Digital Signal Processing Reference
In-Depth Information
CONSECUTIVE DIFFERENCE SPECTRA (PADE)
RESIDUAL or ERROR SPECTRA
1.5
1.5
N/4 = 512
1
B
0
=4T
1
N = 2048
B
0
=4T
N/8 = 256
0.5
0.5
0
0
−0.5
−0.5
FPT
(−)
(N/4) − FPT
(−)
(N/8)
FFT(N) − FPT
(+)
(N)
−1
−1
−1.5
−1.5
5
4
3
2
1
5
4
3
2
1
(i) Chemical shift (ppm)
(iv) Chemical shift (ppm)
1.5
1.5
N/2 = 1024
1
B
0
=4T
1
N = 2048
B
0
=4T
N/4 = 512
0.5
0.5
0
0
−0.5
−0.5
FPT
(−)
(N/2) − FPT
(−)
(N/4)
FFT(N) − FPT
(−)
(N)
−1
−1
−1.5
−1.5
5
4
3
2
1
5
4
3
2
1
(ii) Chemical shift (ppm)
(v) Chemical shift (ppm)
1.5
1.5
N = 2048
N = 2048
1
B
0
=4T
1
B
0
=4T
N/2 = 1024
0.5
0.5
0
0
−0.5
−0.5
FPT
(−)
(N) − FPT
(−)
(N/2)
FPT
(+)
(N) − FPT
(−)
(N)
−1
−1
−1.5
−1.5
5
4
3
2
1
5
4
3
2
1
(iii) Chemical shift (ppm)
(vi) Chemical shift (ppm)
FIGURE 7.15
The three consecutive absorption difference spectra at 4T from the
FPT
(−)
computed via Re(P
−
/Q
−
)[N/4]−Re(P
−
/Q
−
)[N/8] (top left
panel), Re(P
−
/Q
−
)[N/2]−Re(P
−
/Q
−
)[N/4] (middle left panel) and
Re(P
−
/Q
−
)[N]−Re(P
−
/Q
−
)[N/2] (bottom left panel), where N is the full
length (N = 2048) of the time signal which has been encoded in Ref. [141].
Also shown here are the three residual absorption spectra computed at the
full signal length N = 2048 for Re(F)−Re(P
K
/Q
K
) (top right panel),
Re(F)−Re(P
−
K
/Q
−
K
) (middle right panel) and Re(P
+
/Q
+
)−Re(P
−
/Q
−
)
(bottom right panel).
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