From 0b9a7c7b6c3bc7aebc62101fe2e435f265736d50 Mon Sep 17 00:00:00 2001
From: aaaakshat <33050725+aaaakshat@users.noreply.github.com>
Date: Wed, 3 Nov 2021 16:12:24 -0400
Subject: [PATCH 01/13] Add example 10.5

---
 ch10.r | 17 +++++++++++++++++
 1 file changed, 17 insertions(+)
 create mode 100644 ch10.r

diff --git a/ch10.r b/ch10.r
new file mode 100644
index 0000000..bbdec77
--- /dev/null
+++ b/ch10.r
@@ -0,0 +1,17 @@
+#############
+# Chapter 10.2 Mean and correlation functions
+
+## Example 10.5
+
+# R code for Example 10.5
+x = matrix(0, 1000, 20)
+t = seq(-2, 2, (2+2)/999)
+
+for (i in 1:20) {
+    x[,i] = runif(1) * cos(2 * pi * t)
+}
+
+matplot(t, x, lwd=2, col="gray")
+lines(t, 0.5*cos(2*pi*t), lwd=4, col="darkred")
+grid()
+

From 0a36938c516fdd45c6d46563e3ea70c6381d45f7 Mon Sep 17 00:00:00 2001
From: aaaakshat <33050725+aaaakshat@users.noreply.github.com>
Date: Wed, 3 Nov 2021 16:17:54 -0400
Subject: [PATCH 02/13] Add example 10.6

---
 ch10.r | 15 ++++++++++++++-
 1 file changed, 14 insertions(+), 1 deletion(-)

diff --git a/ch10.r b/ch10.r
index bbdec77..365ffea 100644
--- a/ch10.r
+++ b/ch10.r
@@ -12,6 +12,19 @@ for (i in 1:20) {
 }
 
 matplot(t, x, lwd=2, col="gray")
-lines(t, 0.5*cos(2*pi*t), lwd=4, col="darkred")
 grid()
+lines(t, 0.5*cos(2*pi*t), lwd=4, col="darkred")
+
+## Example 10.6
+
+# R code for Example 10.6
+x = matrix(0, 1000, 20)
+t = seq(-2, 2, (2+2)/999)
 
+for (i in 1:20) {
+    x[,i] = cos(2*pi*t+2*pi*runif(1))
+}
+
+matplot(t, x, lwd=2, col="gray")
+grid()
+lines(t, 0*cos(2*pi*t), lwd=4, col="darkred")

From f3d92c34c0c9acbe12d9ee6b30053ade41610305 Mon Sep 17 00:00:00 2001
From: aaaakshat <33050725+aaaakshat@users.noreply.github.com>
Date: Wed, 10 Nov 2021 10:27:50 -0500
Subject: [PATCH 03/13] Add example 10.7

---
 ch10.r | 32 ++++++++++++++++++++++++++++++++
 1 file changed, 32 insertions(+)

diff --git a/ch10.r b/ch10.r
index 365ffea..16e0fa9 100644
--- a/ch10.r
+++ b/ch10.r
@@ -28,3 +28,35 @@ for (i in 1:20) {
 matplot(t, x, lwd=2, col="gray")
 grid()
 lines(t, 0*cos(2*pi*t), lwd=4, col="darkred")
+
+## Example 10.8
+
+# R code for Example 10.7
+x = matrix(0, 21, 20)
+t = 0:20
+
+for (i in 1:20) {
+    x[,i] = runif(1) ^ t
+}
+
+stem <- function(x,y,pch=1,...){
+    if (missing(y)){
+        y = x
+        x = 1:length(x) 
+    }
+    for (i in 1:length(x)){
+        lines(c(x[i],x[i]), c(0,y[i]), ...)
+    }
+    lines(c(x[1]-2,x[length(x)]+2), c(0,0), ...)
+}
+
+matplot(t, x, pch=1, col="gray", lwd=2)
+grid()
+
+for (i in 1:ncol(x)) {
+    stem(t, x[,i], col="gray", lwd=2)
+}
+stem(t, 1/(t+1), col="darkred", lwd=2, pch=1, type="o")
+
+
+

