How to find the location of approximately equal value in vector?

I having Z =10.7000 and ACF(auto correlation function)

ACF =

Columns 1 through 6

         0   -1.0000   -1.8478   -2.2678   -2.0719   -1.2071

Columns 7 through 12

    0.2242    1.9749    3.6955    5.0000    5.5433    5.0962

Columns 13 through 18

    3.6027    1.2071   -1.7549   -4.8033   -7.3910   -9.0000

Columns 19 through 24

   -9.2388   -7.9246   -5.1334   -1.2071    3.2856    7.6317

Columns 25 through 30

   11.0866   13.0000   12.9343   10.7530    6.6641    1.2071

here i want to find out approximately equal value of Z in ACF and also location of the ACF value. Here the Z value is approximately equal to 10.7530 of ACF and it present at location of ACF(28). Help me to write the code for find approximately equal value of Z in ACF and its location(28).

Answer 1

[Stephen23]

You should calculate the absolute differences, and then use min to get the closest value:

 >> Z = 10.7000;
 >> ACF = [0,-1.0000,-1.8478,-2.2678,-2.0719,-1.2071,0.2242,1.9749,3.6955,5.0000,5.5433,5.0962,3.6027,1.2071,-1.7549,-4.8033,-7.3910,-9.0000,-9.2388,-7.9246,-5.1334,-1.2071,3.2856,7.6317,11.0866,13.0000,12.9343,10.7530,6.6641,1.2071]
 >> [~,idx] = min(abs(Z-ACF))
 idx =
        28
 >> out = ACF(idx)
 out =  10.753

[vinod kumar govindu]

while using"~" it showing error like Expression or statement is incorrect--possibly unbalanced (, {, or [.

can you tell me how to rectify this?

[vinod kumar govindu]

Its working thank you stephen.

[vinod kumar govindu]

Dear stephen,

how to find closest value of Z with in particular range

that means i want to find closest value from greater than ACF(25). when we using min with abs it compares form starting that is ACF(0).

hoe to find Z closest value from >ACF(25)?

[Walter Roberson]

StartAt = 25;
[~,idx] = min(abs(Z-ACF(StartAt:end));
idx = idx + StartAt - 1;

[vinod kumar govindu]

Dear Roberson, idx = idx + StartAt - 1 what it means? it gives the index value of closest value?

[Walter Roberson]

The code Stephen had,

[~,idx] = min(abs(Z-ACF))

finds the index where the scalar Z is closest to one of the values in the full vector ACF.

Suppose you wanted to skip the first entry in ACF, then you could use

[~,idx] = min(abs(Z-ACF(2:end)))

then an index value output of 1 would mean the first position relative to ACF(2:end), so if you want to know the position relative to the entire ACF array, you have to add 1 -- the difference between the starting point of 2 and the typical starting point of 1.

Just the same way, if you want to search only ACF(25:end) you can use

[~,idx] = min(abs(Z-ACF(25:end));

and now an idx value of 1 would correspond to the beginning of ACF(25:end). If you wanted to know the location relative to all of ACF, you would have to add 24 to idx -- the difference between the starting point of 25 and the typical starting point of 1.

So the formula to find the location relative to all of ACF becomes

idx + (starting point minus 1)

and I coded it with a variable for the starting point so you could adjust the starting point easily.

[vinod kumar govindu]

Thank you Roberson for your valuable explanation

[vinod kumar govindu]

Dear Walter Roberson ,

here i posted my code my aim is to find out the auto correlation and cross correlation of the given signals x,y,z.

Auto correlation can be done by compare signal x with itself with some delay. cross correlation can be done by compare twp different signals x,y. I attached a picture contains ACF and CCF equations. In that there is mistake in CCF. It is CCF only not CCF(k). ACF(k) is a auto correlation of x(n) with delayed signal x(n-k). I used symsum function for summation but i am getting error. Given below i posted the error which i got while using symsum funtion.

??? Attempted to access IRx1(0); index must be a positive integer or logical.

Error in ==> G12 at 26 ACF1(i,n)=bug+((IRx1(n)+j.*QRx1(n)).*(IRx1(n-i)-j.*QRx1(n-i)));

I dont know it is correct function for the summation of complex signals.

