Expression 6: StartFraction, .5 Over StartRoot, left parenthesis, log left parenthesis, 1 plus "N" , right parenthesis , right parenthesis , EndRoot , EndFraction Start sum from "i" equals 1 to "N" , end sum, left brace, mod left parenthesis, StartFraction, log left parenthesis, "i" , right parenthesis Over log left parenthesis, 2 , right parenthesis , EndFraction , 1 , right parenthesis equals 0 : cos left parenthesis, StartFraction, 2 pi "i" Over "N" , EndFraction "c" Subscript, 2 , Baseline left parenthesis, "x" , "i" , right parenthesis plus phi left parenthesis, "i" , right parenthesis , right parenthesis , 0 , right brace.5log1+NN∑i=1modlogilog2,1=0:cos2πiNc2x,i+ϕi,0
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Expression 7: Start sum from "i" equals 1 to 2 Superscript, "N" , Baseline , end sum, cosine left parenthesis, StartFraction, 2 pi 2 Superscript, "i" , Baseline Over 2 Superscript, "N" , Baseline , EndFraction "x" plus phi left parenthesis, 2 Superscript, "i" , Baseline , right parenthesis , right parenthesis2N∑i=1cos2π2i2Nx+ϕ2i
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Expression 8: phi left parenthesis, "x" , right parenthesis equals 2 pi left parenthesis, mod left parenthesis, sin left parenthesis, 10 to the 4th power "x" , right parenthesis 10 to the 4th power , 1 , right parenthesis , right parenthesis plus "c" Subscript, 1 , Baseline left parenthesis, "x" , right parenthesisϕx=2πmodsin104x104,1+c1x
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Expression 9: "c" Subscript, 1 , Baseline left parenthesis, "i" , right parenthesis equals "v" times "i" times "t"c1i=v·i·t
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Expression 10: "c" Subscript, 2 , Baseline left parenthesis, "x" , "i" , right parenthesis equals "x" minus "T" StartRoot, StartFraction, 9.9 1 Over "i" , EndFraction , EndRoot "t"c2x,i=x−T9.91it
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Expression 11: "t" equals 989.9 3 2t=989.932
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Expression 12: "y" equals negative 2 left brace, 0 less than or equal to "x" less than or equal to "N" , right bracey=−20≤x≤N