The Signal class¶
The Signal class and its subclasses¶
Warning
This subsection can be a bit confusing for beginners. Do not worry if you do not understand it all.
HyperSpy stores the data in the BaseSignal
class, that is
the object that you get when e.g. you load a single file using
load()
. Most of the data analysis functions are also contained in
this class or its specialized subclasses. The BaseSignal
class contains general functionality that is available to all the subclasses.
The subclasses provide functionality that is normally specific to a particular
type of data, e.g. the Signal1D
class provides
common functionality to deal with onedimensional (e.g. spectral) data and
EELSSpectrum
(which is a subclass of
Signal1D
) adds extra functionality to the
Signal1D
class for electron energyloss
spectroscopy data analysis.
The table below summarises all the
specialised BaseSignal
subclasses currently distributed
with HyperSpy.
The signals
module, which contains all available signal subclasses,
is imported in the user namespace when loading HyperSpy. In the following
example we create a Signal2D instance from a 2D numpy array:
>>> im = hs.signals.Signal2D(np.random.random((64,64)))
>>> im
<Signal2D, title: , dimensions: (64, 64)>
The different signals store other objects in what are called attributes. For
examples, the data is stored in a numpy array in the
data
attribute, the original parameters in the
original_metadata
attribute, the mapped parameters
in the metadata
attribute and the axes
information (including calibration) can be accessed (and modified) in the
AxesManager
attribute.
Signal initialization¶
Many of the values in the AxesManager
can be
set when making the BaseSignal
object.
>>> dict0 = {'size': 10, 'name':'Axis0', 'units':'A', 'scale':0.2, 'offset':1}
>>> s = hs.signals.BaseSignal(np.random.random((10,20)), axes=[dict0, dict1])
>>> s.axes_manager
<Axes manager, axes: (20, 10)>
Name  size  index  offset  scale  units
================  ======  ======  =======  =======  ======
          
Axis1  20   2  0.1  B
Axis0  10   1  0.2  A
This also applies to the metadata
.
>>> metadata_dict = {'General':{'name':'A BaseSignal'}}
>>> metadata_dict['General']['title'] = 'A BaseSignal title'
>>> s = hs.signals.BaseSignal(np.arange(10), metadata=metadata_dict)
>>> s.metadata
├── General
│ ├── name = A BaseSignal
│ └── title = A BaseSignal title
└── Signal
├── binned = False
└── signal_type =
Binned and unbinned signals¶
Signals that are a histogram of a probability density function (pdf) should
have the signal.metadata.Signal.binned
attribute set to
True
. This is because some methods operate differently in signals that are
binned.
Changed in version 1.0: Simulation
, SpectrumSimulation
and ImageSimulation
classes removed.
The default value of the binned
attribute is shown in the
following table:
BaseSignal subclass 
binned 

