K
y(n) = \sum_{k=1} c_k e^{j2\pi f_k (n-\frac{N+1}{2})} + \nu(n), \quad n = 1, 2, \dots, N
(1)
where $c_k = a_k + jb_k$ is complex amplitude coefficient, $a_k$ and $b_k$ are the real-valued, real and imaginary components
of the complex coefficient $c_k$, $f_k$ is the frequency of the $k^{th}$ component and $\nu(n)$ for $n = 1, 2, \dots, N$ are i.i.d. complex
Gaussian random variables: $\nu(n) \sim CN(0, \sigma^2)$ representing the additive noise.
1. Define the parameter vector $\theta$ and the observation vector $y$ for this problem. Write an explicit form for the
PDF of $y$ given $\theta$, $f_y(y|\theta)$.
2. Compute the FIM and the CRLB. To simplify the derivation, use the well-known result of the CRLB for a
Complex Gaussian process (see \"Fundamentals of Statistical Processing, Volume I: Estimation Theory\" by
Steven M. Kay).