From fd7215c8e39b1cb983821c0a96bb860c9e1cccf3 Mon Sep 17 00:00:00 2001
From: aaaakshat <33050725+aaaakshat@users.noreply.github.com>
Date: Wed, 10 Nov 2021 16:14:55 -0500
Subject: [PATCH 04/13] Finish examples 10.11

---
 ch10.r | 19 +++++++++++++++++++
 1 file changed, 19 insertions(+)

diff --git a/ch10.r b/ch10.r
index 16e0fa9..6763fb3 100644
--- a/ch10.r
+++ b/ch10.r
@@ -58,5 +58,24 @@ for (i in 1:ncol(x)) {
 }
 stem(t, 1/(t+1), col="darkred", lwd=2, pch=1, type="o")
 
+## Example 10.11
 
+# R code for Example 10.11: Plot the time function
+t = seq(-2, 2, len = 1000)
+x = matrix(0, 1000, 20)
+
+for (i in 1:20) {
+    x[,i] = runif(1) * cos(2*pi*t)
+}
+
+matplot(t, x, lwd=2, col="gray", type="l", lty="solid", xaxp=c(-2,2, 8))
+grid()
+lines(t, 0.5*cos(2*pi*t), lwd=5, col="darkred")
+points(numeric(20), x[501,], lwd=2, col="darkorange")
+points(numeric(20) + 0.5, x[626,], lwd=2, col="blue", pch=4)
+
+# R code for Example 10.11: Plot the autocorrelation function
+t = seq(-1, 1, len=1000)
+R = (1/3)*outer(cos(2*pi*t), cos(2*pi*t))
+image(t, t, R, col=topo.colors(255), xlab="t_1", ylab="t_2")
 

From 1ee487b26bac78c935f668b38ecf25eb265690f7 Mon Sep 17 00:00:00 2001
From: aaaakshat <33050725+aaaakshat@users.noreply.github.com>
Date: Thu, 11 Nov 2021 13:32:24 -0500
Subject: [PATCH 05/13] Finish example 10.14

---
 ch10.r | 49 +++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 49 insertions(+)

diff --git a/ch10.r b/ch10.r
index 6763fb3..d83b5db 100644
--- a/ch10.r
+++ b/ch10.r
@@ -79,3 +79,52 @@ t = seq(-1, 1, len=1000)
 R = (1/3)*outer(cos(2*pi*t), cos(2*pi*t))
 image(t, t, R, col=topo.colors(255), xlab="t_1", ylab="t_2")
 
+## Example 10.12
+
+# R code for Example 10.11: Plot the time function
+t = seq(-2, 2, len = 1000)
+x = matrix(0, 1000, 20)
+
+for (i in 1:20) {
+    x[,i] = cos((2*pi*t) + (2*pi*runif(1)))
+}
+
+matplot(t, x, lwd=2, col="gray", type="l", lty="solid", xaxp=c(-2,2, 8))
+grid()
+lines(t, 0*cos(2*pi*t), lwd=5, col="darkred")
+points(numeric(20), x[501,], lwd=2, col="darkorange")
+points(numeric(20) + 0.5, x[626,], lwd=2, col="blue", pch=4)
+
+# R code for Example 10.12: Plot the autocorrelation function
+t = seq(-1, 1, len=1000)
+R = toeplitz(0.5*(cos(2*pi*t)))
+image(t, t, R, col=topo.colors(255), ylim=c(1,-1), xlab="t_1", ylab="t_2")
+
+#############
+# Chapter 10.3 Wide sense stationary processes
+
+## Example 10.14
+
+# R code to demonstrate autocorrelation
+
+# Figure 1
+Xa = rnorm(1000)
+Xa2 = rnorm(1000)
+
+plot(Xa, type="l", lwd=2, col="blue")
+grid()
+lines(Xa2, lwd=2)
+
+# Figure 2
+N = 1000
+T = 1000
+X = matrix(rnorm(N*T), N, T)
+xc = matrix(0, N, 2*T-1)
+
+for (i in 1:N) {
+    xc[i,] = ccf(X[i,], X[i,], lag.max=2*T-1)$acf/T
+}
+
+plot(xc[1,], type="l", lwd=2, col="darkblue")
+lines(xc[2,], lwd=2)
+

