RSRC LVINLBVW  D@<[R%KV ُ B~<yWLVIN gauss_demo.viLVINGaussian White Noise.vi78 @error&@@ Gaussian Noise Pattern @seed@ standard deviation @samplesPTH09Analysis 1siggen.llbGaussian White Noise.viLVINGeneral Histogram.vi  @@ X@@ HistogramT@@DP @ lower @ upper*@lowerupperbothneithers inclusionBins@@ Axis@ max.@P @total @below @above # outside@ min @error @# bins@lowerupper inclusionPTH04Analysis 5stat.llbGeneral Histogram.viLVINStd Deviation and Variance.vi>: @@ X,@Sample PopulationWeighting (Sample) @ mean@ standard deviation@ variancePTH0@analysis baseanly.llbStd Deviation and Variance.vi((Pp c$ c P   c^P"@P@flg@oRt@eofudfP Number of Samplesp dfdP txdP oldP ext P @vP0@PP@P!!!!l@bP0   !!!    $@P0!!!B@8PPb P         @P b P         @P  cP"@P@flg@oRt@eofudf*P@ Gaussian Distributed Noisex@ dfdP@ txdP@ oldP@ ext P @vP0@PP@P!!!!l@bP0   !!!    $@P0!!!B@8PPb P         @P b P         @P  c@P"@P@flg@oRt@eofudfXP@4P@@ Axis@@@ y HistogramHistogram of Noise Values0x@"P@ @ dfd0P@"P@ @ txd0P@"P@ @ old0P@"P@ @ ext P    P   RP"@P@flg@oRt@eofudf P Meanx dfdP txdP oldP ext c VP"@P@flg@oRt@eofudfP Std. 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Dev.H@P@@ Axis@ Residuals, Gaussian - HistogramTPgauss_demo.vi This VI is designed to acqaint you with gaussian distributed random numbers. The gaussian white noise VI is used to generate a user selected number of random numbers that follow the gaussian distribution with mean of zero and standard deviation of one. This generator generates a long (fixed) sequence of random numbers. We select a subset of these random numbers by using the uniform random number generator to choose a (random) starting value. The random numbers are displayed sequentially in the order in which they are generated. There should be no correlation in the sequence of values, e.g. they should be uniformly distributed about positive and negative values. Next a histogram of the values is generated. The values are classified into one of 21 bins varying between -4 and +4. The classified data is known as a histogram. It is ploted as a bar chart. Superimposed is a gaussian random distribution of mean zero and standard deviation one. The x values are obtained from the bins generated in the histogram. Each x vaule is the mean of the extreme values (min and max) of each bin. The gaussian function must be calculated so that it corresponds to the histogram. Thus one calculates N*G(x)*Dx as a function of x where, N is the total number of random numbers generated, and Dx is the width of the bins. Revised 4-3-03 by jbcDǓE)DDCM)4ǀ<fv9IEIEIEIEI9 DTHPDl88 ~ &@ Number of Samples|p8 @error&@@ Gaussian Noise Pattern @seed@ standard deviation @samples @error6&@@ Gaussian Noise Pattern @seed$@ standard deviation @samples @ number: 0 to 1 @ variance @ mean8,@Sample PopulationWeighting (Sample)@@ X~: @@ X,@Sample PopulationWeighting (Sample) @ mean@ standard deviation@ variance @@ AxisdX@@4P@@ Axis@@@ y HistogramHistogram of Noise Values!0*P0!!!:*@@ Gaussian Distributed NoiseB2P@@ Axis@@ Histogram$@@ Histogram@ 4(P@@ Axis@ @@ yTH@P@@ Axis@ Residuals, Gaussian - Histogram0$@P0!!!(@lowerupper inclusion @# bins@ min>.@P @total @below @above # outside@ max`T@@DP @ lower @ upper*@lowerupperbothneithers inclusionBinsL@  @@ X@@ HistogramT@@DP @ lower @ upper*@lowerupperbothneithers inclusionBins@@ Axis@ max.