False 

False 

True 

True 


True 
False 

False 

False 

False 
To change the default value:
>>> s.metadata.Signal.binned = True
Generic tools¶
Below we briefly introduce some of the most commonly used tools (methods). For
more details about a particular method click on its name. For a detailed list
of all the methods available see the BaseSignal
documentation.
The methods of this section are available to all the signals. In other chapters methods that are only available in specialized subclasses.
Mathematical operations¶
A number of mathematical operations are available
in BaseSignal
. Most of them are just wrapped numpy
functions.
The methods that perform mathematical operation over one or more axis at a time are:
Note that by default all this methods perform the operation over all navigation axes.
Example:
>>> s = hs.signals.BaseSignal(np.random.random((2,4,6)))
>>> s.axes_manager[0].name = 'E'
>>> s
<BaseSignal, title: , dimensions: (6, 4, 2)>
>>> # by default perform operation over all navigation axes
>>> s.sum()
<BaseSignal, title: , dimensions: (6, 4, 2)>
>>> # can also pass axes individually
>>> s.sum('E')
<Signal2D, title: , dimensions: (4, 2)>
>>> # or a tuple of axes to operate on, with duplicates, by index or directly
>>> ans = s.sum((1, s.axes_manager[1], 'E', 0))
>>> ans
<BaseSignal, title: , dimensions: (1)>
>>> ans.axes_manager[0]
<Scalar axis, size: 1>
The following methods operate only on one axis at a time:
All numpy ufunc can operate on BaseSignal
instances, for example:
>>> s = hs.signals.Signal1D([0, 1])
>>> s.metadata.General.title = "A"
>>> s
<Signal1D, title: A, dimensions: (2)>
>>> np.exp(s)
<Signal1D, title: exp(A), dimensions: (2)>
>>> np.exp(s).data
array([ 1. , 2.71828183])
>>> np.power(s, 2)
<Signal1D, title: power(A, 2), dimensions: (2)>
>>> np.add(s, s)
<Signal1D, title: add(A, A), dimensions: (2)>
>>> np.add(hs.signals.Signal1D([0, 1]), hs.signals.Signal1D([0, 1]))
<Signal1D, title: add(Untitled Signal 1, Untitled Signal 2), dimensions: (2)>
Notice that the title is automatically updated. When the signal has no title a new title is automatically generated:
>>> np.add(hs.signals.Signal1D([0, 1]), hs.signals.Signal1D([0, 1]))
<Signal1D, title: add(Untitled Signal 1, Untitled Signal 2), dimensions: (2)>
Functions (other than unfucs) that operate on numpy arrays can also operate
on BaseSignal
instances, however they return a numpy
array instead of a BaseSignal
instance e.g.:
>>> np.angle(s)
array([ 0., 0.])
Indexing¶
Indexing a BaseSignal
provides a powerful, convenient and
Pythonic way to access and modify its data. In HyperSpy indexing is achieved
using isig
and inav
, which allow the navigation and signal dimensions
to be indexed independently. The idea is essentially to specify a subset of the
data based on its position in the array and it is therefore essential to know
the convention adopted for specifying that position, which is described here.
Those new to Python may find indexing a somewhat esoteric concept but once mastered it is one of the most powerful features of Python based code and greatly simplifies many common tasks. HyperSpy’s Signal indexing is similar to numpy array indexing and those new to Python are encouraged to read the associated numpy documentation on the subject.
Key features of indexing in HyperSpy are as follows (note that some of these features differ from numpy):
HyperSpy indexing does:
Allow independent indexing of signal and navigation dimensions
Support indexing with decimal numbers.
Support indexing with units.
Use the image order for indexing i.e. [x, y, z,…] (HyperSpy) vs […,z,y,x] (numpy)
HyperSpy indexing does not:
Support indexing using arrays.
Allow the addition of new axes using the newaxis object.
The examples below illustrate a range of common indexing tasks.
First consider indexing a single spectrum, which has only one signal dimension
(and no navigation dimensions) so we use isig
:
>>> s = hs.signals.Signal1D(np.arange(10))
>>> s
<Signal1D, title: , dimensions: (10)>
>>> s.data
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> s.isig[0]
<Signal1D, title: , dimensions: (1)>
>>> s.isig[0].data
array([0])
>>> s.isig[9].data
array([9])
>>> s.isig[1].data
array([9])
>>> s.isig[:5]
<Signal1D, title: , dimensions: (5)>
>>> s.isig[:5].data
array([0, 1, 2, 3, 4])
>>> s.isig[5::1]
<Signal1D, title: , dimensions: (6)>
>>> s.isig[5::1]
<Signal1D, title: , dimensions: (6)>
>>> s.isig[5::2]
<Signal1D, title: , dimensions: (3)>
>>> s.isig[5::2].data
array([5, 7, 9])
Unlike numpy, HyperSpy supports indexing using decimal numbers or string (containing a decimal number and an units), in which case HyperSpy indexes using the axis scales instead of the indices.
>>> s = hs.signals.Signal1D(np.arange(10))
>>> s
<Signal1D, title: , dimensions: (10)>
>>> s.data
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> s.axes_manager[0].scale = 0.5
>>> s.axes_manager[0].axis
array([ 0. , 0.5, 1. , 1.5, 2. , 2.5, 3. , 3.5, 4. , 4.5])
>>> s.isig[0.5:4.].data
array([1, 2, 3, 4, 5, 6, 7])
>>> s.isig[0.5:4].data
array([1, 2, 3])
>>> s.isig[0.5:4:2].data
array([1, 3])
>>> s.axes_manager[0].units = 'µm'
>>> s.isig[:'2000 nm'].data
array([0, 1, 2, 3])
Importantly the original BaseSignal
and its “indexed self”
share their data and, therefore, modifying the value of the data in one
modifies the same value in the other. Note also that in the example below
s.data is used to access the data as a numpy array directly and this array is
then indexed using numpy indexing.
>>> s = hs.signals.Signal1D(np.arange(10))
>>> s
<Signal1D, title: , dimensions: (10,)>
>>> s.data
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> si = s.isig[::2]
>>> si.data
array([0, 2, 4, 6, 8])
>>> si.data[:] = 10
>>> si.data
array([10, 10, 10, 10, 10])
>>> s.data
array([10, 1, 10, 3, 10, 5, 10, 7, 10, 9])
>>> s.data[:] = 0
>>> si.data
array([0, 0, 0, 0, 0])
Of course it is also possible to use the same syntax to index multidimensional
data treating navigation axes using inav
and signal axes using isig
.
>>> s = hs.signals.Signal1D(np.arange(2*3*4).reshape((2,3,4)))
>>> s
<Signal1D, title: , dimensions: (3, 24)>
>>> s.data
array([[[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]],
[[12, 13, 14, 15],
[16, 17, 18, 19],
[20, 21, 22, 23]]])
>>> s.axes_manager[0].name = 'x'
>>> s.axes_manager[1].name = 'y'
>>> s.axes_manager[2].name = 't'
>>> s.axes_manager.signal_axes
(<t axis, size: 4>,)
>>> s.axes_manager.navigation_axes
(<x axis, size: 3, index: 0>, <y axis, size: 2, index: 0>)
>>> s.inav[0,0].data
array([0, 1, 2, 3])
>>> s.inav[0,0].axes_manager
<Axes manager, axes: (4)>
Name  size  index  offset  scale  units
================  ======  ======  =======  =======  ======
          
t  4   0  1  <undefined>
>>> s.inav[0,0].isig[::1].data
array([3, 2, 1, 0])
>>> s.isig[0]
<BaseSignal, title: , dimensions: (3, 2)>
>>> s.isig[0].axes_manager
<Axes manager, axes: (3, 2)>
Name  size  index  offset  scale  units
================  ======  ======  =======  =======  ======
x  3  0  0  1  <undefined>
y  2  0  0  1  <undefined>
          
