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Обратное дискретное преобразование Лапласа

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Предмет: Теория Автоматического Управления

Тема: Обратное дискретное преобразование Лапласа

1. Обратное дискретное преобразование Лапласа

Решетчатая функция – это результат временного квантования непрерывного
сигнала – которая представляет значение непрерывного сигнала в
дискретные моменты времени. Решетчатая функция получается перемножением
непрерывной функции на сигма-функцию. Ее можно определить по ее
изображению, используя различные способы:

1. С помощью формул обратного дискретного преобразования Лапласа.

2. С помощью разложения на простые дроби.

3. С помощью разложения в степенной ряд.

В данном реферате мы рассмотрим обратное дискретного преобразование
Лапласа.

2. Определение оригинала с помощью формул обратного дискретного
преобразования Лапласа

Для непрерывных оригиналов обратное преобразование Лапласа имеет вид:
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 (1)

Для нахождения формул обратного дискретного преобразования Лапласа
установим связь между плоскостями p и z. Отображение плоскости P в
плоскость Z осуществляется с помощью подстановки z = epT.

Так как p = c+j, то z = epT = ecTe jT, где ecT- модуль z, а T- фаза z.

Если с = 0, то
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a01000000ef0008000000320a9004661001000000ef0015000000fb02c0fe00000000000
09001010000000402001054696d6573204e657720526f6d616e000067040000002d01010
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3010000006a0008000000320ac002700401000000650008000000320ac0024e000100000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picscalex100010009000003ae0100000300150000000000050000000902000000000400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.

С?????е ??у ????я? p и z ????? ? ?с. 3.
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0100fc00040000002e01010031000000320a0100fc0019000400000000001c0268012b6a
202020202020202020202020202020202020202020202000110008000800080008000800
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2d01030004000000f0010b00040000002d0101000800000026060f000600ffffffff0100
040000002d010000030000000000 z = e
pTpicscalex960100090000038005000008003d00000000001400000026060f001e00fff
fffff040014000000576f72640e004d6963726f736f667420576f7264050000000b02000
00000050000000c022301460113000000fb0200000000000000000000000000cc0000000
1436f7572696572204e657700cc00040000002d01000007000000fc020000dfdfdf00000
0040000002d01010009000000fa02000001000000000000022200040000002d010200070
000001804ec00fe002500370007000000fc020000ffffff000000040000002d010300040
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000000000040000002d01040008000000250302000100910033019100040000002d01010
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00201010015000000fb02e7ff0000000000009001000000000440001054696d6573204e6
57720526f6d616e000000040000002d01020005000000090200000000050000001402050
00000040000002e0101000e000000320a050000000200040000000000460123012020060
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00000140201000c00040000002e01010032000000320a01000c001a00040000000000460
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015000000fb02e2ff0000000000009001000000cc0440001254696d6573204e657720526
f6d616e00cc00040000002d010600040000002e01010011000000320a0100ec000400040
00000000046012301efeb2e5a10000f0008001200040000002e010000040000002d01050
004000000f0010600050000001402a884b0a204000000020101000400000002010100040
000002d01050005000000140224000000040000002e0101002b000000320a24000000150
004000000000046012301202020202020202020202020202020202020202054000800080
008000800080008000800080008000800080008000800080008000800080008000800080
01300040000002e0100000500000014023f01000015000000fb02edff000000000000900
1000000000440001054696d6573204e657720526f6d616e000000040000002d010600050
0000014023300b300040000002e0101000d000000320a3300b3000100040000000000460
1230134000900040000002e010000050000001402a884b0a2040000002d0105000400000
002010100040000000201010004000000020101000400000002010100040000002d01050
00500000014026a000000040000002e01010011000000320a6a000000040004000000000
046012301202020540800080008001300040000002e010000050000001402a884b0a2040
000002d01060005000000140279002b00040000002e0101000d000000320a79002b00010
00400000000004601230133000900040000002e010000050000001402a884b0a20400000
02d0105000500000014026a003400040000002e01010037000000320a6a0034001d00040
000000000460123012020202020202020202020202020202020202020202020202020202
031000800080008000800080008000800080008000800080008000800080008000800080
0080008000800080008000800080008000800080008000f00040000002e0100000500000
01402a884b0a204000000020101000400000002010100040000002d01050005000000140
28d000000040000002e0101003d000000320a8d000000210004000000000046012301202
020202020202020202020202020202020202020202020202020202020202054000800080
008000800080008000800080008000800080008000800080008000800080008000800080
00800080008000800080008000800080008000800080008001300040000002e010000050
000001402a884b0a2040000002d0106000500000014029c001301040000002e0101000d0
00000320a9c00130101000400000000004601230131000900040000002e0100000500000
01402a884b0a2040000002d0105000500000014028d001c01040000002e0101001000000
0320a8d001c0103000400000000004601230120202b00080008001100040000002e01000
0050000001402a884b0a204000000020101000400000002010100050000001402b000000
0040000002e0101003d000000320ab000000021000400000000004601230120202020202
0202020202020202020202020433c302020202020202020433e203000080008000800080
008000800080008000800080008000800080008000800080008000800140011000f00080
008000800080008000800080008001400110008000f00040000002e01000005000000140
2a884b0a204000000020101000400000002010100050000001402d300000005000000140
2a884b0a204000000020101000400000002010100040000002d010500050000001402f60
00000040000002e01010022000000320af60000000f00040000000000460123012020202
020202020202020202020540008000800080008000800080008000800080008000800080
0080008001300040000002e010000050000001402a884b0a2040000002d0106000500000
0140205018300040000002e0101000d000000320a0501830001000400000000004601230
132000900040000002e010000050000001402a884b0a2040000002d01020004000000020
101001000000026060f001600ffffffff00008f000000ffffffff9400000024010000090
00000fa02000002000000000000002200040000002d010700040000002d0104000800000
0250302009100010091002101040000002d01010004000000f0010700040000002d01030
00800000026060f000600ffffffff01001000000026060f001600ffffffff00002300000
08f0000003a000000a600000009000000fa02000002000000000000002200040000002d0
10700040000002d0104000800000025030200370091002500a300040000002d010100040
00000f0010700040000002d0103000800000026060f000600ffffffff010010000000260
60f001600ffffffff0000350000008f0000004c000000a600000009000000fa020000020
00000000000002200040000002d010700040000002d01040008000000250302003700910
04900a300040000002d01010004000000f0010700040000002d0103000800000026060f0
00600ffffffff01001000000026060f001600ffffffff0000350000007d0000004c00000
09400000009000000fa02000002000000000000002200040000002d010700040000002d0
1040008000000250302003700910049007f00040000002d01010004000000f0010700040
000002d0103000800000026060f000600ffffffff01001000000026060f001600fffffff
f0000230000007d0000003a0000009400000009000000fa0200000200000000000000220
0040000002d010700040000002d01040008000000250302003700910025007f000400000
02d01010004000000f0010700040000002d0103000800000026060f000600ffffffff010
0040000002d010000030000000000