The procedure is to multiply the x(n) with it self by giving delay x(n-k) and add all those to get ACF.

Help me to solve this coding.

    clc;
    close all;
    clear all;
    IRx1=[2.50582817101952,2.41713141145528,1.86841439304153,0.605047602894921,-0.703566724847468,-1.53347690224738,-2.68534618710372,-3.37564979764617,-3.60976457774389,-3.31964450712546,-2.66522613876526,-1.77623560339244,-0.492474329662971,0.160290587013230,0.507220033329129,0.312331782163865,0.113076760989049,-0.510845957116963,-1.02537238124377,-1.54315957923986,-1.92651006745793,-2.07761357141181,-1.96179000520892,-1.61605886905197,-0.998502032475426,-0.606791167516796,-0.408862392930745,-0.721810897897046,-1.03865928287495,-1.67596511911259,-2.17900191449449,-3.22455973533726,-4.20122236827395,-4.88936414084140,-4.98588492090064,-4.64611986699242,-3.89295986195026,-2.85016108345810,-1.51000979182552,-0.114053165824088,1.08073054478529,1.85120398545085,2.05071399629919,1.55713172662244,0.577854501379098,-0.781845566782136,-2.28138320255862,-3.59143240245656,-4.48240785969556,-4.80042560007416,-4.49335459690561,-3.61773210916393,-2.28811421907310,-0.616269087330731,1.34646211479523,2.58576397249433,3.18726452764764,3.55099127809478,3.39245771843159,2.67982568751591,1.28811220734259,0.290545697789977,-1.11083900436137,-2.24846907912449,-3.41008937840863,-4.08132603131973,-4.19202057140981,-3.75598274404288,-2.86511558343952,-1.33166071513922,-0.0888600143436430,1.04383587114973,1.90146530084647,2.36534314627888,2.37807964444616,1.94943719786547,1.15254387997119,0.111265653064370,-1.01930534408229,-2.44869015588492,-3.23965758371861,-3.36628409964266,-3.50424270023697,-3.29456430470408,-2.80531710517118,-2.14315533001624,-1.47170964682503,-0.795233104046106,-0.346629678415243,0.243676163193890,0.0561703047489547,-0.740610277561049,-1.27386267061423,-2.08480520623948,-2.43267440079923,-2.76937121834168,-2.99337398387634,-3.08558943524334,-3.04783986140056,-3.07230565610149,-2.94490942924285,-2.64367433237923,-2.33302680338966,-1.83789598292898,-1.97823772406445,-1.93937035972245,-2.20625565463774,-2.23887113241593,-2.58437228749598,-3.52733915198916,-4.07019344900751,-4.31937286306846,-4.82277220060252,-5.11817728167131,-5.13481364324164,-4.84209660869776,-4.24673283123647,-3.54290123157843,-2.67022083716594,-1.34112096240404,-0.847195923908771,-0.136621642288736,-0.113124944412861,-0.346362291440859,-0.812589735653853,-1.43525740508435,-2.31980008066570,-2.47632619329387];
    IRx2=[1.01460425716151,0.789387892284636,0.465419065393918,-0.270674605261502,-0.324209579543460,-0.786127887110611,-1.31672413476201,-1.68974069580242,-1.68683326153294,-1.91463828346887,-1.99070592373177,-1.86159099936316,-1.51752077197991,-0.954746832721099,-0.209994594029173,0.811346972019044,1.61404780608856,1.96001533542083,2.49485352039829,2.76882719749157,2.73797080108476,2.39139122359568,1.75505098733065,0.892009683076733,0.0815037131794636,-1.01857047035352,-2.02213961753928,-2.93877580921443,-3.23294982923665,-2.99973300999368,-2.91528946965527,-2.01533398528999,-0.768915862561078,0.673940528188069,2.12014743798596,3.07912747337142,4.14769021857149,4.55429333026318,4.33404517081416,3.48728067593388,2.11504461592450,0.408386612077747,-1.37865630550980,-2.93271295825688,-4.10799835209611,-4.78408173369122,-4.46062915666738,-3.45118437406266,-1.90549976700760,-0.0589501797260740,1.80599108593936,3.40640695154048,4.54526003105368,5.18679223295696,5.33036875356390,4.48934454418814,3.04699266357109,1.54593614053326,0.135501358878592,-1.09302611399635,-1.85