Señales discretas - Control digital ejercicios PDF

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Ejercicios de Señales Discretas 1) Integral y la diferencia x ( n )=

{2

−n

0,∧n< 0 +3 n ,∧n ≥ 0

n -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

x(n)

∑x(n)

Δx(n)

∇x(n)

0 0 -1 1 3.5 6.25 9.125 12.0625 15.03125 18.015625 21.007812 5 24.003906 3 27.001953 1 30.000976 6 33.000488 3 36.000244 1 39.000122 1 42.000061

0 0 -1 0 3.5 9.75 18.875 30.9375 45.96875 63.984375 84.992187 5 108.99609 4 135.99804 7 165.99902 3 198.99951 2 234.99975 6 273.99987 8 315.99993 9 360.99996 9 408.99998 5 459.99999 2 513.99999 6 570.99999 8 630.99999

0 0 2 2.5 2.75 2.875 2.9375 2.96875 2.984375 2.9921875 2.9960937 5 2.9980468 8 2.9990234 4 2.9995117 2 2.9997558 6 2.9998779 3 2.9999389 6 2.9999694 8 2.9999847 4 2.9999923 7 2.9999961 9 2.9999980 9 2.9999990 5 2.9999995

0 0 -1 2 2.5 2.75 2.875 2.9375 2.96875 2.984375 2.9921875

45.000030 5 48.000015 3 51.000007 6 54.000003 8 57.000001 9 60.000001

2.9960937 5 2.9980468 8 2.9990234 4 2.9995117 2 2.9997558 6 2.9998779 3 2.9999389 6 2.9999694 8 2.9999847 4 2.9999923 7 2.9999961 9 2.9999980 9 2.9999990

9

x(n)

700 600 500 400 300 200 100 0 0 -100

-5

2

5

x(n) ∑x(n) Δx(n) ∇x(n) 5

10

15

20

25

n

x ( n )=

{2

−n

0,∧n< 0 +5 n+n2 ,∧n≥ 0

x(n)

∑x(n)

∆x(n)

∇x(n)

-3 -2 -1 0 1 2 3 4 5 6

0 -2 -2 1 6.5 14.25 24.125 36.0625 50.03125 66.015625

0 -2 -4 -3 3.5 17.75 41.875 77.9375 127.96875 193.984375

0 -2 0 3 5.5 7.75 9.875 11.9375 13.96875 15.984375

7

84.007812 5 104.00390 6 126.00195 3 150.00097 7 176.00048 8 204.00024 4 234.00012 2 266.00006 1 300.00003

277.992187 5 381.996093 8 507.998046 9 657.999023 4 833.999511 7 1037.99975 6 1271.99987 8 1537.99993 9 1837.99996

-2 0 3 5.5 7.75 9.875 11.9375 13.96875 15.984375 17.992187 5 19.996093 8 21.998046 9 23.999023 4 25.999511 7 27.999755 9 29.999877 9 31.999939

n

8 9 10 11 12 13 14 15

33.999969 5 35.999984

17.992187 5 19.996093 8 21.998046 9 23.999023 4 25.999511 7 27.999755 9 29.999877 9 31.999939 33.999969

1 336.00001 5 374.00000 8 414.00000 4 456.00000 2 500.00000 1

16 17 18 19 20

9 2173.99998 5 2547.99999 2 2961.99999 6 3417.99999 8 3917.99999 9

7 37.999992 4 39.999996 2 41.999998 1 43.999999 500.00000 1

5 35.999984 7 37.999992 4 39.999996 2 41.999998 1 43.999999

4500 4000 3500 3000 2500

x(n) ∑x(n) ∆x(n) ∇x(n)

2000 1500 1000 500 0 -5

0

5

10

-500

2) Escalonado en magnitud

x ( n )=α 1 x (n )= x ( n )=

{4

−n

{

α 1=2

0,∧n< 0 2∗(2 +3 n),∧n ≥ 0 −n

0,∧n< 0 +6 n ,∧n≥ 0

15

20

25

1400 1200 1000

x(n)

800 �(� ) ∑�(� ) △�(� ) ∇x(n)

600 400 200 -5

0

0

5

10

-200

n

α 2=−3

x ( n )=α 2 x (n )= x ( n )=

{

0, ∧n< 0 −3∗(2−n+3 n),∧n≥ 0

0 {−6 0,−9∧n...