>>> s.isig[0].data
array([[ 0, 4, 8],
[12, 16, 20]])
Independent indexation of the signal and navigation dimensions is demonstrated further in the following:
>>> s = hs.signals.Signal1D(np.arange(2*3*4).reshape((2,3,4)))
>>> s
<Signal1D, title: , dimensions: (3, 24)>
>>> s.data
array([[[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]],
[[12, 13, 14, 15],
[16, 17, 18, 19],
[20, 21, 22, 23]]])
>>> s.axes_manager[0].name = 'x'
>>> s.axes_manager[1].name = 'y'
>>> s.axes_manager[2].name = 't'
>>> s.axes_manager.signal_axes
(<t axis, size: 4>,)
>>> s.axes_manager.navigation_axes
(<x axis, size: 3, index: 0>, <y axis, size: 2, index: 0>)
>>> s.inav[0,0].data
array([0, 1, 2, 3])
>>> s.inav[0,0].axes_manager
<Axes manager, axes: (4)>
Name  size  index  offset  scale  units
================  ======  ======  =======  =======  ======
          
t  4   0  1  <undefined>
>>> s.isig[0]
<BaseSignal, title: , dimensions: (2, 3)>
>>> s.isig[0].axes_manager
<Axes manager, axes: (3, 2)>
Name  size  index  offset  scale  units
================  ======  ======  =======  =======  ======
x  3  0  0  1  <undefined>
y  2  0  0  1  <undefined>
          
