2018-11-06 16:34:48 +00:00
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## -*- python -*-
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import numpy as np
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CONST_DTYPE=np.dtype([('points', np.complex64),
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2018-11-12 17:28:02 +00:00
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('symbols', np.int32)])
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2018-11-06 16:34:48 +00:00
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def n_psk(n,x):
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"""n-ary PSK constellation"""
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return np.complex64(np.exp(2j*np.pi*x/n))
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def freq_est(z):
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"""Data-Aided Frequency Estimation for Burst Digital Transmission,
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Umberto Mengali and M. Morelli, IEEE TRANSACTIONS ON COMMUNICATIONS,
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VOL. 45, NO. 1, JANUARY 1997"""
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L0 = len(z)
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N = L0//2
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R = np.zeros(N+1, dtype=np.complex64)
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for i in range(N+1):
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R[i] = 1.0/(L0-i)*np.sum(z[i:]*np.conj(z[0:L0-i])) ## eq (3)
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m = np.arange(N+1, dtype=np.float32)
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w = 3*((L0-m)*(L0-m+1)-N*(L0-N))/(N*(4*N*N - 6*N*L0 + 3*L0*L0-1)) ## eq (9)
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mod_2pi = lambda x : np.mod(x-np.pi, 2*np.pi) - np.pi
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return np.sum(w[1:] * mod_2pi(np.diff(np.angle(R)))) ## eq (8)
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if __name__ == '__main__':
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idx=np.arange(3)
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z=np.exp(1j*idx*0.056+1j)
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print(freq_est(z)/0.056)
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