Solve Yule Walker equation

ch10.r

@@ -157,3 +157,28 @@ grid()
 legend(-2, 0.19, legend=c("R_x(t)", "R_y(t)"), col=c("gray", "darkorange"), lty=1:1, lwd=2)
 lines(seq(-20, 20, by=0.001), h2, lwd=2, col="darkorange")
 
+#############
+# Chapter 10.6 Optimal linear filter
+
+## Solve the Yule Walker equation
+
+# R code to solve the Yule Walker Equation
+
+y = scan("./ch10_LPC_data.txt")
+K = 10
+N = 320
+y_corr = ccf(y, y, lag.max=2*length(y)-1)$acf
+R = toeplitz(y_corr[N + 1:K-1])
+lhs = y_corr[N + 1:K]
+h = solve(R, lhs)
+
+# Figure 1
+plot(y, lwd = 4, col="blue", type="l")
+grid()
+legend(10, 0.1, legend=c("Y[n]"), col=c("blue"), lty=1:1, lwd=4)
+
+# Figure 2
+plot(y_corr, lwd = 4, type="l")
+grid()
+legend(10, 0.9, legend=c("R_y[k]"), col=c("black"), lty=1:1, lwd=4)
+