Question

10. Given [n 1,4,1,4,1,1 starting at index zero. (a) Calculate the estimated mean mix and estimated variance σ? of x[n] (b) Propose a third order anticausal FIR filterh[n] with h[Oso that the output sigmal ylz,1,2,3,4 has smaller variance than iepu signaculaic (approximately) the variance 67 of ylnl, n 1,2,3,4. Specify the type of your pro- posal filter [n. (c) Propose a third order anticausal FIR filter g[n] with g[0] = 1 so that the output signal inl gInxn,n1,2,3,4 is zero-mean. Specify the type of your proposal filter g[n

PLEASE SOLVE WITH EVERY DETAIL AND SHOW EVERY STEP & FORMULAS

Answer 1

x[n] = {1, 4, 1, 4, 1, 1}

a) mean = (x₀ + x₁ + x₂ + x₃ + x₄ + x₅) / 6

= (1 + 4 + 1 + 4 + 1 + 1) / 6

= 2

variance = | (1-2)² + (4-2)² + (1-2)² + (4-2)² + (1-2)² +(1-2)²| / 6

= 2

b) Select rectangular window function for computation as it simplest for computation purpose.

Now in this question it is asked that the output signal 1/n should have similar variance than the input signal x[n]. Also, any sampling frequency or pass band cut off frequency is not given. So, in this case the design criteria would be to carefully select a suitable sampling frequency and pass band cut off frequency