135 lines
3.8 KiB
ReStructuredText
135 lines
3.8 KiB
ReStructuredText
None
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Signal
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======
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Functions in the ``signal`` module can be called by prepending them by
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``scipy.signal.``. The module defines the following two functions:
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1. `scipy.signal.sosfilt <#sosfilt>`__
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2. `scipy.signal.spectrogram <#spectrogram>`__
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sosfilt
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-------
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``scipy``:
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https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.sosfilt.html
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Filter data along one dimension using cascaded second-order sections.
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The function takes two positional arguments, ``sos``, the filter
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segments of length 6, and the one-dimensional, uniformly sampled data
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set to be filtered. Returns the filtered data, or the filtered data and
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the final filter delays, if the ``zi`` keyword arguments is supplied.
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The keyword argument must be a float ``ndarray`` of shape
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``(n_sections, 2)``. If ``zi`` is not passed to the function, the
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initial values are assumed to be 0.
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.. code::
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# code to be run in micropython
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from ulab import numpy as np
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from ulab import scipy as spy
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x = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
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sos = [[1, 2, 3, 1, 5, 6], [1, 2, 3, 1, 5, 6]]
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y = spy.signal.sosfilt(sos, x)
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print('y: ', y)
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.. parsed-literal::
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y: array([0.0, 1.0, -4.0, 24.0, -104.0, 440.0, -1728.0, 6532.000000000001, -23848.0, 84864.0], dtype=float)
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.. code::
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# code to be run in micropython
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from ulab import numpy as np
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from ulab import scipy as spy
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x = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
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sos = [[1, 2, 3, 1, 5, 6], [1, 2, 3, 1, 5, 6]]
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# initial conditions of the filter
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zi = np.array([[1, 2], [3, 4]])
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y, zf = spy.signal.sosfilt(sos, x, zi=zi)
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print('y: ', y)
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print('\n' + '='*40 + '\nzf: ', zf)
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.. parsed-literal::
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y: array([4.0, -16.0, 63.00000000000001, -227.0, 802.9999999999999, -2751.0, 9271.000000000001, -30775.0, 101067.0, -328991.0000000001], dtype=float)
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========================================
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zf: array([[37242.0, 74835.0],
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[1026187.0, 1936542.0]], dtype=float)
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spectrogram
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-----------
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In addition to the Fourier transform and its inverse, ``ulab`` also
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sports a function called ``spectrogram``, which returns the absolute
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value of the Fourier transform. This could be used to find the dominant
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spectral component in a time series. The arguments are treated in the
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same way as in ``fft``, and ``ifft``.
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.. code::
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# code to be run in micropython
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from ulab import numpy as np
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from ulab import scipy as spy
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x = np.linspace(0, 10, num=1024)
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y = np.sin(x)
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a = spy.signal.spectrogram(y)
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print('original vector:\t', y)
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print('\nspectrum:\t', a)
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.. parsed-literal::
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original vector: array([0.0, 0.009775015390171337, 0.01954909674625918, ..., -0.5275140569487312, -0.5357931822978732, -0.5440211108893639], dtype=float64)
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spectrum: array([187.8635087634579, 315.3112063607119, 347.8814873399374, ..., 84.45888934298905, 347.8814873399374, 315.3112063607118], dtype=float64)
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As such, ``spectrogram`` is really just a shorthand for
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``np.sqrt(a*a + b*b)``:
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.. code::
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# code to be run in micropython
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from ulab import numpy as np
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from ulab import scipy as spy
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x = np.linspace(0, 10, num=1024)
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y = np.sin(x)
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a, b = np.fft.fft(y)
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print('\nspectrum calculated the hard way:\t', np.sqrt(a*a + b*b))
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a = spy.signal.spectrogram(y)
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print('\nspectrum calculated the lazy way:\t', a)
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.. parsed-literal::
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spectrum calculated the hard way: array([187.8635087634579, 315.3112063607119, 347.8814873399374, ..., 84.45888934298905, 347.8814873399374, 315.3112063607118], dtype=float64)
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spectrum calculated the lazy way: array([187.8635087634579, 315.3112063607119, 347.8814873399374, ..., 84.45888934298905, 347.8814873399374, 315.3112063607118], dtype=float64)
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