code in python

Consider the autorgressive moving average (ARMA) process given by S[n] = V[m] +1V (n 1] + b}Sn - 1). (1) where Vin] ~ N(0,1) and V [n) and V (m) are independent for n + m. Assume there is a scenario where we cannot observe Sim) but we can obeserve X[n] given by X[n] = Sin] + E[n]. (2) where En] ~ N(0,1) and Eln) and E(m) are independent for n m. In this problem we shall design a Wiener filter for estimating S[n) from X[m). 1.4.1 2.1 (p) Estimate the autocorrelation of X[n), Rxx[k] - EX[n]X[ne - k), and cross-correlation between Xin] and S(n), Rsx{k} = EX [n]s[m - k] for k = 0,1,2 in the following two cases 1. do = = 12. 19 = 1, y = 0,5 You can do this numerically by eg, generate some data according the above equations and use np.correlate (look at eg exercise 9 for an example for calculating the autocorrelation). Of course, if your prefer to calculate Rxx[k) and/or Rsxkj analytically, it is also OK. 1.4.2 2.2 (p) The optimal parameters for a second order FIR Wiener can be obtained by solving the following equation (see also slides from Lecture 12) [7.2017 [rxx[0] =*[1] [2] *[1Oprxx{1 (3) [r32] [tx*[2] .x[1] x*(0) Use this to estimate the impulse repsons, h, for the FIR Wiener filter for the cases 1. = R1 = 1 2. do = 1, b =0.5. You can use e.g. scipy.linalg,solve. 1.4.3 2.3 (p) Estimate the accuracy of the predictions in a way you think is suitable 109