>>> s.isig[0].data
array([[ 0, 4, 8],
[12, 16, 20]])
The same syntax can be used to set the data values in signal and navigation dimensions respectively:
>>> s = hs.signals.Signal1D(np.arange(2*3*4).reshape((2,3,4)))
>>> s
<Signal1D, title: , dimensions: (3, 24)>
>>> s.data
array([[[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]],
[[12, 13, 14, 15],
[16, 17, 18, 19],
[20, 21, 22, 23]]])
>>> s.inav[0,0].data
array([0, 1, 2, 3])
>>> s.inav[0,0] = 1
>>> s.inav[0,0].data
array([1, 1, 1, 1])
>>> s.inav[0,0] = s.inav[1,1]
>>> s.inav[0,0].data
array([16, 17, 18, 19])
Signal operations¶
BaseSignal
supports all the Python binary arithmetic
operations (+, , *, //, %, divmod(), pow(), **, <<, >>, &, ^, ),
augmented binary assignments (+=, =, *=, /=, //=, %=, **=, <<=, >>=, &=,
^=, =), unary operations (, +, abs() and ~) and rich comparisons operations
(<, <=, ==, x!=y, <>, >, >=).
These operations are performed elementwise. When the dimensions of the signals are not equal numpy broadcasting rules apply independently for the navigation and signal axes.
Warning
Hyperspy does not check if the calibration of the signals matches.
In the following example s2 has only one navigation axis while s has two. However, because the size of their first navigation axis is the same, their dimensions are compatible and s2 is broadcasted to match s’s dimensions.
>>> s = hs.signals.Signal2D(np.ones((3,2,5,4)))
>>> s2 = hs.signals.Signal2D(np.ones((2,5,4)))
>>> s
<Signal2D, title: , dimensions: (2, 34, 5)>
>>> s2
<Signal2D, title: , dimensions: (24, 5)>
>>> s + s2
<Signal2D, title: , dimensions: (2, 34, 5)>
In the following example the dimensions are not compatible and an exception is raised.
>>> s = hs.signals.Signal2D(np.ones((3,2,5,4)))
>>> s2 = hs.signals.Signal2D(np.ones((3,5,4)))
>>> s
<Signal2D, title: , dimensions: (2, 34, 5)>
>>> s2
<Signal2D, title: , dimensions: (34, 5)>
>>> s + s2
Traceback (most recent call last):
File "<ipythoninput55044bb11a0bd9>", line 1, in <module>
s + s2
File "<string>", line 2, in __add__
File "/home/fjd29/Python/hyperspy/hyperspy/signal.py", line 2686, in _binary_operator_ruler
raise ValueError(exception_message)
ValueError: Invalid dimensions for this operation
Broadcasting operates exactly in the same way for the signal axes:
>>> s = hs.signals.Signal2D(np.ones((3,2,5,4)))
>>> s2 = hs.signals.Signal1D(np.ones((3, 2, 4)))
>>> s
<Signal2D, title: , dimensions: (2, 34, 5)>
>>> s2
<Signal1D, title: , dimensions: (2, 34)>
>>> s + s2
<Signal2D, title: , dimensions: (2, 34, 5)>
Inplace operators also support broadcasting, but only when broadcasting would not change the left most signal dimensions:
>>> s += s2
>>> s
<Signal2D, title: , dimensions: (2, 34, 5)>
>>> s2 += s
Traceback (most recent call last):
File "<ipythoninput64fdb9d3a69771>", line 1, in <module>
s2 += s
File "<string>", line 2, in __iadd__
File "/home/fjd29/Python/hyperspy/hyperspy/signal.py", line 2737, in _binary_operator_ruler
self.data = getattr(sdata, op_name)(odata)
ValueError: nonbroadcastable output operand with shape (3,2,1,4) doesn\'t match the broadcast shape (3,2,5,4)
Iterating external functions with the map method¶
Performing an operation on the data at each coordinate, as in the previous example,
using an external function can be more easily accomplished using the
map()
method:
>>> import scipy.ndimage
>>> image_stack = hs.signals.Signal2D(np.array([scipy.misc.ascent()]*4))
>>> image_stack.axes_manager[1].name = "x"
>>> image_stack.axes_manager[2].name = "y"
>>> image_stack.map(scipy.ndimage.rotate,
... angle=45,
... reshape=False)
>>> # clip data to integer range
>>> image_stack.data = np.clip(image_stack.data, 0, 255)
>>> collage = hs.stack([image for image in image_stack], axis=0)
>>> collage.plot()
The map()
method can also take variable
arguments as in the following example.
>>> import scipy.ndimage
>>> image_stack = hs.signals.Signal2D(np.array([scipy.misc.ascent()]*4))
>>> image_stack.axes_manager[1].name = "x"
>>> image_stack.axes_manager[2].name = "y"
>>> angles = hs.signals.BaseSignal(np.array([0, 45, 90, 135]))
>>> image_stack.map(scipy.ndimage.rotate,
... angle=angles.T,
... reshape=False)
New in version 1.2.0: inplace
keyword and nonpreserved output shapes
If all function calls do not return identicallyshaped results, only navigation information is preserved, and the final result is an array where each element corresponds to the result of the function (or arbitrary object type). As such, most HyperSpy functions cannot operate on such Signal, and the data should be accessed directly.
The inplace
keyword (by default True
) of the
map()
method allows either overwriting the current
data (default, True
) or storing it to a new signal (False
).
>>> import scipy.ndimage
>>> image_stack = hs.signals.Signal2D(np.array([scipy.misc.ascent()]*4))
>>> angles = hs.signals.BaseSignal(np.array([0, 45, 90, 135]))
>>> result = image_stack.map(scipy.ndimage.rotate,
