#!/usr/bin/env python
"""
Gaussian Apodization
^^^^^^^^^^^^^^^^^^^^
"""
# %%
# In this example, we will use the
# :py:class:`~mrsimulator.signal_processor.apodization.Gaussian` class to perform a
# Gaussian convolution on an example dataset. The function
# used for this apodization is defined as follows
#
# .. math::
#
#    f(x) = e^{-2 \pi^2 \sigma^2  x^2}
#
# where :math:`\sigma` is the standard deviation of the Gaussian function and is
# parameterized by the full width as half maximum (FWHM) as
#
# .. math::
#
#   \sigma = \frac{\text{FWHM}}{2\sqrt{2\ln 2}}
#
# Below we import the necessary modules
# sphinx_gallery_thumbnail_number = 1
import csdmpy as cp
import numpy as np
from mrsimulator import signal_processor as sp

# %%
# First we create ``processor``, an instance of the
# :py:class:`~mrsimulator.signal_processor.SignalProcessor` class. The required
# attribute of the SignalProcessor class, *operations*, is a list of operations to which
# we add a :py:class:`~mrsimulator.signal_processor.apodization.Gaussian` object
# sandwiched between two Fourier transformations.
processor = sp.SignalProcessor(
    operations=[
        sp.IFFT(),
        sp.apodization.Gaussian(FWHM="75 Hz"),
        sp.FFT(),
    ]
)

# %%
# Next we create a CSDM object with a test dataset which our signal processor will
# operate on. Here, the dataset spans 500 Hz with a delta function centered at
# 0 Hz.
test_data = np.zeros(500)
test_data[250] = 1
csdm_object = cp.CSDM(
    dependent_variables=[cp.as_dependent_variable(test_data)],
    dimensions=[cp.LinearDimension(count=500, increment="1 Hz", complex_fft=True)],
)

# %%
# Now to apply the processor to the CSDM object, use the
# :py:meth:`~mrsimulator.signal_processor.SignalProcessor.apply_operations` method as
# follows
processed_dataset = processor.apply_operations(dataset=csdm_object).real

# %%
# To see the results of the Gaussian apodization, we create a simple plot using the
# ``matplotlib`` library.
import matplotlib.pyplot as plt

fig, ax = plt.subplots(1, 2, figsize=(8, 3.5), subplot_kw={"projection": "csdm"})
ax[0].plot(csdm_object, color="black", linewidth=1)
ax[0].set_title("Before")
ax[1].plot(processed_dataset.real, color="black", linewidth=1)
ax[1].set_title("After")
plt.tight_layout()
plt.show()