Digital Low-pass Elliptic filter design
The flow calculates zeroes and poles, draws plot of Low-pass digital Elliptic filter, as well shows calculated order and number of second-order blocks for implementation. To start, on the dashboard please enter your desired parameters: fc/fs - the end of passband (normalized frequency); fp/fs - the beginning of stopband (normalized frequency); pul - passband ripples, dB; sl - stopband attenuation, dB. By changing position of fp/fs slider try to get calculated order as close as possible to even number (e.g. 5.99, not 6.01!). Otherwise sl value will slightly differ from desired.
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\nvar ze=[[],[]];\nvar po=[[],[]];\n\nvar rea=[];\nvar ima=[];\nvar xy=[];\n\n//var fd=flow.get('fd');\nvar fd=1.0;\nvar fc=flow.get('fc');\nvar fp=flow.get('fp');\n//if (fp<=fc){node.error(\"fp should be > fc\");}\nvar pul=flow.get('pul');\nvar sl=flow.get('sl');\nvar a2=Math.pow(10,(0.1*sl));\n //a2=10^(0.1*sl)\n var e3=Math.pow(10,(0.1*pul));\n//e3=10^(0.1*pul): \nvar e2=e3-1.0;\nvar am=Math.sqrt(e2);\n //xm=tan(pi()*fc/fd)\n var xm= Math.tan(Math.PI*fc/fd);\n //xk=xm/tan(pi()*fp/fd)\n var xk= xm/Math.tan(Math.PI*fp/fd);\n var vv=Math.PI*fc/fd;\n //rk=sqrt(1-xk*xk)\n var rk=Math.sqrt(1.0-xk*xk);\n //xk1=am/sqrt(a2-1): xk12=sqrt(1-xk1*xk1)\n var xk1=am/Math.sqrt(a2-1.0);\n var xk12=Math.sqrt(1.0-xk1*xk1);\n \n //****************************************\n// var ee= the3(1000.0,1.0);\n// node.warn(ee);\n \n var b1=ElIn(rk);\n\n \n //node.warn(b7);\n //node.warn(vv);\n var b2=ElIn(xk12);\n var b3=ElIn(xk);\n var b4=ElIn(xk1);\n var b5=b3*b2/b4/b1;\n flow.set('b5',b5);\n flow.set('sl',sl);\n flow.set('pul',pul);\n var nn=Math.floor(b5+1.0);\n //******************************************\n// node.warn('Resultto->');\n//node.warn(b5);\n//msg.payload='b5';\n /*:dlt=0.001/abs(nn-5.5)/10\n#;rer=fmod($nn,2);?>\n nn=floor(b5+1) \nprint \"*****************************\"\n print \" Calculated Filter Order N= : \";\n print b5\n#****************************************************\n#*************Ok************************************\n*/\n\n var u0=-b1/b2*Math.log((Math.sqrt(e3)+1.0)/am);\n var q=Math.exp(-Math.PI*b1/b3);\n var q1=Math.exp(-Math.PI*b3/b1);\n var pr=b3/nn;\n \n \n //**************************************************************************************************\n sm[0]=-b1; sm[1]=u0;\n nn=Math.floor(nn/2);\n \n \n for (var m = 0; m<=nn-1; m++) { \n lm[m]=2*m+1;\n //node.warn(sm[m]); \n }\n\n/* print \"**** Z-plane Zeroes : ****\"\ntext$[1]=\"****Z-plane Poles : **** \"\n # $text [3]=\"Where A1=2*Re{Pole}, A2= -((Re{Pole})^2+(Im{Pole})^2),\n # B1=2*(Re{Pole} - Re{Zero}), B2=A2+1\"; $text [4]=\" \";*/\n/***************************************************************************************/\n\n\n\n\n\n \n for (var i = 0; i<=1; i++) { \n var rr=sm[i];\n //node.warn(sm[i]);\n for (var j = 0; j<=nn-1; j++) { \n //if (i=1 and