... angle=angles.T,
... inplace=False,
... reshape=True)
100%████████████████████████████████████████████ 4/4 [00:00<00:00, 18.42it/s]
>>> result
<BaseSignal, title: , dimensions: (4)>
>>> image_stack.data.dtype
dtype('O')
>>> for d in result.data.flat:
... print(d.shape)
(512, 512)
(724, 724)
(512, 512)
(724, 724)
The execution can be sped up by passing parallel
keyword to the
map()
method:
>>> import time
>>> def slow_func(data):
... time.sleep(1.)
... return data + 1
>>> s = hs.signals.Signal1D(np.arange(20).reshape((20,1)))
>>> s
<Signal1D, title: , dimensions: (201)>
>>> s.map(slow_func, parallel=False)
100%██████████████████████████████████████ 20/20 [00:20<00:00, 1.00s/it]
>>> # some operations will be done in parallel:
>>> s.map(slow_func, parallel=True)
100%██████████████████████████████████████ 20/20 [00:02<00:00, 6.73it/s]
Note
HyperSpy implements threadbased parallelism for the map()
method. You can control the number of threads that are created by passing an integer value
to the max_workers
keyword argument. By default, it will use min(32, os.cpu_count())
.
New in version 1.4: Iterating over signal using a parameter with no navigation dimension.
In this case, the parameter is cyclically iterated over the navigation dimension of the input signal. In the example below, signal s is multiplied by a cosine parameter d, which is repeated over the navigation dimension of s.
>>> s = hs.signals.Signal1D(np.random.rand(10, 512))
>>> d = hs.signals.Signal1D(np.cos(np.linspace(0., 2*np.pi, 512)))
>>> s.map(lambda A, B: A * B, B=d)
100%██████████ 10/10 [00:00<00:00, 2573.19it/s]
Cropping¶
Cropping can be performed in a very compact and powerful way using
Indexing . In addition it can be performed using the following
method or GUIs if cropping signal1D or signal2D. There is also a general crop()
method that operates in place.
Rebinning¶
New in version 1.3: rebin()
generalized to remove the constrain
of the new_shape
needing to be a divisor of data.shape
.
The rebin()
methods supports rebinning the data to
arbitrary new shapes as long as the number of dimensions stays the same.
However, internally, it uses two different algorithms to perform the task. Only
when the new shape dimensions are divisors of the old shape’s, the operation
supports lazyevaluation and is usually faster.
Otherwise, the operation requires linear interpolation.
For example, the following two equivalent rebinning operations can be performed lazily:
>>> s = hs.datasets.example_signals.EDS_SEM_Spectrum().as_lazy()
>>> print(s)
<LazyEDSSEMSpectrum, title: EDS SEM Spectrum, dimensions: (1024)>
>>> print(s.rebin(scale=[2]))
<LazyEDSSEMSpectrum, title: EDS SEM Spectrum, dimensions: (512)>
>>> s = hs.datasets.example_signals.EDS_SEM_Spectrum().as_lazy()
>>> print(s.rebin(new_shape=[512]))
<LazyEDSSEMSpectrum, title: EDS SEM Spectrum, dimensions: (512)>
On the other hand, the following rebinning operation requires interpolation and cannot be performed lazily:
>>> spectrum = hs.signals.EDSTEMSpectrum(np.ones([4, 4, 10]))
>>> spectrum.data[1, 2, 9] = 5
>>> print(spectrum)
<EDSTEMSpectrum, title: , dimensions: (4, 410)>
>>> print ('Sum = ', spectrum.data.sum())
Sum = 164.0
>>> scale = [0.5, 0.5, 5]
>>> test = spectrum.rebin(scale=scale)
>>> test2 = spectrum.rebin(new_shape=(8, 8, 2)) # Equivalent to the above
>>> print(test)
<EDSTEMSpectrum, title: , dimensions: (8, 82)>
>>> print(test2)
<EDSTEMSpectrum, title: , dimensions: (8, 82)>
>>> print('Sum =', test.data.sum())
Sum = 164.0
>>> print('Sum =', test2.data.sum())
Sum = 164.0
>>> spectrum.as_lazy().rebin(scale=scale)
Traceback (most recent call last):
File "<ipythoninput2649bca19ebf34>", line 1, in <module>
spectrum.as_lazy().rebin(scale=scale)
File "/home/fjd29/Python/hyperspy3/hyperspy/_signals/eds.py", line 184, in rebin
m = super().rebin(new_shape=new_shape, scale=scale, crop=crop, out=out)
File "/home/fjd29/Python/hyperspy3/hyperspy/_signals/lazy.py", line 246, in rebin
"Lazy rebin requires scale to be integer and divisor of the "
NotImplementedError: Lazy rebin requires scale to be integer and divisor of the original signal shape
Folding and unfolding¶
When dealing with multidimensional datasets it is sometimes useful to transform the data into a two dimensional dataset. This can be accomplished using the following two methods:
It is also possible to unfold only the navigation or only the signal space:
Splitting and stacking¶
Several objects can be stacked together over an existing axis or over a
new axis using the stack()
function, if they share axis
with same dimension.
>>> image = hs.signals.Signal2D(scipy.misc.ascent())
>>> image = hs.stack([hs.stack([image]*3,axis=0)]*3,axis=1)
>>> image.plot()
An object can be split into several objects
with the split()
method. This function can be used
to reverse the stack()
function:
>>> image = image.split()[0].split()[0]
>>> image.plot()
Fast Fourier Transform (FFT)¶
The fast Fourier transform
