Signal Processing

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"""Perform a convolution with a linear time-variant system."""

import numpy as np
from acoustic_toolbox.signal import convolve as convolveLTV
from scipy.signal import convolve as convolveLTI

"""Input signal"""
u = np.array([1, 2, 3, 4, 3, 2, 1], dtype="float")

"""Impulse responses where each column represents an impulse response."""
C = np.array(
    [
        [1, 1, 1, 1, 1, 1, 1],
        [2, 2, 2, 2, 2, 2, 2],
        [3, 3, 3, 3, 3, 3, 3],
        [4, 4, 4, 4, 4, 4, 4],
    ],
    dtype="float",
)

"""The array C represents here a linear time-invariant system."""
y_ltv = convolveLTV(u, C)
y_lti = convolveLTI(u, C[:, 0])
"""Check whether the output is indeed the same."""
print(np.all(y_ltv == y_lti))
print("LTV:" + str(y_ltv))
print("LTI:" + str(y_lti))

"""Let's now use a time-variant system."""
C = np.array(
    [
        [1, 2, 3, 4, 3, 2, 1],
        [2, 3, 4, 5, 4, 3, 2],
        [3, 4, 5, 6, 5, 4, 3],
        [4, 5, 6, 7, 6, 5, 4],
    ],
    dtype="float",
)

y_ltv = convolveLTV(u, C)
y_lti = convolveLTI(
    u, C[:, 0]
)  # We use now only the first impulser response for the LTI.
"""Is the result still equal?"""
print(np.all(y_ltv == y_lti))
print("LTV:" + str(y_ltv))
print("LTI:" + str(y_lti))

"""Perform a convolution with a linear time-variant system.""" import numpy as np from acoustic_toolbox.signal import convolve as convolveLTV from scipy.signal import convolve as convolveLTI """Input signal""" u = np.array([1, 2, 3, 4, 3, 2, 1], dtype="float") """Impulse responses where each column represents an impulse response.""" C = np.array( [ [1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 2, 2], [3, 3, 3, 3, 3, 3, 3], [4, 4, 4, 4, 4, 4, 4], ], dtype="float", ) """The array C represents here a linear time-invariant system.""" y_ltv = convolveLTV(u, C) y_lti = convolveLTI(u, C[:, 0]) """Check whether the output is indeed the same.""" print(np.all(y_ltv == y_lti)) print("LTV:" + str(y_ltv)) print("LTI:" + str(y_lti)) """Let's now use a time-variant system.""" C = np.array( [ [1, 2, 3, 4, 3, 2, 1], [2, 3, 4, 5, 4, 3, 2], [3, 4, 5, 6, 5, 4, 3], [4, 5, 6, 7, 6, 5, 4], ], dtype="float", ) y_ltv = convolveLTV(u, C) y_lti = convolveLTI( u, C[:, 0] ) # We use now only the first impulser response for the LTI. """Is the result still equal?""" print(np.all(y_ltv == y_lti)) print("LTV:" + str(y_ltv)) print("LTI:" + str(y_lti))