Digital Signal Processing Reference
In-Depth Information
FAST PADE TRANSFORM (FPT): SIGNAL LENGTH N/M, N = 2048, M = 1 − 32
3
3
PADE: FPT
(−)
PADE: FPT
(−)
B
0
=7T
B
0
=7T
2.5
2.5
N/32 = 64
N/4 = 512
2
2
1.5
1.5
1
1
0.5
0.5
0
0
5
4
3
2
1
5
4
3
2
1
(i) Chemical shift (ppm)
(iv) Chemical shift (ppm)
3
3
PADE: FPT
(−)
PADE: FPT
(−)
B
0
=7T
B
0
=7T
2.5
2.5
N/16 = 128
N/2 = 1024
2
2
1.5
1.5
1
1
0.5
0.5
0
0
5
4
3
2
1
5
4
3
2
1
(ii) Chemical shift (ppm)
(v) Chemical shift (ppm)
3
3
PADE: FPT
(−)
PADE: FPT
(−)
B
0
=7T
B
0
=7T
2.5
2.5
N/8 = 256
N = 2048
2
2
1.5
1.5
1
1
0.5
0.5
0
0
5
4
3
2
1
5
4
3
2
1
(iii) Chemical shift (ppm)
(vi) Chemical shift (ppm)
FIGURE 7.8
Pade absorption spectra using the FPT
(−)
and the FID encoded at B
0
=7T
[141] with 5 partial signal lengths (N/32 = 64,N/16 = 128,N/8 = 256,N/4 =
512,N/2 = 1024) and the full signal length N = 2048.
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