Введение в цифровую обработку сигналов

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Text of Введение в цифровую обработку сигналов

( )

, 2002

,

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.......................................................................................................................................3 ..........................................................................................................................................................3 .......................................................................................................................................................4 ...............................................................................................................................................................4 ................................................................................................................5 ......................................................................................................................................5 () ......................................................................................................................6 .......................................................................................................................................................7 ...............................................................................................................................................................8 .............................................................................................................................8 .....................................................................................................................................................11 .............................................................................................................................................................12 .................................................................................................................................................................12 .....................................................................................................................................................13 .............................................................................................................................................................13 ...........................................................................................................................................................14 ..................................................................................................15 ................................................................................................................................................15 ............................................................................................................................................18 ................................................................................................................................................18 .....................................................................................................................................................19 .............................................................................................................................................................20 ................................................................................................................................................20 ......................................................................................................................................20 . .......................................................................................23 ......................................................................................................................................................24 ...................................................................................................................................................29 .....................................................................................................................................................30 ...........................................................................................................................................................30 ............................................................................32 ............................................................................................................................................32 - ...........................................................................................................................34 ..................................................................................................................35 .................................................................................................39 ............................................................................................................................................41 ..............................................................................41 ..............................................................................................................41 ..........................................................................................41 ...............................................................................................................................41 ........................................................................................................................42 .............................................................................................................................43

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(). , . . - . , , x(t). . . x(t) y(t). : x(t ) y (t ) . , .. x(t ) y (t ) , x(t + T ) y (t + T ) . , , . . . , , , , . , : x1 (t ) y1 (t ) x 2 (t ) y 2 (t ) , x1 (t ) + x 2 (t ) y1 (t ) + y 2 (t ) . t. . , ( ), 2 , ( ) , .

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: 1. () . 2. . ( ). , .. (-). ? , , .. t = t = + . ( - , , - 0), . . .

x(t ) y (t ) , 1. , y(t)=cos(t)+sin(3t). ? x(t)=sin(t)+sin(2t),

2. x(t)=2sin(t)-cos(3t). ? 3. , ( ) .

1. , .. sin(3t), . . , sin(2t) , .. . 2. , A sin(t + ) + B sin(t + ) , A, B, - . 3. x1 (t ) 1 y1 (t ) 2 z1 (t ) x 2 (t ) 1 y 2 (t ) 2 z 2 (t ) . 1 x1 (t ) + x 2 (t ) y1 (t ) + y 2 (t ) , , y1 (t ) + y 2 (t ) 2 z1 (t ) + z 2 (t ) . , 1 2 x1 (t ) + x 2 (t ) z1 (t ) + z 2 (t ) , .

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(, ) ( ). . . , . ( ) . . , , , . () . , - , (, analogue-to-digital converter, ADC). , , . : ? . , . , . , . () . ( ). , .. . , , . , . , F ( F), F . --: , F, 2F

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. . . , , . , , 20 . , 40 , - . , . , , - (, digital-to-analogue converter, DAC). , , - , -. - 44100 . , CD 44100 .

() , ( )? . , , , , , . (aliasing). , , 20 , - (, ) 39 , . 44.1 . , , 44.1 = 22.05 ( 2 ). .. 22.05 , , , 5 . , 5 . , . , , . , , , . ? , 6

. . , , . , (-, low-pass filters) , , , . (cutoff frequency) . . -, .. . - . , , - . 44.1 , 22 . , , 22 (, ), , 22 ( ). , 22 . , , ( ). - . , . . , 11 5.5 . ( , ). - , .

1. , 8 . ? ? 2. 44 - . 24 . ? ? ? 3. , - ?

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1. , 8 0 4 . 4 , 4 . 2. 22 , . .. 24 , , , 22 24 . ( 22 ) 20 22 . , 20 22 . , , .. 20 . 3. , .. . .

, , , . x[n] ( ), y[n] (. 1). , .

3

2

1

0

1

2

3

. 1. : , . , , .. . , . - ( - ).

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1, n = 0 - () [n] = , .. 0, n 0 (. 2).1

3

2

1

0

1

2

3

. 2. -. , , (. 3). , x[n] x[n] =i =

x[i] [n i] . -

+

, x[i] . n, x[n]=x[n]*1, .. 0, - .

. 3. -. -. - . [n] h[n] (. 4). , h[n] ( -), . , , h[n]. (. 5).

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[n]3 2 1

1

h[n]0 1 2 3 3 2 1

1

0

1

2

3

. 4. -.

x[n]3 2 1 0 1 2 3

x[1] [n + 1]3 2 1 0 1 2 3

x[1] h[n + 1]3 2 1 0 1 2 3

x[0] [n]3 2 1 0 1 2 3

x[0] h[n]3 2 1 0 1 2 3

x[1] [n 1]3 2 1 0 1 2 3

x[1] h[n 1]3 2 1 0 1 2 3

y[n]3 2 1 0 1 2 3

. 5. h[n].

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y[n] x[n] : y[n] =k =

x[n k ] h[k ] . h[n]

+

(impulse response) , .. (-). . .