681416548019,-2.15661323317940,-2.32274156157063,-1.88578807031514,-1.04852785251823,0.0680470909691132,1.28358265681183,2.42637788797044,3.35703514167297,3.64767743571924,3.98742663931683,4.00581733933059,3.73109093230059,3.21309282961231,2.51322792193615,1.69750401007136,0.833207984444164,-0.0116689660343153,-0.768138496031731,-1.55330142621117,-1.97458482357104,-2.15477811425155,-1.87735825878768,-1.21139358892745,-0.236527845717644,0.916737394288882,2.02731175399555,3.11127236571521,3.76594186553903,4.15152292241076,3.65721802838211,2.68922312868832,1.35424397679989,-0.422175665866012,-1.47203008503273,-2.72588745633588,-3.60988696547965,-3.97459918433722,-3.75578630206334,-2.70609884338261,-2.18677889085995,-0.724861849873928,0.705065802834293,1.64916146563410,2.43886933811804,2.42744868507788,1.80584985609909,0.908696622442396,-0.705707238128764,-2.27270189339574,-3.37234227805187,-4.20160175589701,-4.17172206185601,-3.55339005011385,-2.42912689725117,-1.31805658267917,0.239514364570606,1.47991933586132,2.36459637723685,2.56164473359209,2.55384087296497,1.60993379649284,0.629564432592203,-0.645304518556036,-1.97479167479100,-3.10148212130029,-3.80003159784154,-3.94619491777448];
    IRx3=[-0.993128890005284,-1.76594777520882,-2.31949979637286,-2.21870218475863,-2.45080409040613,-2.28219201343847,-1.02229193980455,0.453921919149053,1.90050025467925,2.59193207732919,2.69060034703535,2.15307465169026,1.05521829466591,-0.413379640224464,-2.00515321844758,-3.31946860669385,-4.41984467230870,-5.23501910734096,-5.16606973083684,-4.46543527319935,-3.25160209193610,-1.72671153217760,-0.140190359696800,1.25484213325138,2.02459808250948,2.62069605149156,2.60946644908517,2.09571076461969,1.01910162812756,-0.269202255127129,-1.23809167199613,-2.47193225700054,-3.38135220256387,-3.83434288531237,-3.68937515950887,-3.39741304134523,-2.42972386681567,-1.50374882556885,-0.508048999212305,0.404545935881431,1.10330611589675,1.49838880640620,1.55228571196290,1.34281769078276,0.842640828669976,-0.0527018153170412,-0.713595602532179,-1.26283024770965,-1.61665181987407,-1.72898418633932,-1.59713183999718,-1.26040333662297,-0.752932366670609,-0.0577665529710810,0.374250486357905,0.941611680965764,1.08213296963860,1.27444212679685,1.21015441855056,0.785605530968928,-0.180891381312223,-0.928904425156226,-1.73454047225642,-2.77036791374945,-3.73068718741744,-4.34861858499960,-4.53295554566547,-4.26883529651507,-3.61886401478481,-2.36423308245108,-1.43888043407460,-0.627189322960582,-0.0783446858768140,0.105958148447062,-0.111671539130095,-0.698782517051578,-1.55953435306677,-2.55178800751300,-3.51170697380857,-3.96060456182168,-4.42738941481774,-4.26437253555307,-4.15000793763006,-3.71955395095441,-3.03386608743514,-2.19598516647012,-1.39928527264283,-0.563069421120779,-0.0488066084850562,0.0229426002962217,-0.166071205981264,-0.696044288513010,-1.47745602544096,-2.36416001821257,-3.14726579723785,-4.02850927072230,-4.71723059101617,-5.10569764618782,-5.12914144917017,-4.99809288524002,-3.92091606240318,-3.00656913581731,-1.91111082249582,-0.565619991349472,0.283627761416091,0.947356788212610,0.948578976391194,0.906033103627324,0.165663577711276,-0.528126599095243,-1.75073591909251,-2.76186496190158,-4.01400972532222,-4.97621829735726,-5.52200879346877,-5.24556962852168,-4.80996281212845,-4.17173805622293,-3.24903463733582,-2.23274479585379,-0.979573531993498,0.423167172481398,1.16521650753348,1.49978408672960,1.36002336661019,0.741577094736565,-0.289522665579945,-1.60088092364450];
