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Engineering · Electrical Engineering
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Consider a sinusoidal signal x[n] embedded in White Gaussian noise (WGN), which can be represented as x[n] = A exp(j(2πf0n + φ)) + w[n], n = 0, 1, 2, · · · , N − 1, where A > 0 is the real-valued amplitude, 0 < f0 < 0.5 is the frequency, φ is the phase and w[n] is the complex WGN with mean 0 and variance σ 2 .

Find the maximum likelihood estimate (MLE) of the amplitude A, the phase φ and the frequency f0 of the complex-valued signal x[n].

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