Рис. 1

Точки на мнимой оси дискретной плоскости будут повторяться, поэтому на
плоскости можно выделить бесконечное множество полос с шириной п (0.. п
, п ..2п и т. д.), которые дают одно и тоже изображение в плоскости Z.
Корни в плоскости P являются периодическими, повторяющимися и заключены
в любую из полос. Если С > 0, что соответствует правой полуплоскости, то
амплитуда z > 1.

Интегрировать можно по частотам расположенным в любой из полос, считая
ее как основную, а значения интеграла в других полосах просуммировать.
Для удобства интегрирования в качестве основной полосы принимаем полосу
частот от -п /2 до п/

При переходе в плоскость Z интегрирование осуществляется по замкнутому
контуру.

Пример 7. Определить непрерывную функцию, если ее дискретное изображение
определяется соотношением

picscalex100010009000003060100000300170000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c026004a0091200000026060f001a00ffffffff00001000
0000c0ffffffbaffffff600900001a0400000b00000026060f000c004d61746854797065
0000d00009000000fa02000010000000000000002200040000002d010000050000001402
500253050500000013025002c30817000000fb0240fe0000000000009001010000cc0402
001054696d6573204e657720526f6d616e2043797200cc67040000002d01010008000000
320ac0021509010000002e0008000000320a2004df0701000000310008000000320a2004
6505010000007a0008000000320aa401a906010000007a0008000000320ac002d2020100
0000290008000000320ac0020002010000007a0008000000320ac0020b01010000002800
08000000320ac002400001000000780010000000fb0240fe000000000000900100000002
0002001053796d626f6c0002040000002d01020004000000f001010008000000320a2004
9406010000002d0008000000320ac002ec03010000003d000a00000026060f000a00ffff
ffff01000000000010000000fb021000070000000000bc02000000cc0102022253797374
656d00cc040000002d01010004000000f0010200030000000000

Решение: Определяем значения полюсов z1 = 1, их количество n = 1 и

кратность m = 1. Используя формулу обратного дискретного преобразования,
определяем оригинал
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Т. е. заданному изображению соответствует единичная функция.

