Estimation with multiple observations: A sinusoidal signal A cos$(0\mathrm{.}01$n$)$ is sent over an additive Gaussian noise channel. The observations are given by Yn $=$ A cos$(0\mathrm{.}01$n$)+$Zn

for n $=1,2,..,1000$ where Zn$\text{'}$s are i$.$i$.$d$.$ zero mean Gaussian random variables with

variance $0\mathrm{.}04.$ The amplitude A of the signal is unknown. A and Zi's are independent. The

observations are given in the attached $.$mat file.

a$)$ Find the maximum likelihood estimator of the amplitude A$.$

b$)$ Calculate the maximum likelihood estimate of amplitude A using the first N samples of

the given data. Choose N as $10,100,$ and $1000,$ and for each case calculate the absolute

error between the estimated and the true value of A$,$ i$.$e$.|$A $-$ Atrue$|$ where Atrue N$=1\mathrm{.}6.$Interpret the results.

The file contains a variable named y$.$ This variable is of type numpy.ndarray and size $(1000,1).$ This represents a single$-$column dataset.

Visualization of $\text{'}$y$\text{'}$ Variable