Complete chapter 10.5

ch10.r

@@ -128,3 +128,32 @@ for (i in 1:N) {
 plot(xc[1,], type="l", lwd=2, col="darkblue")
 lines(xc[2,], lwd=2)
 
+#############
+# Chapter 10.5 Wide sense stationary processes
+
+## Example 10.15
+
+# R code for Example 10.15
+t = seq(-10, 10, by=0.001)
+L = length(t)
+X = rnorm(L)
+h = 10 * sapply((1 - abs(t)), max, 0) / 1000
+Y = convolve(X, h, type=c("circular"))
+
+# Figure 1
+plot(t, X, lwd=1, col="gray", type="l")
+grid()
+legend(6, 3.8, legend=c("X(t)", "μ_x(t)", "Y(t)", "μ_y(t)"), col=c("gray", "black", "darkorange", "yellow"), lty=c(1, 1, 1, 3), lwd=c(1, 4, 3, 4), bg="white")
+abline(h=0, lwd=4, lty=1, col="yellow")
+lines(t, Y, lwd=3, col="darkorange")
+abline(h=0, lwd=4, lty=3)
+
+# Figure 2
+h2 = convolve(h, h, type="open")
+Rx = numeric(40001)
+Rx[20001] = 0.2
+plot(seq(-20, 20, by=0.001), Rx, lwd=2, col="gray", type="l", xlim=c(-2,2), ylim=c(-0.05, 0.2))
+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")
+