Пример 8. Определить непрерывную функцию, если дискретное изображение
имеет вид

Решение: Определяем значения полюсов z1 = 1, их количество n = 1 и

кратность m =

О???я? ?и??л, ????я ???у ????о ?????о ?е??з??ия
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Пример 9. Определить непрерывную функцию, если дискретное изображение
имеет вид
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Решение: Определяем значения полюсов z1 = 1, их количество n = 1 и
кратность m = Используя формулу обратного дискретного преобразования,
определяем оригинал
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Пример 10. Определить непрерывную функцию, если ее дискретное
изображение равно
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Решение: Определяем значения полюсов z1 = d, их количество n = 1 и

кратность m = 1. Используя формулу обратного дискретного преобразования,
определяем оригинал

picscalex10001000900000313030000030015000000000005000000090200000000040
0000002010100050000000102ffffff00040000002e01180005000000310201000000050
000000b0200000000050000000c022008a02c1200000026060f001a00ffffffff0000100
00000c0ffffffabffffff602c0000cb0700000b00000026060f000c004d6174685479706
50000d00109000000fa02000010000000000000002200040000002d01000005000000140
27802e70a0500000013027802b90e15000000fb0240fe000000000000900101000000040
2001054696d6573204e657720526f6d616e000066040000002d01010008000000320a6a0
73316010000002e0008000000320a6a07d01201000000650008000000320a6a078e10010
00000290008000000320a6a07ae0f01000000740008000000320a6a07dc0e01000000280
008000000320a6a071f0e01000000780008000000320a6a07e9060100000065000800000
0320a6a076104010000005d0008000000320a6a071c02020000006e5408000000320a6a0
72701010000005b0008000000320a6a074e0001000000780008000000320ae802262c010
000002e0008000000320ae8027f2701000000650008000000320ae802832301000000640
008000000320ae802cd1f010000007a0009000000320ae802b51c030000006c696d00080
00000320ae8024a16010000007a0008000000320ae8029b1401000000290008000000320
ae802441301000000640008000000320ae802bc10010000007a0008000000320ae802c70
f01000000280008000000320a48049d0d01000000640008000000320a4804150b0100000
07a0008000000320acc01800c010000007a0009000000320ae8025d07030000006c696d0
008000000320ae8026104010000005d0008000000320ae8021c02020000006e540800000
0320ae8022701010000005b0008000000320ae8024e0001000000780015000000fb0280f
e0000000000009001010000000402001054696d6573204e657720526f6d616e000066040
000002d01020004000000f001010008000000320aa1066c1501000000740008000000320
aa1068509020000006e5408000000320a1f021b2a020000006e5408000000320a1f02b92
4010000006e0008000000320a1f02b620010000006e0008000000320a6f04871e0100000
0640008000000320a6f045b1c010000007a0008000000320a1f02cf18010000003100080
00000320a1f023317010000006e0008000000320a6f042f0901000000640008000000320
a6f040307010000007a0010000000fb0280fe00000000000090010100000200020010537
96d626f6c0002040000002d01010004000000f001020008000000320aa1067c140100000
0610008000000320aa106950801000000610008000000320a1f022b29010000006100100
00000fb0280fe0000000000009001000000020002001053796d626f6c0002040000002d0
1020004000000f001010008000000320aa106c013010000002d0008000000320aa106d90
7010000002d0008000000320a1f026f28010000002d0008000000320a6f04051d0100000
0ae0008000000320a1f020118010000002d0008000000320a6f04ad0701000000ae00100
00000fb0240fe0000000000009001000000020002001053796d626f6c0002040000002d0
1010004000000f001020008000000320a6a077711010000003d0008000000320a6a07e60
b01000000de0008000000320a6a079005010000003d0008000000320ae80226260100000
03d0008000000320ae8022322010000003d0008000000320ae802e81a010000003d00080
00000320aa203c71901000000fa0008000000320a7804c71901000000fb0008000000320
af201c71901000000f90008000000320aa2032a0a01000000ea0008000000320a78042a0
a01000000eb0008000000320af2012a0a01000000e90008000000320ae8026f150100000
0d70008000000320ae802e411010000002d0008000000320ae8021d0f01000000d700080
00000320a48043d0c010000002d0008000000320ae8029005010000003d000a000000260
60f000a00ffffffff01000000000010000000fb021000070000000000bc02000000cc010
2022253797374656d00cc040000002d01020004000000f0010100030000000000

Пример 11. Определить непрерывную функцию, если ее дискретное
изображение равно
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Решение: Определяем значения полюсов z1 = 1, z2 = d, их количество

n = 2 и кратность m = 1. Используя формулу обратного дискретного
преобразования, определяем оригинал
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Пример 1 Определить непрерывную функцию, если ее дискретное изображение
равно
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Решение: Определяем значения полюсов z1 = d их количество n = 1 и
кратность m = 1. Используя формулу обратного дискретного преобразования,
определяем оригинал
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3. Определение оригинала с помощью разложения на простые дроби

Дискретное изображение можно разложить на простые дроби и, используя
табличные значения изображений для каждой составляющей, входящей в
разложение, найти оригиналы.