    QRx1=[-0.144718579660555,0.995946652625673,2.05637645961698,2.61196347518716,3.25632649951836,3.08746302178533,2.45005524983264,1.52879189873049,0.0795600257263762,-0.903503642646553,-1.66384374630175,-2.07219543395580,-1.73663051946867,-1.22493813342171,-0.511968187169972,0.111113406512994,0.796516202647878,0.977755843153328,1.25462033881561,1.24592323194847,0.996209115120566,0.609489969080677,0.223354235342819,-0.0248956407188340,-0.232342453639286,0.174464228212001,0.807619460912736,1.49311646218381,2.21645131610826,2.67054620724355,3.06251300887572,3.09478595401401,2.63306697209545,1.73954071310858,0.532969121848919,-0.652371421489012,-1.45428721135333,-2.28225224335881,-2.60690673920328,-2.34235411873884,-1.51408904246930,-0.255026384528728,1.21922118882082,3.02115178742696,4.10050381643365,4.96903735582075,4.81132933804762,4.04180574992444,2.79181617599615,1.27442184206188,-0.255083903745787,-1.54528645820358,-2.42200036300971,-2.78267604719178,-2.42252639176325,-1.52142442818247,-0.307372780120042,1.16373862378014,2.59566895376017,3.82281007709030,4.68018360704009,5.05114433673019,4.82593849729210,4.20732887404119,3.07060487849618,1.62519161882054,0.0818617642666102,-1.34270890438126,-2.45728108780638,-3.18997435899711,-3.26264000733367,-2.85030338447939,-2.03755274312990,-0.961712703315067,0.208817912882685,1.29975076000225,2.15604845685741,2.66356786203298,2.76429227850948,2.60505351129691,1.84689048244303,0.820028928366605,-0.0623265017645658,-0.862750087599546,-1.46018221335862,-1.77273253255276,-1.73167622697005,-1.53061294715227,-1.07761129848942,-0.782769139847865,0.0264483256493230,0.436887172479494,0.789414211727582,0.727446167963397,0.756415264991138,0.618513152633964,0.393549801823466,0.131886491958235,-0.114912262481089,-0.545127730055126,-0.510377281509120,-0.512557411426055,-0.391659486423605,-0.0710516328225203,0.00509349801989560,0.426987287620363,0.627750665719879,0.943494833829077,1.35343204458950,1.54615610141597,1.51295396896865,1.31529822675633,0.856736949102081,0.198390357042307,-0.569333696382446,-1.32418460730406,-1.92388745351658,-2.45670604169471,-2.70052375902505,-2.08229123921291,-1.73603019307446,-1.13987994071623,-0.474015604873290,0.162399114708555,0.674102061951758,0.524785424561854,0.214556638570243,-0.0938660949699451];
    QRx2=[1.25748821083559,1.59232820540285,1.89211923520759,1.88099181061371,1.75907167934012,1.82428183523391,1.78041254700247,1.56472843457122,1.04088165066503,0.646556290077192,0.128310603656031,-0.450501773794132,-1.00480904530030,-1.45912613104007,-1.72868619330447,-1.91466170173093,-1.52145406181707,-0.744755343783896,0.0164457823216737,0.920124206140120,1.87280368258172,2.76798592075878,3.49740829873187,3.96346095177321,3.92634814268997,3.79047264113801,3.25131401251054,2.19516080475489,1.11866898714991,-0.0868644803222537,-1.15381581692583,-2.08217190852378,-2.65256309571722,-2.74086608851374,-2.13703911177943,-1.86213629706259,-0.179665202068858,1.42353419433705,3.09919520661605,4.59655516335476,5.67777383988329,6.15849489368285,5.94162047977465,5.41655735638638,3.89777136864294,1.75659884543326,-0.147314506470493,-1.80654394943821,-2.97361612236474,-3.47952694704350,-3.26168307461630,-2.37373106741707,-0.986656040212108,0.680993458251602,2.66897460606418,4.14915838268406,5.28633393172347,5.56585128716944,5.32155618820885,4.58001729846046,3.68475979062889,2.18321673024426,0.727376002538077,-0.939867972535359,-2.14028958454835,-2.91210522072983,-3.20882166062459,-3.05352877769973,-2.52510818506159,-1.70592670614687,-0.851669664801974,0.0405071413518816,0.874314119614612,1.57491349