scipy.signal¶

Functions in the signal module can be called by prepending them by scipy.signal.. The module defines the following two functions:

scipy.signal.sosfilt
scipy.signal.spectrogram

sosfilt¶

scipy: https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.sosfilt.html

Filter data along one dimension using cascaded second-order sections.

The function takes two positional arguments, sos, the filter segments of length 6, and the one-dimensional, uniformly sampled data set to be filtered. Returns the filtered data, or the filtered data and the final filter delays, if the zi keyword arguments is supplied. The keyword argument must be a float ndarray of shape (n_sections, 2). If zi is not passed to the function, the initial values are assumed to be 0.

# code to be run in micropython

from ulab import numpy as np
from ulab import scipy as spy

x = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
sos = [[1, 2, 3, 1, 5, 6], [1, 2, 3, 1, 5, 6]]
y = spy.signal.sosfilt(sos, x)
print('y: ', y)

y:  array([0.0, 1.0, -4.0, 24.0, -104.0, 440.0, -1728.0, 6532.000000000001, -23848.0, 84864.0], dtype=float)

# code to be run in micropython

from ulab import numpy as np
from ulab import scipy as spy

x = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
sos = [[1, 2, 3, 1, 5, 6], [1, 2, 3, 1, 5, 6]]
# initial conditions of the filter
zi = np.array([[1, 2], [3, 4]])

y, zf = spy.signal.sosfilt(sos, x, zi=zi)
print('y: ', y)
print('\n' + '='*40 + '\nzf: ', zf)

y:  array([4.0, -16.0, 63.00000000000001, -227.0, 802.9999999999999, -2751.0, 9271.000000000001, -30775.0, 101067.0, -328991.0000000001], dtype=float)

========================================
zf:  array([[37242.0, 74835.0],
     [1026187.0, 1936542.0]], dtype=float)

spectrogram¶

In addition to the Fourier transform and its inverse, ulab also sports a function called spectrogram, which returns the absolute value of the Fourier transform. This could be used to find the dominant spectral component in a time series. The arguments are treated in the same way as in fft, and ifft.

# code to be run in micropython

from ulab import numpy as np
from ulab import scipy as spy

x = np.linspace(0, 10, num=1024)
y = np.sin(x)

a = spy.signal.spectrogram(y)

print('original vector:\t', y)
print('\nspectrum:\t', a)

original vector:     array([0.0, 0.009775015390171337, 0.01954909674625918, ..., -0.5275140569487312, -0.5357931822978732, -0.5440211108893639], dtype=float64)

spectrum:    array([187.8635087634579, 315.3112063607119, 347.8814873399374, ..., 84.45888934298905, 347.8814873399374, 315.3112063607118], dtype=float64)

As such, spectrogram is really just a shorthand for np.sqrt(a*a + b*b):

# code to be run in micropython

from ulab import numpy as np
from ulab import scipy as spy

x = np.linspace(0, 10, num=1024)
y = np.sin(x)

a, b = np.fft.fft(y)

print('\nspectrum calculated the hard way:\t', np.sqrt(a*a + b*b))

a = spy.signal.spectrogram(y)

print('\nspectrum calculated the lazy way:\t', a)

spectrum calculated the hard way:    array([187.8635087634579, 315.3112063607119, 347.8814873399374, ..., 84.45888934298905, 347.8814873399374, 315.3112063607118], dtype=float64)

spectrum calculated the lazy way:    array([187.8635087634579, 315.3112063607119, 347.8814873399374, ..., 84.45888934298905, 347.8814873399374, 315.3112063607118], dtype=float64)