From 05591a8ca0e550221703ab80bbcc2eb4a6d8db7e Mon Sep 17 00:00:00 2001
From: aaaakshat <33050725+aaaakshat@users.noreply.github.com>
Date: Thu, 11 Nov 2021 16:08:47 -0500
Subject: [PATCH 06/13] Complete chapter 10.5

---
 ch10.r | 29 +++++++++++++++++++++++++++++
 1 file changed, 29 insertions(+)

diff --git a/ch10.r b/ch10.r
index d83b5db..bf15c6d 100644
--- a/ch10.r
+++ b/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")
+

From 1944f22d86d4c8525f1aa53c34b3cb65d2cf5e9f Mon Sep 17 00:00:00 2001
From: aaaakshat <33050725+aaaakshat@users.noreply.github.com>
Date: Thu, 11 Nov 2021 16:11:20 -0500
Subject: [PATCH 07/13] Add chapter 10.6 data

---
 ch10_LPC_data.txt | 320 ++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 320 insertions(+)
 create mode 100644 ch10_LPC_data.txt

diff --git a/ch10_LPC_data.txt b/ch10_LPC_data.txt
new file mode 100644
index 0000000..8d71513
--- /dev/null
+++ b/ch10_LPC_data.txt
@@ -0,0 +1,320 @@
+         0
+         0
+         0
+         0
+    0.0000
+         0
+         0
+   -0.0087
+         0
+   -0.0087
+         0
+   -0.0087
+   -0.0087
+   -0.0087
+   -0.0087
+   -0.0087
+         0
+         0
+   -0.0087
+   -0.0087
+    0.0000
+         0
+   -0.0087
+   -0.0087
+   -0.0174
+   -0.0087
+   -0.0087
+   -0.0087
+   -0.0174
+   -0.0174
+   -0.0174
+   -0.0261
+   -0.0087
+   -0.0087
+   -0.0174
+   -0.0174
+   -0.0087
+   -0.0174
+   -0.0174
+         0
+   -0.0087
+   -0.0087
+   -0.0174
+   -0.0261
+   -0.0261
+   -0.0087
+         0
+   -0.0087
+   -0.0174
+   -0.0174
+   -0.0087
+   -0.0087
+   -0.0174
+   -0.0174
+   -0.0087
+   -0.0174
+   -0.0174
+   -0.0087
+         0
+         0
+   -0.0087
+         0
+   -0.0087
+   -0.0174
+   -0.0261
+   -0.0261
+   -0.0174
+   -0.0087
+         0
+   -0.0087
+   -0.0174
+   -0.0087
+         0
+   -0.0087
+   -0.0087
+         0
+    0.0087
+    0.0261
+    0.0174
+    0.0174
+    0.0174
+    0.0261
+    0.0174
+    0.0261
+    0.0174
+    0.0087
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+   -0.0348
+   -0.0435
+   -0.0348
+   -0.0348
+   -0.0435
+   -0.0348
+   -0.0261
+   -0.0348
+   -0.0261
+   -0.0261
+   -0.0348
+   -0.0261
+   -0.0348
+   -0.0348
+   -0.0174
+    0.0087
+    0.0174
+    0.0348
+    0.0435
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+    0.0522
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+    0.0348
+    0.0348
+    0.0174
+    0.0261
+    0.0174
+    0.0087
+    0.0174
+    0.0087
+         0
+   -0.0174
+   -0.0261
+   -0.0348
+   -0.0435
+   -0.0348
+   -0.0435
+   -0.0348
+   -0.0348
+   -0.0348
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+   -0.0261
+   -0.0174
+   -0.0261
+   -0.0261
+   -0.0174
+   -0.0087
+   -0.0087
+         0
+    0.0087
+    0.0174
+    0.0174
+    0.0087
+    0.0261
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+    0.0174
+    0.0174
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+    0.0174
+    0.0261
+    0.0174
+    0.0174
+    0.0174
+    0.0087
+    0.0087
+         0
+         0
+   -0.0087
+   -0.0087
+   -0.0174
+   -0.0174
+   -0.0261
+   -0.0261
+   -0.0261
+   -0.0174
+   -0.0174
+   -0.0261
+   -0.0174
+   -0.0174
+   -0.0087
+         0
+   -0.0087
+   -0.0174
+   -0.0087
+   -0.0174
+   -0.0087
+    0.0087
+         0
+    0.0000
+         0
+    0.0087
+    0.0174
+    0.0174
+    0.0261
+    0.0174
+    0.0174
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+    0.0087
+    0.0261
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+    0.0435
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+   -0.0522
+   -0.0783
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+   -0.0696
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+   -0.0522
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+   -0.0435
+   -0.0696
+   -0.0783
+   -0.0696
+   -0.0783
+   -0.0783
+   -0.0609
+   -0.0261
+         0
+    0.0174
+    0.0435
+    0.0609
+    0.0522
+    0.0435
+    0.0261
+    0.0174
+    0.0261
+    0.0435
+    0.0522
+    0.0609
+    0.0522
+    0.0435
+    0.0348
+    0.0087
+   -0.0174
+   -0.0261
+   -0.0348
+   -0.0522
+   -0.0522
+   -0.0435
+   -0.0522
+   -0.0522
+   -0.0609
+   -0.0696
+   -0.0783
+   -0.0783
+   -0.0696
+   -0.0609
+   -0.0435
+   -0.0174
+   -0.0087
+   -0.0174
+   -0.0174
+   -0.0261
+   -0.0261
+   -0.0087
+   -0.0087
+   -0.0174
+   -0.0174
+   -0.0087
+    0.0087
+    0.0174
+    0.0087
+         0
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+   -0.0087
+         0
+         0
+    0.0087
+    0.0087
+    0.0174
+    0.0174
+    0.0087
+    0.0174
+    0.0087
+    0.0087
+    0.0174
+    0.0087
+    0.0174
+    0.0174
+    0.0261
+    0.0261
+    0.0174
+    0.0087
+   -0.0087
+   -0.0174
+   -0.0261
+   -0.0261
+   -0.0348
+   -0.0261
+   -0.0174
+   -0.0261
+   -0.0261
+   -0.0261
+   -0.0261
+   -0.0261
+   -0.0174
+         0
+         0
+    0.0087
+         0
+    0.0087
+    0.0348
+    0.0348
+    0.0348
+    0.0348
+    0.0435
+    0.0957
+    0.1304
+    0.1217
+    0.0783
+    0.0348
+   -0.0348
+   -0.1130
+   -0.1478
+   -0.1043
\ No newline at end of file