@P @total @below @above # outside@ min @error @# bins@lowerupper inclusion@ y:*P@@ Axis@@ yN>@4P@@ Axis@@@ y Histogram @ Mean@ Std. Dev.{|<LLL\x<<<<<L<<pp<LpLp<<@LLLLLLLLxpLp,HLLH|,@|pLL<Pp,LL,<xP@ ]DH"\H#\ Number of SamplesH=b$vab%vaeHistogram of Noise ValuesHD$GUD$RS Bin ValueV D$HwYf No. in BinHDG**U HistogramwD+1+Demonstration of Gaussian Distributed NoisekJZKZResiduals, Gaussian - HistogramHD$\F--UD$ Bin ValuePDDMeanHEUUU]]  Std. Dev.H@ETTb D$)'4WdbResidual, Gauss - HistN;;0.HDDA)WB)WHDDfGaussian Distributed NoiseHD$tDYD$CD Sample NumberU D$JrXe IntensityHDC((N;;0.HhCHD8CHDC   HB  HDB& ' HDp=N[pN[pcDdaqdbqGaussian White Noise.viMD*w7z*x7ziHDD<IR<IRHDtA;l<lRDBundleXDvw Formula NodeHD@TaTaHDGQ8^Q9^WD Build Array[D.w/wGet Values of x`D%%General Histogram.viHDT@(5(5MDw~x~nHD@:G:GRD]j]jBundletD;""&&( y=(n/sqrt(2*3.14))*exp(-(1/2)*x**2)*Dx;MD%+&+yHDE66HDXE 7 7HD?GlHlHDx?HDF4QA4RAMDw }x }xND#DxHD?iD]]Std Deviation and Variance.vi^DhiWeighting (Sample)HD>HDp>  $$ PP ## %% 77 "X"\ BZB\  (( MM !!FPHP gauss_demo.vi<\FPHP@8<(L<[( @(,`PXL|v/7,  @PGyD=|4 F G!]0  _!yd4  2 a#wb@ 2 @_l!p_p_lc06@ 2 ly!o`o`kdI  _!yd Tp^q'& @ATxz=Tlt0 C8 >4 6T@O@48L" @ :8J!+?fifi]r@ :8L!o`vYo`@ :8K!*nanagh@O`480@ 0 2T(j0 2T-$%k4 3T^Q0 2T-PQl4 3T^Gx4 6T+ (X0 2T(#$m0 8 >4 $8- @ hh 0 8  2  a#wbAGyD5F G!]A2  @_l!_p_pclA2  ly!`o`odk52  a#wbY D M: f#r)v0v0w/x.y-]@   D @x  D xz=Tlt0 K Z>4 6. @O@4&]7] @ :J!fifi]r@ :L!h|vYvYo`@ :K!}nanagh@O`40UJ zUJ 0 2(%&n0 2-78o4 3^0 2("X#]p0 2-BZC]q|d0U8d@PXlt&0 L X@P,^\w80  W4 BL E4  2L V@ :L @p_p_lc@ :L o`o`kd0vLJ4 B ^4  2 U @ : @p_p_lc@ : o`o`kd00x(Dx|'0?4L : f#r)0v0v/w.x-y,,~x<4zTlct<r9D<t]The user enters the number of samples of gaussian distributed random values to be generated. 4 3^(&5$The random numbers are displayed in the order in which they are generated. This allows the user to verify (qualitatively) that there is no correlation among the values in the sequence. L :L "0v0v/w.x-y|eThe mean of the gaussian distributed random numbers is displayed. The value should be close to zero. }The histogram of noise values is plotted. Superimposed is a gaussian distribution with the same standard deviation and mean. L : "0v0v/w.x-ymThe standard deviation of the gaussian distributed random numbers is displayed.The value should be near one. nThe Difference between the calculated Gaussian distribution and the one obtained from the histogram of Gaussian distributed random numbers is shown. The residuals should exhibit an uncertainty given by the Poisson statistics of counting. Thus the standard deviation of each bin of the histogram should be on the order of the square root of the counts in that bin. 0  Z>4 $<(4 6@*X,0  ^C  P& &|&HR8O n 0S h   ''L'|4 v 0@P~B4TA<Sp$b!R343X'(00Hp^q){{ X{%< ()$* *| #$,$\"4 B!D 40 o!D! 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B 8,0@ 3& }@ x#@X#,@##J"4@ <IP<@D$X9(/./@+-/@<@D$8 X[H.0t.@$@.@$..4 @@$t0 .1$,@"G% N @@%%@4@ 2% Fm0@AP%En4tH@0A 3% EnA X!4A&N   4A&MPA34Ad@AP3T}m@4A 2& ~4B34-B+\B*P4BPJP0B@'x(LBPRpJ`)44BL  B@(l'x+(B((L B@(l+(L8B4(2"CB+|+,B((L+\( B@(l'(*P0B5(l) 9:"B2>*B(4B B'3PB8C1$4C/)0PhC*0*P*4CK ,4uz<D*0D*P D)'**P D) **PD*4D0)*=6 K@h D)0+(4D0)*>@K EhDX*4D0)*p<6@ ;h D@(l++\D+(0D5(l(0:2:CB:>0D5(l'H;2":26* D@$/ D@,80,D,H D@,). D@,- D-4D"@P <DDo:l-0- 0DE,ox,D$t@D-2$D+D- D@$.T.