# Signal tools¶

This section summarizes functions operating on the signal data. Besides those implemented in LumiSpy, it highlights functions from HyperSpy that are particularly useful for luminescence spectroscopy data.

## Scaling and normalizing signal data¶

For comparative plotting or a detailed analysis, the intensity of spectra may need to be either scaled by the respective integration times or normalized. The luminescence signal classes provide these functionalities in the methods scale_by_exposure() and normalize().

Both functions can operate directly on the signal (inplace=True), but as default a new signal is returned.

The scaling function can use the integration_time (unit: seconds) provided in the LumiSpy metadata structure (metadata.Acqusition_instrument.Detector.integration_time). Otherwise, the appropriate parameter has to be passed to the function.

>>> scaled = s.scale_by_exposure(integration_time=0.5, inplace=True)


Normalization is performed for the pixel with maximum intensity, Alternatively, the parameter pos in calibrated units of the signal axis can be given to normalize the intensity at this position. Normalization may be convenient for plotting, but should usually not be performed on signals used as input for further analysis (therefore the default is inplace=False).

>>> s.normalize(pos=450)


## Peak positions and properties¶

### Peak identification¶

HyperSpy provides functions to find the positions of maxima or minima in a dataset:

These functions take the axis keyword to define along which axis to perform the operation and return a new signal containing the result.

A much more powerful method to identify peaks is using the peak finding routine based on the downward zero-crossings of the first derivative of a signal: find_peaks1D_ohaver(). This function can find multiple peaks in a dataset and has a number of parameters for fine-tuning the sensitivity, etc.

All of these functions can be performed for a subset of the dataset:

>>> peaks = s.find_peaks1D_ohaver()
>>> peaks = s.isig[100:-100].find_peaks1D_ohaver()


### Peak Width¶

For asymmetric peaks, fitted functions may not provide an accurate description of the peak, in particular the peak width. The function estimate_peak_width() determines the width of a peak at a certain fraction of its maximum value. The default value factor=0.5 returns the full width at half maximum (FWHM).

>>> s.remove_background()
>>> width = s.estimate_peak_width(factor=0.3)


### Calculating the centroid of a spectrum (centre of mass)¶

The function centroid() (based on the utility function com()) is an alternative to finding the position of the maximum intensity of a peak, useful in particular for non-symmetric peaks with pronounced shoulders. It finds the centroid (center of mass) of a peak in the spectrum from the signal axis units (or pixel number) and the intensity at each pixel value. It basically represents a “weighted average” of the peak as such:

$com = \frac{\sum{x_i I_i}}{\sum{I_i}},$

where $$x_i$$ is the wavelength (or pixel number) at which the intensity of the spectrum $$I_i$$ is measured.

This function also works for non-linear axes. For the hyperspy.axes.FunctionalDataAxis, the centroid is extrapolated based on the function used to create the non-uniform axis. For hyperspy.axes.DataAxis, a linear interpolation between the axes points at the center of mass is assumed, but this behaviour can be changed with the kwargs of scipy.interpolate.interp1d() function.

>>> s = lum.signals.LumiSpectrum([[[1, 2, 3, 2, 1, 0]]*2]*3)
>>> s
LumiSpectrum <2,3|5>

>>> ax = s.axes_manager.signal_axes[0]
>>> ax.offset = 200
>>> ax.scale = 100

>>> com = s.centroid()
>>> com
BaseSignal <2,3|>
>>> com.data[0,0]
400.


Note

This function only works for a single peak. If you have multiple peaks, slice the signal beforehand or use the slice parameter (which follows the s.isig[:] convention).

Note

The Jacobian transformation may affect the shape, in particular of broader peaks. It is therefore highly recommended to convert luminescence spectra from wavelength to the energy axis prior to determining the centroid to determine the true emission energy. See e.g. [Wang] and [Mooney].

## Signal statistics and analytical operations¶

Standard statistical operations can be performed on the data or a subset of the data, notably these include max(), min(), sum(), mean(), std(), and var(). Variations of all these functions exist that ignore missing values (NaN) if present, e.g. nanmax().

Integration along a specified signal axis is performed using the function integrate1D().

The numerical derivative of a signal can be calculated using the function derivative(), while the n-th order discrete difference can be calculated using diff().

These functions take the axis keyword to define along which axis to perform the operation and return a new signal containing the result:

>>> area = s.integrate1D(axis=0)


## Replacing negative data values¶

Log-scale plotting fails in the presence of negative values in the dataset (e.g. introduced after background removal). In this case, the utility function remove_negative() replaces all negative values in the data array by a basevalue (default basevalue=1). The default operational mode is inplace=False (a new signal object is returned).

>>> s.remove_negative(0.1)