Digital Signal Processing Reference
In-Depth Information
CONVERGENCE of COMPLEX FREQUENCIES in FPT
(−)
; FID LENGTH: N/M, N = 1024, M = 1−32
Argand Plot: Complex Frequencies; Input (x), Pade (o)
Argand Plot: Complex Frequencies; Input (x), Pade (o)
0
0
13
21
19
18
6
11
15
10
22
0.05
0.1
16
7
24
20
0.05
12
9
8
5
14
23
17
25
0.15
0.1
4
25
0.2
0.15
0.25
0.3
3
1
0.2
0.35
PADE: FPT
(−)
PADE: FPT
(−)
0.4
0.45
2
N/32 = 32
B
0
=1.5T
0.25
N/4 = 256
B
0
=1.5T
5
4
3
2
1
5
4
3
2
1
−
k
) (ppm)
−
k
) (ppm)
(i) Re(
ν
(iv) Re(
ν
Argand Plot: Complex Frequencies; Input (x), Pade (o)
Argand Plot: Complex Frequencies; Input (x), Pade (o)
0
0
13
21
19
18
6
11
15
10
22
16
7
24
20
0.05
24
0.05
12
9
8
5
14
23
17
0.1
0.1
4
25
25
0.15
0.15
3
1
1
0.2
0.2
PADE: FPT
(−)
PADE: FPT
(−)
0.25
N/2 = 512
2
0.25
N/16 = 64
B
0
=1.5T
B
0
=1.5T
5
4
3
2
1
5
4
3
2
1
−
k
) (ppm)
−
k
) (ppm)
(ii) Re(
ν
(v) Re(
ν
Argand Plot: Complex Frequencies; Input (x), Pade (o)
Argand Plot: Complex Frequencies; Input (x), Pade (o)
0
0
13
21
19
18
6
11
15
10
22
16
7
24
24
20
0.05
0.05
14
12
9
8
5
23
17
0.1
0.1
4
25
25
0.15
0.15
3
1
1
0.2
0.2
PADE: FPT
(−)
PADE: FPT
(−)
2
0.25
N/8 = 128
0.25
N = 1024
2
B
0
=1.5T
B
0
=1.5T
5
4
3
2
1
5
4
3
2
1
−
k
) (ppm)
−
k
) (ppm)
(iii) Re(
ν
(vi) Re(
ν
FIGURE 3.15
Convergence of the fundamental complex frequencies reconstructed by the
FPT
(−)
for signal lengths N/32
=
32,N/16 =
64,N/8
=
128,N/4 =
256,N/2 = 512 and N = 1024.
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