- D@,4134D1D/@ D@$t,0t. D@$t 0@4D-hF  D.40DE$t$#8H@D00DE$-%0DE$-! D@$61l64DK /@E2E`$t4E/1|`hE1l4E)h@ 4E"x1%.)0EE$t$$H XP0EE,$o0EE`$t."8 H@ E"`0 0@ E @x0@E2E2$0EE`$.80EE`,, E11$E22$2D E/42, E/.T2d- E/87,4E0/1Xh,E  $,H2 E@5$/`64E0/1DhE5X2 E@43T34,E&h& R,E5$,0 xE2DE,2DE~xj|+(,Dw\N< E%`; %,E$+\1$,h+4E7E` 4E',J84E3_`  E"`5$7L,@EP5Dn@4E 25x D,F65x V0F 35x ,F@ x15XF6/@F6 F@6564F6tF F @x47L,4F0/3h4F" x78F5X6,FP#1$6,Fl"0@7LF26,F#8<7LF5X6$F;<(==>`F;LF :5x 0v0v/w.x-yLF :& 0v0v/w.x-yFmWe need to calculate Dx. This is done by calculating the difference between adjacent elements of the x array.F8F<(FWe need to calculate Dx. This is done by calculating the difference between the values of the x array in adjacent positions in the array. LF :% AG0v0v/w.x-yF?4F K=4G3LG>` G>`4G3G=G?:LLG ~ g"  g\\C  ~(~C g(G'>*@@*G&T/$/rrG& |n|LG 4  [  [GG-))   [ ZG0..;;G LG UU   .   G;1.1.PGWUx{=dKA ZGd?d4G JSh gL@H 2ShO OOP4H jSh P<I 2Sh T>0K 3Sh {,K;XLSh |LK t(d0 %@'346?4K?Z|KU4.T864#''x 0&T& 4 x dX `K `SdShKSA gaussian distribution is calculated for each bin of the histogram. This is superimposed on top of the histogram. Note the following scaling issues. The Gaussian is multiplied by the total number of random numbers. The Gaussian is also multiplied by Dt. This is because G*Dt is the probability of finding a value between x and x +Dx. LK : :F0v0v/w.x-yLK :l (40v0v/w.x-yKA histogram of the gaussian distributed numbers is generated. The numbers are sorted into 21 bins ranging in values between -4 and +4. LK :  Ty`0v0v/w.x-yK ZP LK :  5;0v0v/w.x-yKUKHere we select an appropriate value of x to calculate the value of G(x)*Dx. We extract an element of the x values calculated in the histogram routine. KqWe multiply the random numbers from 0-1 by 10 million so we can randomly obtain 10 million possible seed values.  K The objective here is to generate a random seed for input to the gaussian random number generator. Since the uniform random number generator takes on only random numbers between 0 and 1, we multiply it by 10 million to give a wider range of random starting positions. KThe uniform random number generator is used to get a seed value to randomly select a sample of random numbers from the random number generator.  K A series of gaussian distributed random values characterized by a mean of zero and a standard deviation of one are genserated. A random seed is used to select a different starting value for each set of numbers from among the sequence of (pseudo) random numbers. K5$K 5  56*33* ) 5  f f  _ _rppx   fxKzzCCk\BM\q-3<bx+(=w\N< 5BM\q-3cc\k'v\N</@/j'E/8//'v\N</3`d@/j'*/8//'v\N</3e@/j'?/8//'v\N</\kgg@/j'?/8//'v\N</@/j',/8//'v\N</h@/j'+/8//'v\N</i3g5BM\q\0-34gHj\kB(;JS05BdP7_405B'3PBt0q\k5B7 05B 80M3gh$ h$iD i #i4)Xi5BM\q0KhSH</x5&$,l()'%  xldh ( U4T.864#'x' 0T& &4  x dX`  ( @UUAn *>>n>>@    Yf(/Microsoft Sans SerifMicrosoft Sans SerifMicrosoft Sans Serif01000RSRC LVINLBVW  q@ 4 RSID$=8=d>&G'lT>D<=Dh,>Dd=E|=EL=K,K,VH+Vl+W<,W+W8, XP0+ XX, X,YT ,Yh,Z@,,Z\,Z,[<+[-[,\0,\,\,]8+]+]+"^f/?g0.@g|/Ag@/Bh0/Ch`-Dh-Ei-FiT*Gi|/Hjd/Ijt/Kj/k +k+ k,, k<+kL,k\t,kl,k|x+ k+!k+#k@-&k|-k̸-k-JLp/|/`///x 0 gauss_demo.vi