Design and implementation of a 2048FFT capture spectrum analyzer

MELECON '85/ Volume 11: Digi al Signal P ocessing A. Luque, A. R. Figuei as Vidal, V. Cappellini (eds .) Else ie Science Publishe s B. V. (No h·Holland) I© IEEE 1985 295 DESIGN ~ND IMPLEMENTATION OF A 2048 -FFT CAPTURE SPECTRUM ANALYZER M. ~m e ngual, J. Casamajo , G. Vazquez, J. Laba a Dep o. P ocesado de Se~al en Comunicaciones E.T.S.I. Telecomunicaci6n. Apdo. 30002, 08071 Ba celona, Spain This pape desc ibes he ha dwa e implemen .a ion o a digi al :Spec um analyze which, by using a cap u e p ocess o he signal unde p ocessing, pe o ms some non pa ame ic signal p ocessing echniques. All he possibili ies o implemen a spec um analyze will a ise o a bank il e analysis app oach. When he ins umen wo ks as an o -line p ocesso , he bank il e can be a linea ans o m, which esul s in a FFT as conce ns wi h he analysis o he powe densi y con en o he da a sample. Thus he FFT p ocesso can be iewed as a se o equispaced il e s wi h non-ideal cu -o and seconda y lobes bu op imum o analyze pu e ones in a whi e noise en i onmen . 1. INTRODUCTION Gi en a andom p ocess x ( ) , a way o cha ac e ize i is by means he powe spec al densi y. This is an ideal unc ion which ela es how he signal powe is dis ibu ed in he ecuency domain. ~11 he me hods o es ima ing he powe spec um a ise om a bank o band-pass il e s (al hough hey mus n' be implemen ed necessa ily so). I hese il e s a e signal dependen , pa ame ic me hods a ise and he non-pa ame ic a any o he case. Among he las ones, he mos popula a e hose which make use o he FFT algo i hm. One o hese me hods is he W.O.S.A. (weigh ing o e lapped spec um a e aging). ~nalyze a chi ec u e has been designed o acomplish wi h his me hod. The echnique o es ima e he spec um by means he W.O.S.A. is he ollowing: gi en a signal sample eco d x(n), O.,:n.,:M-1, i is di ided in o L segmen s (wi h possible o e lapping be ween hem) o N poin s each one. Whe e N is he FFT size ha p ocesses he analyze . Each segmen is windowed ( h ee pos- sible windows a e a ailable: ec angula , Ba le and Hanning) and FFT p ocessed. Finally, he modi ied pe iodog ams a e a e aged, by means o an uni o m o exponen ial a e age , o achie e he spec al es ima e. 2. IMPLEMENTATION Fo implemen ing he W.O.S.A. me hod, se e al a chi ec u e models a e employed, which a e complexi y-p ice dependen s. I he FFT p ocesso is high speed enough, i could be hough o disposse wo memo y bu - e s; while one o hem is adqui ing signal, CH 2185-7/85/0000-0295(8)/$01.00 ©19851EEE he F T o he o he is he way in which anal yze s. To achie e audio equencies, i echniques and, in any pu pose a chi ec u es. one is e alua ed. This wo k eal ime spec um eal ime analysis upon is necessa y bi -slice case, he use o special This is a adeo when one is no in e es ed in an expensi e ins umen . The o he possibili y is ha o adqui ing he signal unde es ("cap u e"), s o ing i in a memo y bu e and es ima ing he powe spec um densi y o -line. An a chi ec u e o achie e his idea is much mo e simple and allows he use o con en ional 16 bi mic op ocesso s. Al hough a ]JP design can' achie e eal ime p ocessing upon a bandwid h o 20 KHz, howe e i is possible eal ime p o·cessing un il 2 KHz (depending upon he speed p ocessing and he FFT size). Ou design is acco dingly wi h his philosophy. Fo cap u ing he signal i is p o ided 20 K wo d o s a ic RAM. All he associa ed unc ions he analyze achie es a e suppo ed in a 2048 sample FFT. I is well known ha spec al esolu ion is closely ela ed o he in e se o he ime domain wid h o he window. So ha spec al esolu ion in he W.O.S.~. me hod 1s dependen upon he ime du a ion o he 2048 poin s. Howe e , because o he 20 K wo ds o signal s o ed, i is possible h oughou he buil in "zoom FFT" o achie e a spec al esolu ion en imes g ea e he W.O.S.~. Besides, ano he 12 K wo d s a ic [lM·I a e sup- po ed in he basic model o allow in ennedia e esul s. ~ u he enla gemen o 32 K ·1. is o eseen. So i will be possible o slo e ideal measu emen s and compa e wi h ac ual one's. 296 M. Amengual e al. RAM ~OM ·~u-~ u ::=:::;> kT ~l loiAL C:o cTil•UJUI. l j C.P.V. I "' .I ;"P. iC 6IDaO ! IIWU+-- l &I!&O~O ~ -(- c:.>~.,A.OLJ.QI. 4~ ~ ~ A niA&.INOiNc; - Sg_ - "'lo T -1 1011 1 j::j 8 8 1 . ._ _...,, .I +--- <.-. ,...