of a signal can be computed using the fft()
method. By default,
the FFT is calculated with the origin at (0, 0), which will be displayed at the
bottom left and not in the centre of the FFT. Conveniently, the shift
argument of the
the fft()
method can be used to center the output of the FFT.
In the following example, the FFT of a hologram is computed using shift=True
and its
output signal is displayed, which shows that the FFT results in a complex signal with a
real and an imaginary parts:
>>> im = hs.datasets.example_signals.reference_hologram()
>>> fft_shifted = im.fft(shift=True)
>>> fft_shifted.plot()
The strong features in the real and imaginary parts correspond to the lattice fringes of the hologram.
For visual inspection of the FFT it is convenient to display its power spectrum
(i.e. the square of the absolute value of the FFT) rather than FFT itself as it is done
in the example above by using the power_spectum
argument:
>>> im = hs.datasets.example_signals.reference_hologram()
>>> fft = im.fft(True)
>>> fft.plot(True)
Where power_spectum
is set to True
since it is the first argument of the
plot()
method for complex signal.
When power_spectrum=True
, the plot will be displayed on a log scale by default.
The visualisation can be further improved by setting the minimum value to display to the 30th
percentile; this can be done by using vmin="30th"
in the plot function:
>>> im = hs.datasets.example_signals.reference_hologram()
>>> fft = im.fft(True)
>>> fft.plot(True, vmin="30th")
The streaks visible in the FFT come from the edge of the image and can be removed by
applying an apodization function to the original
signal before the computation of the FFT. This can be done using the apodization
argument of
the fft()
method and it is usually used for visualising FFT patterns
rather than for quantitative analyses. By default, the socalled hann
windows is
used but different type of windows such as the hamming
and tukey
windows.
>>> im = hs.datasets.example_signals.reference_hologram()
>>> fft = im.fft(shift=True)
>>> fft_apodized = im.fft(shift=True, apodization=True)
>>> fft_apodized.plot(True, vmin="30th")
Inverse Fast Fourier Transform (iFFT)¶
Inverse fast Fourier transform can be calculated from a complex signal by using the
ifft()
method. Similarly to the fft()
method,
the shift
argument can be provided to shift the origin of the iFFT when necessary:
>>> im_ifft = im.fft(shift=True).ifft(shift=True)
Changing the data type¶
Even if the original data is recorded with a limited dynamic range, it is often
desirable to perform the analysis operations with a higher precision.
Conversely, if space is limited, storing in a shorter data type can decrease
the file size. The change_dtype()
changes the data
type in place, e.g.:
>>> s = hs.load('EELS Signal1D Signal2D (highloss).dm3')
Title: EELS Signal1D Signal2D (highloss).dm3
Signal type: EELS
Data dimensions: (21, 42, 2048)
Data representation: spectrum
Data type: float32
>>> s.change_dtype('float64')
>>> print(s)
Title: EELS Signal1D Signal2D (highloss).dm3
Signal type: EELS
Data dimensions: (21, 42, 2048)
Data representation: spectrum
Data type: float64
In addition to all standard numpy dtypes, HyperSpy supports four extra dtypes
for RGB images for visualization purposes only: rgb8
, rgba8
,
rgb16
and rgba16
. This includes of course multidimensional RGB images.
The requirements for changing from and to any rgbx
dtype are more strict
than for most other dtype conversions. To change to a rgbx
dtype the
signal_dimension
must be 1 and its size 3 (4) 3(4) for rgb
(or
rgba
) dtypes and the dtype must be uint8
(uint16
) for
rgbx8
(rgbx16
). After conversion the signal_dimension
becomes 2.
Most operations on signals with RGB dtypes will fail. For processing simply
change their dtype to uint8
(uint16
).The dtype of images of
dtype rgbx8
(rgbx16
) can only be changed to uint8
(uint16
) and
the signal_dimension
becomes 1.
In the following example we create a 1D signal with signal size 3 and with
dtype uint16
and change its dtype to rgb16
for plotting.
>>> rgb_test = np.zeros((1024, 1024, 3))
>>> ly, lx = rgb_test.shape[:2]
>>> offset_factor = 0.16
>>> size_factor = 3
>>> Y, X = np.ogrid[0:lx, 0:ly]
>>> rgb_test[:,:,0] = (X  lx / 2  lx*offset_factor) ** 2 + \
... (Y  ly / 2  ly*offset_factor) ** 2 < \
... lx * ly / size_factor **2
>>> rgb_test[:,:,1] = (X  lx / 2 + lx*offset_factor) ** 2 + \
... (Y  ly / 2  ly*offset_factor) ** 2 < \
... lx * ly / size_factor **2
>>> rgb_test[:,:,2] = (X  lx / 2) ** 2 + \
... (Y  ly / 2 + ly*offset_factor) ** 2 \
... < lx * ly / size_factor **2
>>> rgb_test *= 2**16  1
>>> s = hs.signals.Signal1D(rgb_test)
>>> s.change_dtype("uint16")
>>> s
<Signal1D, title: , dimensions: (1024, 10243)>
>>> s.change_dtype("rgb16")
>>> s
<Signal2D, title: , dimensions: (1024, 1024)>
>>> s.plot()
Transposing (changing signal spaces)¶
New in version 1.1.
transpose()
method changes how the dataset