Пример 13. Определить непрерывную функцию, если ее дискретное
изображение определяется соотношением

picscalex1000100090000033d0200000300150000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02e004001c1200000026060f001a00ffffffff00001000
0000c0ffffffb9ffffffc01b0000990400000b00000026060f000c004d61746854797065
0000100109000000fa02000010000000000000002200040000002d010000050000001402
50025a050500000013025002c70f15000000fb0240fe0000000000009001010000000402
001054696d6573204e657720526f6d616e0000c0040000002d01010008000000320ac002
4a1b01000000200008000000320ac002121b010000002e0008000000320ac0022b170100
0000650008000000320ac0025d1401000000640008000000320ac002f413010000002000
09000000320ac0025f10030000002020200015000000fb0240fe00000000000090010100
00cc0402001054696d6573204e657720526f6d616e00ccc0040000002d01020004000000
f001010009000000320ac002af1103000000e320200015000000fb0240fe000000000000
9001010000000402001054696d6573204e657720526f6d616e0000c0040000002d010100
04000000f001020008000000320ac0022710010000002c0008000000320a2004370f0100
0000290008000000320a2004e00d01000000640008000000320a2004580b010000007a00
08000000320a2004d00902000000292808000000320a2004bf0801000000310008000000
320a20044c06010000007a0008000000320a2004570501000000280008000000320a9e01
0f0d01000000290008000000320a9e01b80b01000000640008000000320a9e0129090100
0000310008000000320a9e015e0801000000280008000000320a9e01af07010000007a00
08000000320ac0020a0301000000290008000000320ac0020002010000007a0008000000
320ac0020b0101000000280008000000320ac0024e0001000000780015000000fb0280fe
0000000000009001010000000402001054696d6573204e657720526f6d616e0000c00400
00002d01020004000000f001010008000000320af701c71901000000540010000000fb02
80fe0000000000009001010000020002001053796d626f6c0002040000002d0101000400
0000f001020008000000320af701d71801000000610010000000fb0280fe000000000000
9001000000020002001053796d626f6c0002040000002d01020004000000f00101000800
0000320af7011b18010000002d0010000000fb0240fe0000000000009001000000020002
001053796d626f6c0002040000002d01010004000000f001020008000000320ac002d215
010000003d0008000000320a2004800c010000002d0008000000320a2004740701000000
2d0008000000320a9e01580a010000002d0008000000320ac002f303010000003d000a00
000026060f000a00ffffffff01000000000010000000fb021000070000000000bc020000
00cc0102022253797374656d00cc040000002d01020004000000f0010100030000000000

Решение: Представим x(z) в виде простых дробей
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Значения параметров A и B находим методом неопределенных коэффициентов
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Определение оригинала с помощью разложения дискретного изображения в
степенной ряд

Для выхода импульсного элемента можно записать соотношение
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Таким образом, формула прямого дискретного преобразования может быть
использована для получения оригинала по изображению, так как x[nT] в
формуле прямого дискретного преобразования представляет значения
непрерывного сигнала в дискретные моменты времени.

Любая x(z) представляет отношение степенных полиномов.
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 (5)

Если это отношение разложить в ряд по степеням z, то коэффициенты при z
представляют собой значения оригинала. Дробно – рациональную функцию
можно разложить в ряд путем деления числителя на знаменатель или
представить в виде суммы простых дробей.

Пример 14. Определить непрерывную функцию, если ее дискретное
изображение определяется соотношением
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Решение: Выполняем почленное деление полиномов

z z-d

-z+d 1+dz-1+d2z-2 +…+dnz-n

d

-d+d2z-1

d2z-1

-d2z-1+d3z-2

d3z-2

По полученным значениям x[nT] строим график функции приведенный на рис.
2.

