We are interested in a low frequency signal, but unfortunately our biasfree measurements of the signal   are disturbed by noise. We model our recorded signal as a deterministic low frequency component...

We are interested in a low frequency signal, but unfortunately our biasfree measurements of the signal
  are disturbed by noise. We model our recorded signal as a deterministic low frequency component (the one we are interested in) plus a stationary stochastic process (the noise). We have reasons to believe that the covariance function, r(τ), of the noise can be approximated with

In order to suppress the noise, we consider the following two options:

Where
  are two different approximations of the low frequency signal of our interest.

(a) Why are
  less affected by noise than our original measurements,

(b) There is a trade-off in selecting N (or M). Explain!

(c) How large must we choose N in order for the variance of Y_N(n) to be less than 0.1? How large must we choose M in order for the variance of Z_M(n) to be less than 0.1?

(d) Compare the values of N and M in the previous question. Give an explanation of the difference.