Apodization

[1]:

import spectrochempy as scp
from spectrochempy.core.units import ur

SpectroChemPy's API - v.0.8.1
©Copyright 2014-2025 - A.Travert & C.Fernandez @ LCS

Introduction

As an example, apodization is a transformation particularly useful for preprocessing NMR time domain data before Fourier transformation. It generally helps for signal-to-noise improvement.

[2]:

# read an experimental spectra
path = scp.pathclean("nmrdata/bruker/tests/nmr/topspin_1d")

# the method pathclean allow to write pth in linux or window style indifferently
dataset = scp.read_topspin(path, expno=1, remove_digital_filter=True)
dataset = dataset / dataset.max()  # normalization

# store original data
nd = dataset.copy()

# show data
nd

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MPL Configuration directory: /home/runner/.config/matplotlib
Stylelib directory: /home/runner/.config/matplotlib/stylelib

[2]:

NDDataset: [complex128] dimensionless (size: 12411)[topspin_1d expno:1 procno:1 (FID)]

Summary

name

:

topspin_1d expno:1 procno:1 (FID)

author

:

runner@fv-az1436-235

created

:

2025-03-23 01:42:42+00:00

history

:

2025-03-23 01:42:42+00:00> Binary operation truediv with `(2283.5096153847107-2200.383064516033j) pp` has been performed

Data

title

:

intensity

values

:

...

R[ 0.4717 1 ... 3.96e-05 -1.135e-05]
I[0.0003036 0 ... 6.533e-05 -3.403e-05]

size

:

12411 (complex)

Dimension `x`

size

:

12411

title

:

F1 acquisition time

coordinates

:

[ 0 4 ... 4.964e+04 4.964e+04] µs

Plot of the Real and Imaginary original data

[3]:

nd.plot(xlim=(0.0, 15000.0))
nd.plot(imag=True, data_only=True, clear=False, color="r")

[3]:

../../_images/userguide_processing_apodization_5_1.png

Exponential multiplication

[4]:

nd.plot(xlim=(0.0, 15000.0))
_ = nd.em(lb=300.0 * ur.Hz)
nd.plot(data_only=True, clear=False, color="g")

[4]:

../../_images/userguide_processing_apodization_7_1.png

Warning: processing function are most of the time applied inplace. Use inplace=False option to avoid this if necessary

[5]:

nd = dataset.copy()  # to go back to the original data
nd.plot(xlim=(0.0, 5000.0))
ndlb = nd.em(lb=300.0 * ur.Hz, inplace=False)  # ndlb contain the processed data
nd.plot(data_only=True, clear=False, color="g")  # nd dataset remain unchanged
ndlb.plot(data_only=True, clear=False, color="b")

[5]:

../../_images/userguide_processing_apodization_9_1.png

Of course, imaginary data are also transformed at the same time

[6]:

nd.plot(imag=True, xlim=(0, 5000), color="r")
ndlb.plot(imag=True, data_only=True, clear=False, color="b")

[6]:

../../_images/userguide_processing_apodization_11_1.png

If we want to display the apodization function, we can use the retapod=True parameter.

[7]:

nd = dataset.copy()
nd.plot(xlim=(0.0, 5000.0))
ndlb, apod = nd.em(
    lb=300.0 * ur.Hz, inplace=False, retapod=True
)  # ndlb contain the processed data and apod the
# apodization function
ndlb.plot(data_only=True, clear=False, color="b")
apod.plot(data_only=True, clear=False, color="m", linestyle="--")

[7]:

../../_images/userguide_processing_apodization_13_1.png

Shifted apodization

[8]:

nd = dataset.copy()
nd.plot(xlim=(0.0, 5000.0))
ndlb, apod = nd.em(
    lb=300.0 * ur.Hz, shifted=1000 * ur.us, inplace=False, retapod=True
)  # ndlb contain the processed data and apod the apodization function
ndlb.plot(data_only=True, clear=False, color="b")
apod.plot(data_only=True, clear=False, color="m", linestyle="--")

[8]:

