The signal $x[n]$ with autocorrelation function $R_x[k]=4+2cos(\frac{2k}{32})$ is asked to be estimated from the observation $Y[n]=x[n]+V[n]$ with a $M=8$ tap FIR filter. $V[n]$ is a zero$-$mean white Gaussian noise with variance $0\mathrm{.}04.x[n]$ and $V[n]$ are assumed to uncorrelated zero mean wide$-$sense stationary random processes. $Y[n]$ is given in the attached mat file.

a$.$ Write a code to find the desired FIR filter coefficients. Plot the filter impulse response.

b$.$ Find the estimate hat$(x)[n]$ by filtering $Y[n]$ with obtained FIR filter. Plot $Y[n]$ and hat$(x)[n].$

Return the figures and code in a single pdf file.