Digital Signal Processing Reference
In-Depth Information
EXACT QUANTIFICATION by FAST PADE TRANSFORM OUTSIDE the UNIT CIRCLE, FPT
(−)
; FID LENGTH: N
P
= 256
Absolute Values of Amplitudes: Input (x), Pade (o)
Absorption Total Shape Spectrum
0.25
18
PADE: FPT
(−)
B
0
=1.5T
PADE: FPT
(−)
B
0
=1.5T
N
P
= 256
N
P
= 256
0.2
14
5+6+7
6
2
0.15
3
14+15
10
1
7
15
16+17
16
0.1
8
9
8
22+23
9
22
6
17
14
10
12
25
5
21
19
20
11+12
1+2
3+4
0.05
20
10
19
4
21
13
18
25
24
24
23
18
2
11
13
0
0
5
4
3
2
1
5
4
3
2
1
(i) Chemical shift (ppm)
(iv) Chemical shift (ppm)
(Absolute Values of Amplitudes)/(Imaginary Frequencies)
Absorption Component Shape Spectra
18
7
PADE: FPT
(−)
PADE: FPT
(−)
B
0
=1.5T
B
0
=1.5T
N
P
= 256
6
N
P
= 256
6
14
6
5
4
10
15
3
15
7
6
7
16
2
16
22
8
22
9
21
19
20
8
9
17
14
12
19
20
21
5
1
3
10
1
17
18
14
12
2
5
25
3
10
2
18
13
1
24
11
4
2
23
25
24
13
11
4
23
0
0
5
4
3
2
1
5
4
3
2
1
(ii) Chemical shift (ppm)
(v) Chemical shift (ppm)
Argand Plot: Harmonic Variables; Input (
•
), Pade (o)
Argand Plot: Complex Frequencies; Input (x), Pade (o)
0
13
0
21
19
18
6
25
11
N
P
= 256
B
0
=1.5T
15
10
22
16
7
24
20
0.05
12
9
8
5
24
14
−0.2
ANALYTICAL
CONTINUATION
INSIDE the UNIT CIRCLE:
23
17
23
22
0.1
21
−0.4
20
4
19
25
18
−0.6
17
|z| < 1
0.15
16
3
15
1
|z| > 1
14
13
−0.8
12
0.2
PADE:
FPT
(−)
z
−
11
10
PADE: FPT
(−)
9
8
7
6
−1
5
N
P
= 256
−
k
)
1
2
k
= exp(−2i
πτ
ν
0.25
B
0
=1.5T
4
2
3
1
0.8
0.6
0.4
0.2
0
5
4
3
2
1
(iii) Re(z
k
)
−
k
) (ppm)
(vi) Re(
ν
FIGURE 3.14
Configurations of the reconstructed spectral parameters in the FPT
(−)
. Panel
(i): the absolute values|d
−
k
|of the amplitudes d
−
k
at the corresponding chem
ical shifts, Re(ν
k
). Panel (ii): the ratios|d
−
k
|/Im(ν
−
k
) that are proportional to
the peak heights. Panel (iii): distributions of poles via the harmonic variable
z
−
k
in the complex z
−
−plane.
Panel (vi): distributions of the fundamental
complex frequencies ν
−
k
in the complex ν
−
−plane.
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