902664,2.08961027424417,2.38518328361133,2.44437288087680,2.26371843129368,1.85394131721738,1.59842253507776,0.711185513135204,0.0404410173761393,-1.01883306281697,-1.89543095968338,-2.45170009387046,-2.58418936090662,-2.22354516228131,-1.40250297386122,-0.142751951346500,1.59542559405902,2.93768034088717,4.05373057297677,4.77627132908852,4.82664828257853,4.11455681138587,3.49068770809641,2.43703556765478,1.13299280408855,-0.192807969927715,-1.40172126792556,-1.95224338365755,-2.12390938625579,-1.65547574874616,-0.458219572865563,1.07830126344190,2.51125426751961,4.13485781495850,4.96487384457950,5.32729501591053,5.29550758377778,4.46931759931741,3.02864828865319,1.65029660558493,0.362393361769723,-0.594496557791115,-0.988543113338450,-0.925025563983850,-0.334419146424679,0.716880119341661,1.79250194692824,3.22379242483073,4.31309335618836,5.20263838196125,5.57918860188955,5.35976324760898,4.57171837761737,3.35665430473978,1.92253002265421];
    QRx3=[1.61469434821989,1.28110087283433,0.593981423858839,-0.0746609794962341,-0.891803824646148,-2.19303462998841,-2.62044173173250,-2.33773458592233,-1.14868797987302,0.187752799404550,1.72921097658605,3.20949521901254,4.35189005875512,4.96422758117794,4.93938714967720,4.08414134060692,3.03450684126624,1.89291039683914,0.263892352374029,-1.21185894615126,-2.29786178930600,-2.82730994360425,-2.73002447245140,-2.04185996536298,-0.978459491542767,0.463296101102056,1.96310381648816,3.47769048065473,4.28572284988762,4.48069796806336,4.52430480758476,3.96142604376931,2.96223292698943,1.69588086517021,0.269549938642862,-0.470169450225313,-1.59577743807407,-2.08965359044770,-2.20036578610210,-1.94267300943902,-1.38745944463219,-0.647424702259412,0.142727660186499,0.457263258501747,1.02854810107158,1.53119350556719,1.43704558729807,1.09870604559311,0.589409191167250,0.00703713408324849,-0.542958205090700,-0.965174046229494,-1.21383179950569,-1.26407039195322,-1.25897405515521,-0.681320371584185,0.0334979706460327,0.911813186967266,1.84129800199022,2.67248382949417,3.19578726489379,3.23645876594367,3.35429118367439,3.44781140646502,2.88762169576680,2.01590005115277,1.00015989096743,0.0286399105764878,-0.722354919489267,-1.13763940346719,-1.04553560746135,-0.566614389385489,0.215915010612429,1.16617500935677,2.11970048353193,2.91199894737582,3.40662737197769,3.51802519672367,3.22535601020925,2.36107413812950,1.58191148418807,0.582199081336153,-0.245139894736487,-0.973514153843321,-1.48447989900030,-1.69133925164542,-1.56892560973338,-1.08445968606643,-0.360974609164748,0.496588571825767,1.40302979009760,2.17079631650935,2.67736691587632,3.13836637897697,2.38054122224518,1.97100715599610,1.24885416031121,0.307919228543620,-0.722710835794146,-1.50341250319490,-2.01468520812255,-2.68666490478536,-2.97425216528387,-2.89646892777086,-2.52379881302396,-1.49901796224810,-0.506869568406280,0.907651361053495,1.75345622216872,2.55545782056647,2.90248642844106,2.86882256178575,2.29975359926686,1.31819570586921,0.0578257551530834,-1.35655604583865,-2.53551533399583,-3.45158622002622,-4.07401651828128,-4.52543821838908,-4.36880666597097,-3.47644873119799,-2.46651478664132,-1.22740964353534,0.0764465476581728,1.26339866951640,2.15988323096008,2.61759542869763];
    %IRx and QRx are inphase and quadrature phase signals
    x=IRx1+j*QRx1;%IRx1 is inphase signal and QRx1 is quadrature phase
    y=IRx2+j*QRx2;
    z=IRx3+j*QRx3;
    for i=1:128
            j=sqrt(-1);
            syms IRx1 QRx1
            ACF1(i)=symsum((IRx1(n)+j.*QRx1(n)).*(IRx1(n-i)-j.*QRx1(n-i)),n,0,128);
          end