dimensions are interpreted (as signal or navigation axes). By default is
swaps the signal and navigation axes. For example:
>>> s = hs.signals.Signal1D(np.zeros((4,5,6)))
>>> s
<Signal1D, title: , dimensions: (5, 46)>
>>> s.transpose()
<Signal2D, title: , dimensions: (64, 5)>
For T()
is a shortcut for the default behaviour:
>>> s = hs.signals.Signal1D(np.zeros((4,5,6))).T
<Signal2D, title: , dimensions: (64, 5)>
The method accepts both explicit axes to keep in either space, or just a number
of axes required in one space (just one number can be specified, as the other
is defined as “all other axes”). When axes order is not explicitly defined,
they are “rolled” from one space to the other as if the <navigation axes 
signal axes >
wrap a circle. The example below should help clarifying this.
>>> # just create a signal with many distinct dimensions
>>> s = hs.signals.BaseSignal(np.random.rand(1,2,3,4,5,6,7,8,9))
>>> s
<BaseSignal, title: , dimensions: (9, 8, 7, 6, 5, 4, 3, 2, 1)>
>>> s.transpose(signal_axes=5) # roll to leave 5 axes in signal space
<BaseSignal, title: , dimensions: (4, 3, 2, 19, 8, 7, 6, 5)>
>>> s.transpose(navigation_axes=3) # roll leave 3 axes in navigation space
<BaseSignal, title: , dimensions: (3, 2, 19, 8, 7, 6, 5, 4)>
>>> # 3 explicitly defined axes in signal space
>>> s.transpose(signal_axes=[0, 2, 6])
<BaseSignal, title: , dimensions: (8, 6, 5, 4, 2, 19, 7, 3)>
>>> # A mix of two lists, but specifying all axes explicitly
>>> # The order of axes is preserved in both lists
>>> s.transpose(navigation_axes=[1, 2, 3, 4, 5, 8], signal_axes=[0, 6, 7])
<BaseSignal, title: , dimensions: (8, 7, 6, 5, 4, 19, 3, 2)>
A convenience functions transpose()
is available to operate on
many signals at once, for example enabling plotting anydimension signals
trivially:
>>> s2 = hs.signals.BaseSignal(np.random.rand(2, 2)) # 2D signal
>>> s3 = hs.signals.BaseSignal(np.random.rand(3, 3, 3)) # 3D signal
>>> s4 = hs.signals.BaseSignal(np.random.rand(4, 4, 4, 4)) # 4D signal
>>> hs.plot.plot_images(hs.transpose(s2, s3, s4, signal_axes=2))
The transpose()
method accepts keyword argument
optimize
, which is False
by default, meaning modifying the output
signal data always modifies the original data i.e. the data is just a view
of the original data. If True
, the method ensures the data in memory is
stored in the most efficient manner for iterating by making a copy of the data
if required, hence modifying the output signal data not always modifies the
original data.
The convenience methods as_signal1D()
and
as_signal2D()
internally use
transpose()
, but always optimize the data
for iteration over the navigation axes if required. Hence, these methods do not
always return a view of the original data. If a copy of the data is required
use
deepcopy()
on the output of any of these
methods e.g.:
>>> hs.signals.Signal1D(np.zeros((4,5,6))).T.deepcopy()
<Signal2D, title: , dimensions: (64, 5)>
Applying apodization window¶
Apodization window (also known as apodization function) can be applied to a signal
using apply_apodization()
method. By default standard
Hann window is used:
>>> s = hs.signals.Signal1D(np.ones(1000))
>>> sa = s.apply_apodization()
>>> sa.metadata.General.title = 'Hann window'
>>> sa.plot()
Higher order Hann window can be used in order to keep larger fraction of intensity of original signal.
This can be done providing an integer number for the order of the window through
keyword argument hann_order
. (The last one works only together with default value of window
argument
or with window='hann'
.)
>>> im = hs.datasets.example_signals.reference_hologram().isig[:200, :200]
>>> ima = im.apply_apodization(window='hann', hann_order=3)
>>> hs.plot.plot_images([im, ima], vmax=3000, tight_layout=True)
In addition to Hann window also Hamming or Tukey windows can be applied using window
attribute
selecting 'hamming'
or 'tukey'
respectively.
The shape of Tukey window can be adjusted using parameter alpha
provided through tukey_alpha
keyword argument (only used when window='tukey'
).
The parameter represents the fraction of the window inside the cosine tapered region,
i.e. smaller is alpha larger is the middle flat region where the original signal
is preserved. If alpha is one, the Tukey window is equivalent to a Hann window.
(Default value is 0.5)
Apodization can be applied in place by setting keyword argument inplace
to True
.
In this case method will not return anything.
Basic statistical analysis¶
get_histogram()
computes the histogram and
conveniently returns it as signal instance. It provides methods to
calculate the bins. print_summary_statistics()
prints the fivenumber summary statistics of the data.
These two methods can be combined with
get_current_signal()
to compute the histogram or
print the summary statistics of the signal at the current coordinates, e.g:
>>> s = hs.signals.EELSSpectrum(np.random.normal(size=(10,100)))
>>> s.print_summary_statistics()
Summary statistics

