Butterworth_2345poles - ATGS

//version=2
study("Butterworth_2345poles", overlay = true)
// © John F. Ehlers
p1 = input(defval = 7, title = "Period length", type = integer,minval=1) // Period of bars to look back on
pr=input(close,"length",source)
pi=3.14159265
DTR=pi/180 // To convert degrees to radians multiply by this DTR

// filtro de 2 polos
a21=exp(-sqrt(2)*pi/p1)
b21=2*a21*cos(DTR*(sqrt(2)*180/p1))
cf21=(1-b21+a21*a21)/4
cf22=b21
cf23=-a21*a21

but2=cf21*(pr+2*nz(pr[1])+nz(pr[2]))+cf22*nz(but2[1])+cf23*nz(but2[2])


// filtro de 3 polos
a31=exp(-pi/p1)
b31=2*a31*cos(DTR*(1.738*180/p1))
c31=a31*a31
cf31=(1-b31+c31)*(1-c31)/8
cf32=b31+c31
cf33=-(c31+b31*c31)
cf34=c31*c31

but3=cf31*(pr+3*nz(pr[1])+3*nz(pr[2])+nz(pr[3]))+cf32*nz(but3[1])+cf33*nz(but3[2])+cf34*nz(but3[3])

// filtro de 4 polos
a41=exp(-5.8/p1)
b41=2*a41*cos(DTR*(117.5/p1))
c41=exp(-2.4/p1)
d41=2*c41*cos(DTR*(332.3/p1))
cf41=(1-b41+a41*a41)*(1-d41+c41*c41)/16
cf42=b41+d41
cf43=-(a41*a41+b41*d41+c41*c41)
cf44=a41*a41*d41+b41*c41*c41
cf45=-(a41*a41*c41*c41)

but4=cf41*(pr+4*nz(pr[1])+6*nz(pr[2])+4*nz(pr[3])+nz(pr[4]))+cf42*nz(but4[1])+cf43*nz(but4[2])+cf44*nz(but4[3])+cf45*nz(but4[4])

// filtro de 5 polos
a51=exp(-5.08/p1)
b51=2*a51*cos(DTR*(211.4/p1))
c51=exp(-1.94/p1)
d51=2*c51*cos(DTR*(342.6/p1))
e51=exp(-6.28/p1)
cf51=(1-b51+a51*a51)*(1-d51+c51*c51)*(1-e51)/32
cf52=b51+d51+e51
cf53=-(a51*a51+b51*d51+c51*c51+b51*e51+d51*e51)
cf54=a51*a51*d51+b51*c51*c51+a51*a51*e51+b51*d51*e51+c51*c51*e51
cf55=-(a51*a51*c51*c51+a51*a51*d51*e51+c51*c51*b51*e51)
cf56=a51*a51*c51*c51*e51

but5=cf51*(pr+5*nz(pr[1])+10*nz(pr[2])+10*nz(pr[3])+5*nz(pr[4])+nz(pr[5]))+cf52*nz(but5[1])+cf53*nz(but5[2])+cf54*nz(but5[3])+cf55*nz(but5[4])+cf56*nz(but5[5])

plot(but2, title = "Butterworth2", style = line, color = green, transp = 0, linewidth = 2) // Plot it
plot(but3, title = "Butterworth3", style = line, color = yellow, transp = 0, linewidth = 2) // Plot it
plot(but4, title = "Butterworth4", style = line, color = orange, transp = 0, linewidth = 2) // Plot it
plot(but5, title = "Butterworth5", style = line, color = red, transp = 0, linewidth = 2) // Plot it