tabla<\/a><\/p>\n\n\n\n propiedades<\/a><\/p>\n<\/div>\n\n\n\n Referencia<\/strong><\/em>: Lathi Tabla 3.1 p285<\/p>\n\n\n \\gamma_1 \\neq \\gamma_2<\/span>\n\n\n\n tabla<\/a><\/p>\n\n\n\n
\n\n\n\nTabla de suma de convoluci\u00f3n<\/h2>\n\n\n\n
No<\/th> x1<\/sub>[n]<\/th> x2<\/sub>[n]<\/th> x1<\/sub>[n]\u2297x2<\/sub>[n] = x2<\/sub>[n]\u2297x1<\/sub>[n]<\/th><\/tr><\/thead> 1<\/td> \u03b4[n-k]<\/td> x[n]<\/td> x[n-k]<\/td><\/tr> 2<\/td> \\gamma^{n} \\mu[n]<\/span><\/td> \u03bc[n]<\/td> \\frac{1-\\gamma^{n+1}}{1-\\gamma} \\mu[n]<\/span><\/td><\/tr> 3<\/td> \u03bc[n]<\/td> \u03bc[n]<\/td> (n+1) \u03bc[n]<\/td><\/tr> 4<\/td> \\gamma_1^{n} \\mu[n] <\/span><\/td> \\gamma_2^{n} \\mu[n] <\/span><\/td> \\frac{\\gamma_1^{n+1} - \\gamma_2^{n+1}}{\\gamma_1 - \\gamma_2} \\mu[n]<\/span><\/td><\/tr> 5<\/td> \\gamma_1^{n} \\mu[n] <\/span><\/td> \\gamma_2^{n} \\mu[-(n+1) ] <\/span><\/td> \\frac{\\gamma_1}{\\gamma_2 - \\gamma_1} \\gamma_1^{n} \\mu[n] + <\/span>
+ \\frac{\\gamma_2}{\\gamma_2 - \\gamma_1} \\gamma_2^{n} \\mu[-(n+1)] <\/span><\/td><\/tr> <\/td> <\/td> <\/td> |\\gamma_2| > |\\gamma_1|<\/span><\/td><\/tr> 6<\/td> n\\gamma_1^{n} \\mu[n] <\/span><\/td> \\gamma_2^{n} \\mu[n] <\/span><\/td> \\frac{\\gamma_1 \\gamma_2}{(\\gamma_1 - \\gamma_2)^2} \\Big[ \\gamma_2^{n} - \\gamma_1^{n} + \\frac{\\gamma_1 - \\gamma_2}{\\gamma_2}n \\gamma_1^n \\Big] \\mu [n] <\/span><\/td><\/tr> <\/td> <\/td> <\/td> \\gamma_1\\neq \\gamma_2 <\/span><\/td><\/tr> 7<\/td> n \u03bc[n]<\/td> n \u03bc[n]<\/td> \\frac{1}{6} n (n-1) (n+1) \\mu [n] <\/span><\/td><\/tr> 8<\/td> \\gamma^{n} \\mu[n] <\/span><\/td> \\gamma^{n} \\mu[n] <\/span><\/td> (n+1) \\gamma^{n} \\mu[n] <\/span><\/td><\/tr> 9<\/td> \\gamma^{n} \\mu[n] <\/span><\/td> n \\mu[n] <\/span><\/td> \\Big[ \\frac{\\gamma(\\gamma^{n}-1)+n(1-\\gamma)}{(1-\\gamma)^2} \\Big] \\mu[n] <\/span><\/td><\/tr> 10<\/td> |\\gamma_1|^{n} \\cos (\\beta n + \\theta) \\mu [k] <\/span><\/td> |\\gamma_2|^{n}\\mu [n] <\/span><\/td> \\frac{1}{R} \\Big[ |\\gamma_1|^{n+1} \\cos [\\beta (n+1) +\\theta -\\phi] -\\gamma_2 ^{n+1} \\cos (\\theta - \\phi) \\Big] \\mu[n] <\/span><\/td><\/tr> <\/td> <\/td> <\/td> R=\\Big[|\\gamma_1|^2 + \\gamma_2^2 -2|\\gamma_1|\\gamma_2 \\cos(\\beta) \\Big]^{\\frac{1}{2}} <\/span><\/td><\/tr> <\/td> <\/td> <\/td> \\phi = \\tan ^{-1} \\Big[ \\frac{|\\gamma_1| \\sin(\\beta)}{|\\gamma_1| \\cos (\\beta) -\\gamma_2} \\Big] <\/span><\/td><\/tr> 11<\/td> \\mu [n]<\/span><\/td> n\\mu [n] <\/span><\/td> \\frac{n(n+1)}{2}\\mu [n]<\/span> <\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
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