mean: 0.021
std: 0.957
min: 3.991
Q1: 0.608
median: 0.013
Q3: 0.652
max: 2.751
>>> s.get_current_signal().print_summary_statistics()
Summary statistics

mean: 0.019
std: 0.855
min: 2.803
Q1: 0.451
median: 0.038
Q3: 0.484
max: 1.992
Histogram of different objects can be compared with the functions
plot_histograms()
(see
visualisation for the plotting options). For example,
with histograms of several random chisquare distributions:
>>> img = hs.signals.Signal2D([np.random.chisquare(i+1,[100,100]) for
... i in range(5)])
>>> hs.plot.plot_histograms(img,legend='auto')
Setting the noise properties¶
Some data operations require the data variance. Those methods use the
metadata.Signal.Noise_properties.variance
attribute if it exists. You can
set this attribute as in the following example where we set the variance to be
10:
>>> s.metadata.Signal.set_item("Noise_properties.variance", 10)
You can also use the functions set_noise_variance()
and get_noise_variance()
for convenience:
>>> s.set_noise_variance(10)
>>> s.get_noise_variance()
10
For heteroscedastic noise the variance
attribute must be a
BaseSignal
. Poissonian noise is a common case of
heteroscedastic noise where the variance is equal to the expected value. The
estimate_poissonian_noise_variance()
method can help setting the variance of data with
semiPoissonian noise. With the default arguments, this method simply sets the
variance attribute to the given expected_value
. However, more generally
(although the noise is not strictly Poissonian), the variance may be
proportional to the expected value. Moreover, when the noise is a mixture of
white (Gaussian) and Poissonian noise, the variance is described by the
following linear model:
\mathrm{Var}[X] = (a * \mathrm{E}[X] + b) * c
Where a is the gain_factor
, b is the gain_offset
(the Gaussian
noise variance) and c the correlation_factor
. The correlation
factor accounts for correlation of adjacent signal elements that can
be modelled as a convolution with a Gaussian point spread function.
estimate_poissonian_noise_variance()
can be used to
set the noise properties when the variance can be described by this linear
model, for example:
>>> s = hs.signals.Spectrum(np.ones(100))
>>> s.add_poissonian_noise()
>>> s.metadata
├── General
│ └── title =
└── Signal
├── binned = False
└── signal_type =
>>> s.estimate_poissonian_noise_variance()
>>> s.metadata
├── General
│ └── title =
└── Signal
├── Noise_properties
│ ├── Variance_linear_model
│ │ ├── correlation_factor = 1
│ │ ├── gain_factor = 1
│ │ └── gain_offset = 0
│ └── variance = <SpectrumSimulation, title: Variance of , dimensions: (100)>
├── binned = False
└── signal_type =
Speeding up operations¶
Reusing a Signal for output¶
Many signal methods create and return a new signal. For fast operations, the
new signal creation time is nonnegligible. Also, when the operation is
repeated many times, for example in a loop, the cumulative creation time can
become significant. Therefore, many operations on
BaseSignal
accept an optional argument out. If an
existing signal is passed to out, the function output will be placed into
that signal, instead of being returned in a new signal. The following example
shows how to use this feature to slice a BaseSignal
. It is
important to know that the BaseSignal
instance passed in
the out argument must be wellsuited for the purpose. Often this means that
it must have the same axes and data shape as the
BaseSignal
that would normally be returned by the
operation.
>>> s = hs.signals.Signal1D(np.arange(10))
>>> s_sum = s.sum(0)
>>> s_sum.data
array([45])
>>> s.isig[:5].sum(0, out=s_sum)
>>> s_sum.data
array([10])
>>> s_roi = s.isig[:3]
>>> s_roi
<Signal1D, title: , dimensions: (3)>
>>> s.isig.__getitem__(slice(None, 5), out=s_roi)
>>> s_roi
<Signal1D, title: , dimensions: (5)>
Handling complex data¶
The HyperSpy ComplexSignal
signal class and its
subclasses for 1dimensional and 2dimensional data allow the user to access
complex properties like the real and imag parts of the data or the
amplitude (also known as the modulus) and phase (also known as angle or
argument) directly. Getting and setting those properties can be done as
follows:
>>> real = s.real # real is a new HS signal accessing the same data
>>> s.real = new_real # new_real can be an array or signal
>>> imag = s.imag # imag is a new HS signal accessing the same data
>>> s.imag = new_imag # new_imag can be an array or signal
It is important to note that data passed to the constructor of a
ComplexSignal
(or to a subclass), which
is not already complex, will be converted to the numpy standard of
np.complex/np.complex128. data which is already complex will be passed
as is.
To transform a real signal into a complex one use:
>>> s.change_dtype(complex)
Changing the dtype of a complex signal to something real is not clearly defined and thus not directly possible. Use the real, imag, amplitude or phase properties instead to extract the real data that is desired.
Calculate the angle / phase / argument¶
The angle()
function can be used to
calculate the angle, which is equivalent to using the phase property if no
argument is used. If the data is real, the angle will be 0 for positive
values and 2$pi$ for negative values. If the deg parameter is set to
True, the result will be given in degrees, otherwise in rad (default). The
underlying function is the angle()
function.
angle()
will return an appropriate
HyperSpy signal.
Phase unwrapping¶
With the unwrapped_phase()
method the
complex phase of a signal can be unwrapped and returned as a new signal. The
underlying method is unwrap()
, which uses the
algorithm described in [Herraez].
Calculate and display Argand diagram¶
Sometimes it is convenient to visualize a complex signal as a plot of its
imaginary part versus real one. In this case so called Argand diagrams can
be calculated using argand_diagram()
method, which returns the plot as a
Signal2D
. Optional arguments size
and display_range
can be used to change the size (and therefore
resolution) of the plot and to change the range for the display of the
plot respectively. The last one is especially useful in order to zoom
into specific regions of the plot or to limit the plot in case of noisy
data points.
An example of calculation of Aragand diagram is shown for electron holography data.
Add a linear phase ramp¶
For 2dimensional complex images, a linear phase ramp can be added to the
signal via the
add_phase_ramp()
method.
The parameters ramp_x and ramp_y dictate the slope of the ramp in x
and y direction, while the offset is determined by the offset parameter.
The fulcrum of the linear ramp is at the origin and the slopes are given in
units of the axis with the according scale taken into account. Both are
available via the AxesManager
of the signal.