57 lines
1.4 KiB
Python
57 lines
1.4 KiB
Python
import numpy as np
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import scipy as sp
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import matplotlib.pyplot as plt
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DATA_POINTS = 200
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def u(n):
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return np.heaviside(n, 1)
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def main():
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a = 0.9
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n = np.arange(DATA_POINTS)
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x = a**n * u(n)
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# Plot samples of x[n]
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plt.figure()
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plt.stem(n, x)
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plt.xlabel("n")
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plt.ylabel(r"$x[n]$")
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# Plot the analytical DTFT
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numerator = 1
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denominator = [1, -a]
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omega, h_0 = sp.signal.freqz(numerator, denominator, 256)
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plt.figure()
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plt.plot(omega, np.abs(h_0), label="Analytical DTFT")
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plt.xlabel("Frequency")
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plt.ylabel("Magnitude Response")
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# Plot the truncated DTFT for K = 3, 10, 20
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for K in (3, 10, 20):
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omega, h = sp.signal.freqz(x[:K], 1, 256)
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plt.plot(omega, np.abs(h), label=f"Truncated DTFT ($K = {K}$)")
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plt.legend()
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# Calculate the maximum error between the truncated DTFT
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# and the analytical DTFT for values of K from 1 to 200
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k = np.arange(DATA_POINTS)
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coeffs = np.zeros_like(k, dtype=np.float32)
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for i_k in k:
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omega, h_k = sp.signal.freqz(x[:i_k], 1, 256)
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err_k = np.abs(h_0 - h_k)
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coeffs[i_k] = np.max(err_k)
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# Plot the maximum error previously calculated
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plt.figure()
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plt.stem(k, coeffs)
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plt.xlabel("k")
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plt.ylabel("Supremum coefficients of the error")
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plt.show()
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if __name__ == "__main__":
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main()
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