From 6a737a531e6637ba91f4425c96fd7a365fb8458c Mon Sep 17 00:00:00 2001
From: aaaakshat <33050725+aaaakshat@users.noreply.github.com>
Date: Thu, 11 Nov 2021 16:25:51 -0500
Subject: [PATCH 08/13] Solve Yule Walker equation

---
 ch10.r | 25 +++++++++++++++++++++++++
 1 file changed, 25 insertions(+)

diff --git a/ch10.r b/ch10.r
index bf15c6d..24a106f 100644
--- a/ch10.r
+++ b/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)
+

From 39b1cd51eeb5f217a72d21459c4fb5063f8dd398 Mon Sep 17 00:00:00 2001
From: aaaakshat <33050725+aaaakshat@users.noreply.github.com>
Date: Tue, 16 Nov 2021 17:35:32 -0500
Subject: [PATCH 09/13] Add LPC data part 2

---
 ch10_LPC_data_02.txt | 320 +++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 320 insertions(+)
 create mode 100644 ch10_LPC_data_02.txt

diff --git a/ch10_LPC_data_02.txt b/ch10_LPC_data_02.txt
new file mode 100644
index 0000000..a57ddf4
--- /dev/null
+++ b/ch10_LPC_data_02.txt
@@ -0,0 +1,320 @@
+-0.2222
+-0.1481
+-0.0370
+-0.1111
+-0.3333
+-0.5556
+-0.5185
+-0.4444
+-0.3704
+-0.2593
+-0.0370
+0.1481
+0.3333
+0.4444
+0.4815
+0.4074
+0.2593
+0.0370
+0.0741
+0.1852
+0.2593
+0.4074
+0.5556
+0.3704
+0.0741
+-0.1481
+-0.2963
+-0.3704
+-0.4074
+-0.2593
+-0.1852
+-0.2222
+-0.2222
+-0.1852
+-0.2222
+-0.2963
+-0.3333
+-0.3704
+-0.3704
+-0.2963
+-0.1852
+0
+0.0741
+0.0741
+0
+-0.2222
+-0.4074
+-0.4074
+-0.3333
+-0.1852
+-0.0741
+-0.0370
+-0.0741
+-0.1852
+-0.2593
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+-0.1852
+-0.1481
+-0.0370
+0
+0.0741
+0.0741
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+0.0370
+0.0741
+0.2222
+0.2593
+0.3333
+0.3704
+0.4074
+0.3704
+0.2593
+0.1481
+0.1111
+0.0741
+0
+0.0741
+0.0741
+0.0370
+0
+-0.0741
+-0.1111
+-0.1481
+-0.1852
+-0.1111
+-0.0741
+-0.0370
+0.0741
+0.1111
+-0.0370
+-0.1111
+-0.1111
+-0.1852
+-0.2222
+-0.1852
+-0.1111
+-0.0741
+0.0370
+-0.0370
+-0.0370
+-0.0370
+-0.1481
+-0.1852
+-0.1481
+-0.1111
+-0.0370
+0.0741
+0.1481
+0.1111
+0.1111
+0.0741
+0.0370
+-0.0370
+0
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+0.1852
+0.1111
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+-0.0370
+-0.1481
+-0.0370
+0
+0.1852
+0.4074
+0.4074
+0.2593
+0
+-0.2963
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+-0.5926
+-0.4074
+-0.1111
+0.0370
+-0.0370
+-0.2222
+-0.5185
+-0.7037
+-0.7037
+-0.4815
+-0.2593
+-0.0370
+0.0741
+0.0741
+0.1111
+0.0741
+0.0741
+0.1481
+0.2222
+0.1481
+0.2593
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+0
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+-0.2593