[Walter Roberson]

You have not defined n in the above code, but you are using it as the symsum variable.

If you define n as numeric and starting at 1, then you would get an error from the IRX1(n-i) in the case when n and i are 1.

If you define n as sym, then you will get an error from one of the (n) or (n-i) indexing attempts. For one thing, you have IRx1(n) but you start n at 0. More importantly, though, is that you cannot index an array at a sym -- it is not a defined operation.

Do not use symsum() to sum a vector of definite values. Create the vector numerically and sum() it.

j = sqrt(-1);
n = 1 : 128;
IRx1 = sym('IRx1', [1 128]);  %are you sure you want to override the existing array??
QRx1 = sym('QRx1', [1 128]);  %are you sure you want to override the existing array??

for i=1:128
   this_entry = sum( (IRx1(n) + j.*QRx1(n)) .* (IRx1(n-i) - j.*QRx1(n-i)) );
   ACF1(i) = this_entry
 end

However, this is still going to fail because n-i is going to go non-positive and you cannot index arrays of symbols at non-positive numbers any more than you can index arrays of numbers at non-positive numbers.

Should you be circular shifting the vectors or something like that?

IRx1 = sym('IRx1', [1 128]);  %are you sure you want to override the existing array??
QRx1 = sym('QRx1', [1 128]);  %are you sure you want to override the existing array??

plain = complex(IRx1, QRx1);

for i = 1 : 128
  this_entry = sum( plain .* circshift(plain, [1 i]);
  ACF1(i) = this_entry;
end

... it would make more sense to me if you were doing this operation on the numeric arrays rather than symbolic IRx1 and QRx1

[vinod kumar govindu]

Dear Roberson,

when using sym it always showing error like

??? Undefined function or method 'sym' for input arguments of type 'char'.

Error in ==> G12 at 32 IRx1 = sym('IRx1', [1 128]); %are you sure you want to override the existing array??

What is that error mean?

[Walter Roberson]

Which MATLAB version are you using?

Could you confirm that

syms IRx1 QRx1

works, but that

 sym('IRx1')

does not?

Is it possible that you are using the Maple symbolic toolbox instead of Mathwork's MuPAD symbolic toolbox?

[vinod kumar govindu]

I am using MATLAB 7.6.0(R2008a)

and for

 syms IRx1  QRx1

also it showing same error

[Walter Roberson]

It sounds as if you do not have a symbolic toolbox installed, so I do not understand why your earlier code used syms. symsum cannot be used without the Symbolic Toolbox.

It did not make sense to me that you used syms there anyhow.

j = sqrt(-1);
n = 1 : 128;

for i=1:128
   this_entry = sum( (IRx1(n) + j.*QRx1(n)) .* (IRx1(n-i) - j.*QRx1(n-i)) );
   ACF1(i) = this_entry
 end

However, this will have the problem I described before. You are allowing i to exceed n, which is going to lead to negative subscripts.

I suspect your code should look more like

plain = complex(IRx1, QRx1);

for i = 1 : 128
  this_entry = sum( plain .* circshift(plain, [1 i]);
  ACF1(i) = this_entry;
end