Exact quantum-mechanical, Pad´e-based recovery of spectral parameters - Signal Processing in MRS with Biomedical Applications - page 128

CONVERGENCE of COMPLEX FREQUENCIES in FPT (+) (Left) and FPT (−) (Right); FID LENGTH: N P = 180, 220, 260

Argand Plot: Complex Frequencies; Input (x), Pade (o) Argand Plot: Complex Frequencies; Input (x), Pade (o)

0 0

21 21

19 19

6 18 6

15 10 15 10

22 22

16

7 7

24 20 24 20

0.05 0.05

9 8 5 9 8 5

23

0.1 0.1

4 4

25 25

0.15 0.15

3 3

1 1

0.2 0.2

PADE: FPT (+) PADE: FPT (−)

N P = 180 B 0 =1.5T N P = 180 B 0 =1.5T

0.25

2

0.25

2

5 4 3 2 1 5 4 3 2 1

+
k ) (ppm)

−
k ) (ppm)

(i) Re( (iv) Re(

ν ν

Argand Plot: Complex Frequencies; Input (x), Pade (o) Argand Plot: Complex Frequencies; Input (x), Pade (o)

0 0

13 13

21 21

19 19

18 11 6 18 6

11

15 10 15 10

22 22

16 7 16 7

24 20 24 20

0.05 0.05

12 9 8 5 12 9 8 5

14 14

23 23

17 17

0.1 0.1

4 4

25 25

0.15 0.15

3 3

1 1

Converged

0.2 0.2

PADE: FPT (+) PADE: FPT (−)

N P = 220 B 0 =1.5T N P = 220 B 0 =1.5T

0.25

2

0.25

2

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 13

21 21

19 19

20

18 6 18 6

11 11

15 10 15 10

22 22

16 7 16 7

24 20 24

0.05 0.05

12 9 8 5 12 9 8 5

14 14

23 17 23 17

0.1 0.1

4 4

25 25

0.15 0.15

3 3

1 1

Converged Converged

0.2 0.2

PADE: FPT (+) PADE: FPT (−)

N P = 260 B 0 =1.5T N P = 260 B 0 =1.5T

0.25

2

0.25

2

5 4 3 2 1 5 4 3 2 1

+
k ) (ppm)

−
k ) (ppm)

(iii) Re( ν (vi) Re( ν

FIGURE 3.16
Convergence of the fundamental complex frequencies reconstructed by the
FPT (+)

(left) and FPT (−)

(right) near full convergence for signal lengths

N P = 180, 220, 260.