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+-0.2593
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+0.0741
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+-0.0741
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+0
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+0
+0
+0.0741
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+0
+-0.3333
+-0.7407
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+-0.1111
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+-0.5926
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+-0.3333
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+0
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+-0.5926
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From 93bff7f72c325980c83c27ea01712d78723783fb Mon Sep 17 00:00:00 2001
From: aaaakshat <33050725+aaaakshat@users.noreply.github.com>
Date: Tue, 16 Nov 2021 17:35:46 -0500
Subject: [PATCH 10/13] Finish wiener filtering

---
 ch10.r | 57 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 57 insertions(+)

diff --git a/ch10.r b/ch10.r
index 24a106f..3fbdde1 100644
--- a/ch10.r
+++ b/ch10.r
@@ -182,3 +182,60 @@ 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)
 
+## Predict sample
+
+# R code to predict the samples
+y = scan("./ch10_LPC_data_02.txt")
+K = 10
+N = length(y)
+
+y_corr = ccf(y, y, lag.max=2*N-1)$acf[,,1]
+R = toeplitz(y_corr[N + 1:K-1])
+lhs = y_corr[N + 1:K]
+h = solve(R, lhs)
+
+z = y[311:320]
+yhat = numeric(340)
+yhat[1:320] = y
+
+for (t in 1:20) {
+    predict = t(z) * h
+    z = c(z[2:10], predict)
+    yhat[320+t] = predict
+}
+
+plot(yhat, lwd=3, col="red", type="l")
+grid()
+legend(10, 0.9, legend=c("Prediction", "Input"), col=c("red", "gray"), lty=c(1, 2), lwd=2)
+lines(y, lwd=4, col="gray", lty=2)
+
+## Wiener filter 
+
+# R code for Wiener filtering
+library(pracma)
+w = 0.05 * rnorm(320)
+x = y + w
+
+Ry = ccf(y, y, lag.max=2*length(y)-1)$acf
+Rw = ccf(w, w, lag.max=2*length(w)-1)$acf
+Sy = fft(Ry)
+Sw = fft(Rw)
+H = Sy / (Sy + Sw)
+
+a = x[1:639]
+a[is.na(a)] = 0
+Yhat = H * fft(a[1:639])
+yhat = Re(ifft(Yhat))
+
+# Figure 1
+plot(x, lwd=5, col="gray", type="l")
+grid()
+legend(10, -0.7, legend=c("Noisy Input X[n]", "Wiener Filtered Yhat[n]", "Ground Truth Y[n]"), col=c("gray", "red", "black"), lty=c(1, 1, 2), lwd=2)
+lines(yhat[1:320], lwd=2, col="red")
+lines(y, lwd=2, lty=2)
+
+# Figure 2
+plot(Rw, lwd=4, col="blue", label="h[n]", type="l")
+legend(500, 0.85, legend=c("h[n]"), col=c("blue"), lty=c(1), lwd=c(4))
+grid()
+