__~ . -- Figu e 1. Gene al Block diag am. The ROM memo y uni is also 32 KW size. I isn' oo la ge because da um ables mus be s o ed besides e e ences and p og am i sel . The adquisi ion uni consis in an an ialiasing analog il e bank (C.C.D); a sample and hold and a 12 bi A/D con e e , om which an inpu dynamic ange o abou 72 dB is a ained. The analyze has also been i ed wi h he IEEE- bus, by means o a bus con olle chip. So ha , i can wo k as a pe iphe ic om a hos compu e To pe o m he di e en p ocessing pos- sibili ies, he use manages he analyze h oughou a key boa d; so ha , he ha dwa e design also inco po a es a p og ammable keyboa d con olle . Among he ea u es o his keyboa d con olle chip a e: o es ablish se ial com- munica ions (RS-232) wi h pe iphe ical de ices, as p in e s o plo e s, and also p og amable one gene a o which sample and hold uni . p o ides a go e ns he G a!=hic esul s, and di e en menus a e displayed in an in elligen g aphic e minal which is ~P con olled (by a Z-80 ~P). Com- munica ions be ween he CPU and he g a ic e minal a e also p o ided h oughou he IEEE- bus. The global a chi ec u e o he analyze can be iewed in igu e (1). In his design, he con ol uni , so as he compu a ional uni is he ~p MC68000. THis CPU disposses o 16 in e n egis e s o 32 bi ( 8 da a egis e s and 8 add ess egis e s). In e ac ion be ween he adquisi ion uni o he keyboa d and he CPU is achie ed by in e - up ions. While he g aphic e minal com- munica ions and he RS-232 ones (p o ided by he keyboa d con olle ) a e polling pe o med. Th ee in e nal in e up le els a e allowed. A he highe one, uni adquisi ion and key- boa d a e disabled; his co esponds o he CPU p ocessing ime. A he nex le el, uni adquis i ion is enabled and keyboa d disabled and a he hi d le el, keyboa d and uni adquisi ion a e enabled, bu only keyboa d is unc ionally enabled because he keyboa d clock is ese , so he adquisi ion uni is in idle s a e. Communica ions wi h a hos compu e , al hough, i isn' s ill so wa e de elopped, also will Implemen a ion o a 2048-FFT Cap u e Spec um Analyze 297 be in e up pe o med in he IEEE-bus. The p esen a ion uni , i.e. he !Jl-,lphic e :minal has been designed in elligen (i is suppo ed by a Z-80) o discha ge he MC6BOOO om askes being no ypically compu a ionals. This disposses o a g aphic sc een con olle pe o ms a 512 poin esolu ion in he ho izon al axis and 256 poin esolu ion in he uni ha e ical one. I can be seen a igu e 1, ha no loa ing- poin cop ocesso is included. Because o his, all he ma hema ics ope a ions (ei he linea o non-linea ) mus be pe o med by he 68000 CPU in ixed-poin o ma . Special ou ines ha e been de elopped o e alua e non-linea ma hema ics unc ions: loga i hms, exponen ials and phases. E alua ion o lhal unc ions is w ·(o ·mcd wi h aid [o some signi ica i c alues which a c s o ed in he 110~1 memo y . Fo he loga :i hm e alua ion, i has been implemen ed he algo i hm li) log x = log 2 + log x/2 ( 1) This ecu sion is ollowed un il x is less o equal han a ce ain alue ( 1024), in which case, he loga i hm alue is ound a he able. Exponen ial ecu sion is jus he in e se han he loga i hm one. I xis less han log (1024), hen ex may be ob ained di ec ly om he loga i hms able; i x is g ea he han log 1024 i will be x=n log 2 + log u, whe e log u < log 1024, so he p oblem now is o ind e1n u a he able and inally ex=2n e1n u Fo calcula ing phases, he algo i hm ollowed has been (2) a c g x=TT/2 - a c g 1/x; i x>l ( 2) I x<l hen a c g x is ob ained om abula ed alues. Ob iously, since he CPU wo ks o e in ege numbe s, all numbe s ha a e less han one mus be le shi ed decimal poin s o ed. Also i is s o ed in ROM he cosinus and sinus necessa y alues o compu ing a 2048 poin F.F.T. Fo compu ing a 2048 poin F.F.T. i is necessa y (3). sen 21! i 20411 cos 211 i 20~0 . i =" 0, ... 1023 102 3 I could be su icien s o e (4), i.e. a quad an ( 3) sen 2TT i 2048 ( 4) Ou !'o op imicing execu ion ime i has been abula ed (5) scn 21! i 2048 i 0, ... 1535 ( 5) Indexing om i=O sinus a e ob ained and om i=0+512, cosinus do . Also i has been abula ed he bi - e e sed _ unc ion. The unc ions included in so wa e op ions a e: W.O.S.A., signal enhacemen , spec um a e aging, zoom-FFT, au oco ela ion, Hilbe ans o m, en elope, ins an aneous equency, minimum phase and complex and eal ceps um. O he g aphic ea u es a e included which allow on- line signal edi ion bo h in ime and equency do111ain. I is expec ed o ex end he sys em o pe o ming wo channel signal p ocessing.