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( 071900), , ( 190500) .
MathCAD.
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1.
- - (), (). , , ( ), , . , , , . : . , S(t), .
. , , . (, ), . () .
, F, . . . S(t), F, S(k), k=1,2,3,,
 .(1)
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, S(t) , T. () S(t), T, 2T, 3T,... . ., .
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S(t) [1]:
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(2)
- k-
(. 1).
. 1
(2) , S(t) . sinx/x, . k- t=kT S(kT) , (. . 1).
, . , , . F. . 0 F, ( 90 99 %, ). , , . . :
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S(f) ,
,
.
, , , , F. , .
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, , F, m, :
m>>1, (1) m=2FTc.
 (3)
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u(t) :
(3) , S(t) . S(t) . , , (. 2).
. 2
m , . m . .
:
1) , , , , ;
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2) ( ) . , . . .
, (1), . . ( ).
, (1), F, . F - F, F=1/ - .
, .
2.
:
1) ;
2) .
2.1. ( ).
2.1.1. S(t)=sin(2pF1ct+j), .. t 0 1/2F1c. 1.
1
| j | p/6 | p/4 | p/3 | 2p/3 | 3p/4 | 5p/6 | -p/6 | -p/4 | -p/3 | -2p/3 | -3p/4 | -5p/6 |
2.1.2. Uo. , , .
2.
2
| - | F2c, | , | Uo, | U, | |
| 1, 3, 5 | 1, 0.3, 0.2 | 10 1 | |||
| 1, 3 | 2, 0.5 | 6 0.8 | |||
| 1, 4 | 0.2, 0.4 | 9 0.6 | |||
| 2, 3, 6 | 1, 2, 0.4 | 2.5 | 9 1.5 | ||
| 1, 4, 7 | 1, 0.3, 0.2 | 11 1.5 | |||
| 1, 3, 5 | 1, 0.5, 0.3 | 1.5 | 10 2 | ||
| 2, 4 | 1, 2 | 11 1.5 | |||
| 3, 8 | 1, 1 | 20 1.7 | |||
| 1, 9, 12 | 2, 1, 1.5 | 17 0.5 | |||
| 1, 2 | 1, 0.5 | 5 1.5 | |||
| 4, 8, 9 | 1, 2, 3 | 18 2.5 | |||
| 2, 4, 6, | 6, 3, 2 | 9 1 |
2.2. MathCAD .
2.2.1. 1:= 1/2F1c. F1c: = 1 .
2.2.2. MathCAD. MathCAD , , k- . , .. , MathCAD. fft(s), 2 ( := 128).
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2.2.3. MathCAD k:= 0.. K-1.
2.2.4. dt1:= T1c/K.
2.2.5. MathCAD t1 k := kdt1.
2.2.6. , t t1 k ,
S1 k := sin(2pF1ct1 k+j).
2.3. .
2.3.1. T2: = 1/F2c, F2c - .
2.3.2. 2.2.2 - 2.2.5, T1c, dt1 t1k T2c, dt2 t2 k.
2.3.3. , :
S2 k := 2sin(2p F2c t2 k)+0.5sin(2p 3F2c t2 k)+0.3sin(2p 5F2c t2 k)+1.5.
2.4. .
2.4.1. .
. , 0.1 .
.
1) n:=0.. K/2.
2) , S1, sp1:= fft(S1).
3) msp1n:=|sp1n|.
4) Np , . MathCAD ( ), Np , 2.
5) F1max:=Np/T1c.
6) 1o:=1/2F1max.
2.4.2. .
1) , M1:= 2 T1c F1max+1.
2) , .. dt1, , M1o:= 1o/dt1 .
3) j1:= 0.. M1.
4) MathCAD, m1 j1: = j1 M1o.
5) , k M ( ):
S1mk, j1: = if (k = m1j1 , S1k , 0).
6) , :
S1dk:= å S1m k , j1.
j1
, .
7) 1,
DOS1 j1:= å S1m k, j1.
k
2.5. .
2.5.1. .
1) , , .. F2max.
2)
2o:= 1/2 F2max.
2.5.2. .
1) , M2:= 2T2cF2max+1. - MathCAD fft(S), , s , 2. 2 , 2.
2) 2o:= T2c/M2.
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3) , .. dt2, M2o:= 2o/dt2.
4) j2:= 0.. M2.
5) MathCAD, m2 j2: = j2 M2o.
6) , k M2 ( )
S2mk, j2: = if (k = m2 j2 , S2k , 0).
7) , . , .
S2dk:= å S2m k , j2.
J2
3.
3.1. .
3.1.1. MathCAD S1 k. S1 k = f(t1 k).
3.1.2. , S1d k. S1d k = f(t1 k).
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3.1.3. , j- .
3.1.4. 0/0.
f1 k, j1:= if(t1 k = j1 ×T1o, 1, f k, j1).
3.1.5. f1 k, j1 = f (t1 k).
3.1.6.
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3.1.7. :
S1 k = f(t1 k ) S K k = f (t1 k).
3.1.8. DS k:= S1 k - SK k .
3.1.9. DS k = f (t1 k).
3.2. .
3.2.1. MathCAD S2 k. S2 k = f(t2 k).
3.2.2. , S2d k. S2d k = f(t2 k).
3.2.3. .
1) n:= 0.. K/2.
2)
Sp2d:= fft (S2d).
3)
mSp2 n:= | Sp2d n |.
4) f2 n:= n/T2c.
5) mSp2 n = f (f2 n).
6) S2 k . .
7) 2 - 5 .
8) , .
4.
4.1. .
4.2. , MathCAD .
4.3. .
4.4. , .
4.5. .
4.6. .
4.7. , , , .
5.
5.1. . . .
5.2. . . .
5.3. .
5.4. .
5.5. .
5.6. , : .
5.7.
. . . .: . , 1989. . 63 - 81.
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