From 3374e1cb014132ccfd55b2deff0ac9563cb0c85b Mon Sep 17 00:00:00 2001
From: aaaakshat <33050725+aaaakshat@users.noreply.github.com>
Date: Tue, 16 Nov 2021 20:36:44 -0500
Subject: [PATCH 11/13] Add wiener data

---
 ch10_wiener_deblur_data.txt | 320 ++++++++++++++++++++++++++++++++++++
 1 file changed, 320 insertions(+)
 create mode 100644 ch10_wiener_deblur_data.txt

diff --git a/ch10_wiener_deblur_data.txt b/ch10_wiener_deblur_data.txt
new file mode 100644
index 0000000..a9ecd78
--- /dev/null
+++ b/ch10_wiener_deblur_data.txt
@@ -0,0 +1,320 @@
+   -0.0652
+   -0.0554
+   -0.0422
+   -0.0272
+   -0.0123
+    0.0006
+    0.0102
+    0.0160
+    0.0183
+    0.0183
+    0.0182
+    0.0203
+    0.0273
+    0.0410
+    0.0628
+    0.0924
+    0.1281
+    0.1666
+    0.2038
+    0.2351
+    0.2563
+    0.2648
+    0.2601
+    0.2435
+    0.2185
+    0.1897
+    0.1617
+    0.1386
+    0.1230
+    0.1158
+    0.1166
+    0.1234
+    0.1340
+    0.1458
+    0.1565
+    0.1644
+    0.1685
+    0.1686
+    0.1649
+    0.1583
+    0.1503
+    0.1425
+    0.1363
+    0.1329
+    0.1325
+    0.1347
+    0.1378
+    0.1398
+    0.1383
+    0.1317
+    0.1193
+    0.1022
+    0.0834
+    0.0670
+    0.0578
+    0.0599
+    0.0761
+    0.1065
+    0.1485
+    0.1965
+    0.2432
+    0.2802
+    0.2995
+    0.2950
+    0.2632
+    0.2042
+    0.1211
+    0.0199
+   -0.0917
+   -0.2055
+   -0.3138
+   -0.4105
+   -0.4911
+   -0.5536
+   -0.5975
+   -0.6239
+   -0.6347
+   -0.6325
+   -0.6199
+   -0.5991
+   -0.5719
+   -0.5395
+   -0.5023
+   -0.4602
+   -0.4122
+   -0.3572
+   -0.2942
+   -0.2224
+   -0.1419
+   -0.0539
+    0.0389
+    0.1328
+    0.2233
+    0.3052
+    0.3742
+    0.4267
+    0.4608
+    0.4766
+    0.4758
+    0.4619
+    0.4391
+    0.4124
+    0.3861
+    0.3637
+    0.3475
+    0.3382
+    0.3351
+    0.3362
+    0.3387
+    0.3398
+    0.3365
+    0.3267
+    0.3092
+    0.2843
+    0.2533
+    0.2189
+    0.1848
+    0.1548
+    0.1324
+    0.1200
+    0.1186
+    0.1271
+    0.1429
+    0.1624
+    0.1816
+    0.1972
+    0.2068
+    0.2099
+    0.2074
+    0.2013
+    0.1940
+    0.1878
+    0.1846
+    0.1851
+    0.1892
+    0.1960
+    0.2045
+    0.2132
+    0.2209
+    0.2260
+    0.2272
+    0.2228
+    0.2110
+    0.1903
+    0.1598
+    0.1199
+    0.0721
+    0.0197
+   -0.0329
+   -0.0811
+   -0.1206
+   -0.1485
+   -0.1641
+   -0.1685
+   -0.1647
+   -0.1569
+   -0.1493
+   -0.1454
+   -0.1476
+   -0.1564
+   -0.1711
+   -0.1898
+   -0.2100
+   -0.2295
+   -0.2465
