fbup)  (5) 
Simi larly, fro m  the abo ve eq uations(3) and ( 4 ) fd=(fbdn −fb up) /2Sin c e  f d=(2·f0/C)v,t h e re la tive ve loc ity v i s g ive n b yv= (C /4f0)(fbd n−fbup) ( 6) 
A scan  be s e en fromth e a bo veequat i ons (5 ) and  (6) ,th e  re lativev el o c ityvis  pro por ti onalto t h e d ifferen ce betwee n f b dn a nd  f bup, an d the relativ edistance r  i s p roport i o nal to t he sum of fbdn and fbup .  Theref ore , the  val ues of fb dnand fb upd ecreas e as t he re la tiv e dista n c er d ec reases.
FI G S . 4 A to4C  are  diagra ms showing the pos i tio nal relations hip  bet w e en  th e  u p swe ep and d ownsweep peak f requencies  w h en  there isa  ta rg et appr oaching  at a high re lative ve locity an dther e lat ive distan ce is th erefore r a pidly de creas ing . In t he  fi gures , ther ela tivedistan ce  is ra pidly  d ecreasin g as shown in FIGS. 4A,  4B, a nd 4C  in  this ord er. Whe n the tar getis approac hin g a t a h igh relat ivev el oci t y, th e di f ference b e tw een t he  upsweep an d d own sweep  pe a k freq uenc ies fbup and fbdn increases. Ontheo t her  ha n d, w he n the relative  di st a n ce decre as es, the val ues of f bu p  andfbdn d ecreas e; ther e f or e , thevalu es
 of_an FM-CW_radar. As shown, a_modulating signal_generator_1 applies_a_modulating signal to_a voltage-controlled oscillator_2 for frequency modulation,_and the frequency-modulated_wave_is transmitted out from a transmitting antenna AT, while a portion of the transmitted_signal_is separated_and_fed_into a frequency converter 3_such as a mixer. The_signal reflected_from a target, such as a vehicle traveling_in_front, is received_by a receiving antenna AR, and the received signal_is mixed with the output signal_of the voltage-controlled_oscillator_2_to produce a beat_signal. The beat signal is passed_through a baseband filter 4, and_is converted by an A/D converter 5_into a digital signal; the digital_signal is then supplied to_a CPU_6 where signal processing, such_as a fast_Fourier transform,_is applied to_the digital signal to obtain the_distance and the_relative velocity.
From the above equations (3)_and_(4)fr=(fbdn+fbup)/2
Since fr=(4·Δf/C·Tm)r, the_relative_distance_r is_given byr=(C·Tm/8·Δf) (fbdn+fbup)  (5)
Similarly,_from_the above_equations_(3) and (4)fd=(fbdn−fbup)/2
Since fd=(2·f0/C)v, the relative_velocity_v is given byv=(C/4f0)(fbdn−fbup)  (6)
As can be seen_from the above equations_(5)_and (6), the relative_velocity v is proportional to_the difference between fbdn and fbup,_and the_relative distance_r is proportional to the sum of fbdn and fbup. Therefore,_the values of fbdn and fbup_decrease as the relative_distance r_decreases.
FIGS._4A to 4C_are_diagrams showing_the positional relationship between the upsweep and_downsweep peak_frequencies when there is a target_approaching at a high_relative_velocity and the relative distance is_therefore rapidly decreasing. In the figures,_the relative distance is rapidly_decreasing_as_shown in FIGS. 4A, 4B,_and 4C in this order. When_the target is_approaching at a high relative velocity, the_difference_between the upsweep and downsweep peak_frequencies_fbup and fbdn increases. On the_other_hand,_when the relative distance decreases,_the values of fbup and fbdn_decrease; therefore, the values