j=0) then print text$[1]\n var i1=lm[j];\n var sk=the3(pr*i1,q);\n\n var pk=the3(rr,q1);\n var sv=thet1(sk,q); var sw=thet4(sk,q);\n var pv=thet1(pk,q1); var pw=thet4(pk,q1);\n var sn1=sv/sw/Math.sqrt(xk);var sn2=pv/pw/Math.sqrt(rk);\n var dn1=1.0-xk*xk*sn1*sn1;\n var dn2=Math.sqrt(Math.abs(1.0-rk*rk*sn2*sn2)); var zd=1.0-sn2*sn2*dn1;\n var sor=sn1*dn2*xm/zd;\n var bor=sn2*Math.sqrt(Math.abs(dn1))*Math.sqrt(Math.abs(1.0-sn1*sn1))*Math.sqrt(Math.abs(1.0-sn2*sn2))*xm/zd;\n var zn=(1.0-bor)*(1.0-bor)+sor*sor;\n var re=(1.0-bor*bor-sor*sor)/zn;\n var aim=2.0*sor/zn;\n i1=i*nn+j;\n zepo[i1]=[re,aim];\n rea[i1]=re; ima[i1]=aim;\n if (i===0){ze[j]=zepo[i1];}\n if (i===1){po[j]=zepo[i1];}\n // msg1.payload= zepo; \n\n//node.warn(\" +/-j \");\n//node.warn(aim);\n//next j\n//next i\n// node.warn(zepo[i1]) ; \n } \n }\n//********Grafik**************************************************************************************************\n\nvar picWidth=250;\n sk=Math.PI/picWidth;\n // for i=0 to picWidth-1\nfor ( i = 0; i<=picWidth-1; i++) { \n pk=Math.cos(sk*i); \n pw=Math.sin(sk*i);\n pr=1;rr=1;\n // for j=0 to nn-1\n for ( j=0; j<=nn-1; j++) { \n x1=pk-rea[j]; y1=pw-ima[j];\n y2=pw+ima[j];\n r1=Math.sqrt(x1*x1+y1*y1); r2= Math.sqrt(x1*x1+y2*y2);\n rr=rr*r1*r2;\n x1=pk-rea[nn+j];y1=pw-ima[nn+j];\n y2=pw+ima[nn+j];\n p1=Math.sqrt(x1*x1+y1*y1); p2=Math.sqrt(x1*x1+y2*y2);\n pr=pr*p1*p2 ;\n }\n//next j\n xy[i]=rr/pr;\n}//next i\n\n\n\nvar max=0.0;\n for (j=0; j<= picWidth-1;j++ ){\n if (Math.abs(xy[j])>max){\n max=Math.abs(xy[j]);\n }\n }\n // node.warn(max);\n//next j\n for (j=0; j<= picWidth;j++ ){\n dB=20.0*Math.log10(Math.abs(xy[j]+0.000000001)/max);\n//node.warn(dB);\n if (dB<-100.0) { dB=-100.0;} \n xy[j]=dB; \n }\n // node.warn(xy[2]);node.warn(xy[17]);\n flow.set('xy',xy);\n\n//****End of grafiks**************************\n\n\n\nfunction the3(ds,q) {\n var th=1.0+2.0*(q+q*q*q*q+q*q*q*q*q*q*q*q*q);\n return ds/th/th;\n }\n \n\n\n//#************************************************************\n function thet4(t,q) { \n return 1.0+2.0*(-q*Math.cos(2.0*t)+q*q*q*q*Math.cos(4.0*t)-Math.pow(q,9.0)*Math.cos(6.0*t));\n }\n \n//#*******************************************************\n function thet1(t,q){\n return 2.0*Math.pow(q,0.25)*Math.sin(t)-2.0*Math.pow(q,(9.0/4.0))*Math.sin(3.0*t)+2.0*Math.pow(q,(25.0/4.0))*Math.sin(5.0*t);\n\t}\n\n// #*********Elliptic Integral************************************** \n function ElIn(k) { \n // dim a(15)\n var a=[];\n \n var Theta=[];\n \n a[0]=Math.atan(k/Math.sqrt(1-k*k));\n \n\n Theta[0]=Math.PI/2;\n var p=1.0;\n var i=0;\n var x1=1.0;\n var e=0.1;\n while (e > 0.0000001) {\n var x =2.0/(1.0+Math.sin(a[i]))-1.0;\n var y=Math.sin(a[i])*Math.sin(Theta[i]);\n a[i+1]=Math.atan((Math.sqrt(1.0-x*x))/x);\n Theta[i+1]= 0.5*(Theta[i]+Math.atan(y/Math.sqrt(1.0-y*y)));\n e=1.0-a[i+1]*2/Math.PI;\n \ni=i+1;\n}\n for (var j = 1; 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