+   -0.2599
+   -0.2692
+   -0.2743
+   -0.2755
+   -0.2730
+   -0.2670
+   -0.2575
+   -0.2448
+   -0.2293
+   -0.2116
+   -0.1928
+   -0.1741
+   -0.1564
+   -0.1403
+   -0.1259
+   -0.1126
+   -0.0997
+   -0.0860
+   -0.0706
+   -0.0532
+   -0.0338
+   -0.0133
+    0.0071
+    0.0260
+    0.0419
+    0.0536
+    0.0601
+    0.0612
+    0.0567
+    0.0470
+    0.0325
+    0.0137
+   -0.0090
+   -0.0351
+   -0.0643
+   -0.0961
+   -0.1296
+   -0.1639
+   -0.1972
+   -0.2278
+   -0.2537
+   -0.2727
+   -0.2832
+   -0.2840
+   -0.2741
+   -0.2534
+   -0.2222
+   -0.1812
+   -0.1317
+   -0.0756
+   -0.0152
+    0.0463
+    0.1055
+    0.1591
+    0.2042
+    0.2391
+    0.2632
+    0.2775
+    0.2840
+    0.2853
+    0.2838
+    0.2810
+    0.2776
+    0.2729
+    0.2655
+    0.2534
+    0.2353
+    0.2103
+    0.1785
+    0.1412
+    0.1001
+    0.0575
+    0.0153
+   -0.0247
+   -0.0618
+   -0.0955
+   -0.1258
+   -0.1526
+   -0.1755
+   -0.1939
+   -0.2065
+   -0.2119
+   -0.2090
+   -0.1971
+   -0.1763
+   -0.1478
+   -0.1138
+   -0.0772
+   -0.0413
+   -0.0098
+    0.0144
+    0.0287
+    0.0314
+    0.0221
+    0.0009
+   -0.0308
+   -0.0710
+   -0.1172
+   -0.1664
+   -0.2155
+   -0.2612
+   -0.3006
+   -0.3308
+   -0.3494
+   -0.3548
+   -0.3460
+   -0.3234
+   -0.2883
+   -0.2436
+   -0.1931
+   -0.1413
+   -0.0928
+   -0.0516
+   -0.0203
+   -0.0003
+    0.0087
+    0.0077
+   -0.0013
+   -0.0165
+   -0.0360
+   -0.0585
+   -0.0824
+   -0.1061
+   -0.1274
+   -0.1439
+   -0.1532
+   -0.1531
+   -0.1429
+   -0.1228
+   -0.0948
+   -0.0619
+   -0.0280
+    0.0035
+    0.0296
+    0.0488
+    0.0612
+    0.0681
+    0.0717
+    0.0748
+    0.0795
+    0.0872
+    0.0983
+    0.1119
+    0.1260
+    0.1384
+    0.1467
+    0.1492
+    0.1451
+    0.1346
+    0.1187
+    0.0993
+    0.0784
+    0.0583
+    0.0403
+    0.0256
\ No newline at end of file

From 5d86e7f9b319e8b4a581bbe953846200b8cc04c7 Mon Sep 17 00:00:00 2001
From: aaaakshat <33050725+aaaakshat@users.noreply.github.com>
Date: Tue, 16 Nov 2021 20:36:49 -0500
Subject: [PATCH 12/13] Finish wiener deblurring

---
 ch10.r | 55 ++++++++++++++++++++++++++++++++++++++++++++++++-------
 1 file changed, 48 insertions(+), 7 deletions(-)

diff --git a/ch10.r b/ch10.r
index 3fbdde1..1923c77 100644
--- a/ch10.r
+++ b/ch10.r
@@ -122,7 +122,7 @@ X = matrix(rnorm(N*T), N, T)
 xc = matrix(0, N, 2*T-1)
 
 for (i in 1:N) {
-    xc[i,] = ccf(X[i,], X[i,], lag.max=2*T-1)$acf/T
+    xc[i,] = ccf(X[i,], X[i,], lag.max=2*T-1, pl=FALSE)$acf/T
 }
 
