I am trying to determine the expression of power signal density for a signal given by $x_n=cos(2πf_cn+θ)$. The signal is sampled at $n=0, Δ, 2Δ, 3Δ, ⋯ , NΔ$ in seconds, and $f_c < \frac{1}{2Δ}$.
I have computed that the Fourier Transform of the signal is $e^{iθ}∂(f-f_c) + e^{-iθ}∂(f+f_c)$, but I'm not sure if this is correct.
How would I find the power spectral density expression and frequency resolution for this signal?