Пример 15. Определить непрерывную функцию, если ее дискретное
изображение равно
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Решение:

Выполняем почленное деление полиномов

z+1 z2+z+1

-z-1-z-1 z-1-z-3 +z-4 -z-6+z-7

-z-1

-z-1-z-2-z-3

z-2+ z-3

-z-2-z-3 -z-4

-z-4

-z-4-z-5 -z-6

z-5+z-6

Рис. 3

По полученным значениям x[nT] строим график функции приведенный на рис.
3.

Для ?????я ????? ???и ? ? ?????у ?????ю ??о ?????? лю?й ? ??????х ???в.
В?? ??? за??т ? ?р? ??????я ?????я.

4. Основные теоремы дискретного преобразования Лапласа

1. Т??? ?н???и. И????? ???? ????? р????х ???й ??????т ???? ???а?и ?
?????й
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 (6)

т.е. изображение суммы равно сумме изображений
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.

Теорема запаздывания и упреждения (смещения аргументов). Смещение
оригинала на k соответствует умножению изображения на zk
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 (7)

3. Теорема свертывания в вещественной области (умножения изображений)

Для непрерывных систем
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 (8)

Для дискретных систем
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 (9)

4. Д???я ???а. Т?р?а ?????я в ?????й ???и (ум???я ?????)
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 (10)

5. Теорема о начальном значении функции
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 (11)

6. Теорема о конечном значении функции

picscalex10001000900000327020000030015000000000005000000090200000000040
0000002010100050000000102ffffff00040000002e01180005000000310201000000050
000000b0200000000050000000c02e004c02b1200000026060f001a00ffffffff0000100
00000c0ffffffb4ffffff802b0000940400000b00000026060f000c004d6174685479706
50000100109000000fa02000010000000000000002200040000002d01000005000000140
25002ce230500000013025002162715000000fb0240fe000000000000900101000000040
2001054696d6573204e657720526f6d616e000066040000002d01010008000000320ac00
2b02a02000000292e08000000320ac002a629010000007a0008000000320ac002b228010
00000280008000000320ac002862701000000460008000000320a22042225010000007a0
008000000320aa301402601000000310008000000320aa301fc23010000007a000900000
0320ac002df20030000006c696d0008000000320ac0023b1d010000005d0008000000320
ac002f61a020000006e5408000000320ac002011a010000005b0008000000320ac002131
901000000660009000000320ac0029615030000006c696d000a000000320ac0027312060
0000020202020202008000000320ac002a81102000000292c08000000320ac0027410010
00000700008000000320ac0025d0f01000000280008000000320ac002510d02000000704
609000000320ac002010a030000006c696d0008000000320ac0027306010000002900080
00000320ac002940501000000740008000000320ac002c30401000000280008000000320
ac002f10301000000660009000000320ac0029b00030000006c696d0015000000fb0280f
e0000000000009001010000000402001054696d6573204e657720526f6d616e000066040
000002d01020004000000f001010008000000320a4704c92201000000310008000000320
a4704aa20010000007a0008000000320a47040d15010000006e0008000000320a4704fd0
b01000000300008000000320a4704ba0901000000700008000000320a47042e000100000
0740010000000fb0240fe0000000000009001000000020002001053796d626f6c0002040
000002d01010004000000f001020008000000320aa3010d25010000002d0008000000320
ac002681e01000000de0008000000320ac0025a0701000000de0010000000fb0280fe000
0000000009001000000020002001053796d626f6c0002040000002d01020004000000f00
1010008000000320a4704572101000000ae0008000000320a4704561701000000a500080
00000320a4704d81501000000ae0008000000320a47048b0a01000000ae0008000000320
a4704340201000000a50008000000320a4704b60001000000ae000a00000026060f000a0
0ffffffff01000000000010000000fb021000070000000000bc02000000cc01020222537
97374656d00cc040000002d01010004000000f0010200030000000000 (12)

7. Преобразование смешанного изображения в дискретное
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 (13)

8. Теорема разложения
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Если где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, то
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 (14)

Список литературы

1. Кожевников Н.И., Краснощекова Т.И., Шишкин Н.Е. Ряды и интегралы
Фурье. Теория поля. Аналитические и специальные функции. Преобразования
Лапласа.-М., Наука, 1964

2. Краснов М.Л., Макаренко Г.И. Операционное исчисление. Устойчивость
движения.- М., Наука, 1964.-103 с.

3. Микусинский Я. Операторное исчисление.-М., ИЛ, 1956

4. Сергиенко А.Б. Цифровая обработка сигналов. — 2-е. — Спб: Питер,
2006. — С. 751.

5. Гольденберг Л.М. и др. Цифровая обработка сигналов: Учебное пособие
для вузов. – М.: Радио и связь, 1990.- 256 с.

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