30 lines
897 B
Python
30 lines
897 B
Python
"""
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ECE 09351 - Digital Signal Processing
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Lab 1 Question 6
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Translated from MATLAB by Aidan Sharpe
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Last Modified: January 18, 2025
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"""
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from sympy import *
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from sympy.abc import a, b, t, w
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# Please note that the answers are given as piecewise functions.
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# The conditions are unnecessary, so take the first part of the piecewise result.
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def main():
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# Assume that a and b are positive real numbers
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with assuming(Q.positive(a), Q.positive(b)):
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x_1 = exp(-a*abs(t)) # x1(t) = e^(-a|t|)
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X_1 = integrate(x_1*exp(-1j*w*t), (t, -oo, oo)) # Fourier transform of x1(t)
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print(simplify(X_1))
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x_2 = x_1*cos(b*t) # x2(t) = x1(t)*cos(bt)
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X_2 = integrate(x_2*exp(-1j*w*t), (t, -oo, oo)) # Fourier transform of x2(t)
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print(simplify(X_2))
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if __name__ == "__main__":
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main()
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