../../_images/userguide_processing_apodization_15_1.png

Other apodization functions

Gaussian-Lorentzian apodization

[9]:

nd = dataset.copy()
lb = 10.0
gb = 200.0
ndlg, apod = nd.gm(lb=lb, gb=gb, inplace=False, retapod=True)
nd.plot(xlim=(0.0, 5000.0))
ndlg.plot(data_only=True, clear=False, color="b")
apod.plot(data_only=True, clear=False, color="m", linestyle="--")

[9]:

../../_images/userguide_processing_apodization_18_1.png

Shifted Gaussian-Lorentzian apodization

[10]:

nd = dataset.copy()
lb = 10.0
gb = 200.0
ndlg, apod = nd.gm(lb=lb, gb=gb, shifted=2000 * ur.us, inplace=False, retapod=True)
nd.plot(xlim=(0.0, 5000.0))
ndlg.plot(data_only=True, clear=False, color="b")
apod.plot(data_only=True, clear=False, color="m", linestyle="--")

[10]:

../../_images/userguide_processing_apodization_20_1.png

Apodization using sine window multiplication

Thesp apodization is by default performed on the last dimension.

Functional form of apodization window (cfBruker TOPSPIN manual): \(sp(t) = \sin(\frac{(\pi - \phi) t }{\text{aq}} + \phi)^{pow}\)

where

\(0 < t < \text{aq}\) and \(\phi = \pi ⁄ \text{sbb}\) when \(\text{ssb} \ge 2\)

or

\(\phi = 0\) when \(\text{ssb} < 2\)

\(\text{aq}\) is an acquisition status parameter and \(\text{ssb}\) is a processing parameter (see below) and \(\text{ pow}\) is an exponent equal to 1 for a sine bell window or 2 for a squared sine bell window.

The \(\text{ssb}\) parameter mimics the behaviour of the SSB parameter on bruker TOPSPIN software:

Typical values are 1 for a pure sine function and 2 for a pure cosine function.
Values greater than 2 give a mixed sine/cosine function. Note that all values smaller than 2, for example 0, have the same effect as \(\text{ssb}=1\), namely a pure sine function.

Shortcuts:

sine is strictly an alias of sp
sinm is equivalent to sp with \(\text{pow}=1\)
qsin is equivalent to sp with \(\text{pow}=2\)

Below are several examples of sinm and qsin apodization functions.

[11]:

nd = dataset.copy()
nd.plot()

new, curve = nd.qsin(ssb=3, retapod=True)
curve.plot(color="r", clear=False)
new.plot(xlim=(0, 25000), zlim=(-2, 2), data_only=True, color="r", clear=False)

[11]:

../../_images/userguide_processing_apodization_22_1.png

[12]:

nd = dataset.copy()
nd.plot()

new, curve = nd.sinm(ssb=1, retapod=True)
curve.plot(color="b", clear=False)
new.plot(xlim=(0, 25000), zlim=(-2, 2), data_only=True, color="b", clear=False)

[12]:

../../_images/userguide_processing_apodization_23_1.png

[13]:

nd = dataset.copy()
nd.plot()

new, curve = nd.sinm(ssb=3, retapod=True)
curve.plot(color="b", ls="--", clear=False)
new.plot(xlim=(0, 25000), zlim=(-2, 2), data_only=True, color="b", clear=False)

[13]:

../../_images/userguide_processing_apodization_24_1.png

[14]:

nd = dataset.copy()
nd.plot()

new, curve = nd.qsin(ssb=2, retapod=True)
curve.plot(color="m", clear=False)
new.plot(xlim=(0, 25000), zlim=(-2, 2), data_only=True, color="m", clear=False)

[14]:

../../_images/userguide_processing_apodization_25_1.png

[15]:

nd = dataset.copy()
nd.plot()

new, curve = nd.qsin(ssb=1, retapod=True)
curve.plot(color="g", clear=False)
new.plot(xlim=(0, 25000), zlim=(-2, 2), data_only=True, color="g", clear=False)

[15]:

../../_images/userguide_processing_apodization_26_1.png