 plot(xc[1,], type="l", lwd=2, col="darkblue")
@@ -167,7 +167,7 @@ lines(seq(-20, 20, by=0.001), h2, lwd=2, col="darkorange")
 y = scan("./ch10_LPC_data.txt")
 K = 10
 N = 320
-y_corr = ccf(y, y, lag.max=2*length(y)-1)$acf
+y_corr = ccf(y, y, lag.max=2*length(y)-1, pl=FALSE)$acf
 R = toeplitz(y_corr[N + 1:K-1])
 lhs = y_corr[N + 1:K]
 h = solve(R, lhs)
@@ -207,17 +207,18 @@ for (t in 1:20) {
 plot(yhat, lwd=3, col="red", type="l")
 grid()
 legend(10, 0.9, legend=c("Prediction", "Input"), col=c("red", "gray"), lty=c(1, 2), lwd=2)
-lines(y, lwd=4, col="gray", lty=2)
+lines(y, lwd=4, col="gray", lty=3)
 
 ## Wiener filter 
 
 # R code for Wiener filtering
 library(pracma)
+y = scan("./ch10_LPC_data_02.txt")
 w = 0.05 * rnorm(320)
 x = y + w
 
-Ry = ccf(y, y, lag.max=2*length(y)-1)$acf
-Rw = ccf(w, w, lag.max=2*length(w)-1)$acf
+Ry = ccf(y, y, lag.max=2*length(y)-1, pl=FALSE)$acf
+Rw = ccf(w, w, lag.max=2*length(w)-1, pl=FALSE)$acf
 Sy = fft(Ry)
 Sw = fft(Rw)
 H = Sy / (Sy + Sw)
@@ -225,17 +226,57 @@ H = Sy / (Sy + Sw)
 a = x[1:639]
 a[is.na(a)] = 0
 Yhat = H * fft(a[1:639])
-yhat = Re(ifft(Yhat))
+yhat = Re(ifft(as.vector(Yhat)))
 
 # Figure 1
 plot(x, lwd=5, col="gray", type="l")
 grid()
 legend(10, -0.7, legend=c("Noisy Input X[n]", "Wiener Filtered Yhat[n]", "Ground Truth Y[n]"), col=c("gray", "red", "black"), lty=c(1, 1, 2), lwd=2)
 lines(yhat[1:320], lwd=2, col="red")
-lines(y, lwd=2, lty=2)
+lines(y, lwd=2, lty=3)
 
 # Figure 2
 plot(Rw, lwd=4, col="blue", label="h[n]", type="l")
 legend(500, 0.85, legend=c("h[n]"), col=c("blue"), lty=c(1), lwd=c(4))
 grid()
 
+## Wiener deblurring
+
+# R code to solve the Wiener deconvolution problem
+library(pracma)
+
+conv_same = function(x, y) {
+    s = length(y) / 2
+    e = length(x) + s - 1
+    return (convolve(x, y, type="open")[s:e])
+}
+
+y = scan("./ch10_wiener_deblur_data.txt")
+g = ones(32, 1)/32
+w = 0.02 * rnorm(320)
+s = length(y)/2
+e = length(g) + s - 1
+x = conv_same(y, g) + w
+
+Ry = ccf(y, y, lag.max=2*length(y)-1, pl=FALSE)$acf
+Rw = ccf(w, w, lag.max=2*length(w)-1, pl=FALSE)$acf
+Sy= fft(Ry)
+Sw = fft(Rw)
+a = g[1:639]
+a[is.na(a)] = 0
+G = fft(a[1:639])
+
+H = (Conj(G) * Sy) / (abs(G) ^ 2 * Sy + Sw)
+b = x[1:639]
+b[is.na(b)] = 0
+Yhat = H * fft(b[1:639])
+yhat = Re(ifft(as.vector(Yhat)))
+
+plot(x, lwd=4, col="gray", type="l", ylim=c(-0.7, 0.7))
+grid()
+legend(150, -0.45, legend=c("Noisy Input X[n]", "Wiener Filtered Yhat[n]", "Ground Truth Y[n]"), col=c("gray", "red", "black"), lty=c(1, 1, 2), lwd=2)
+lines(16:(320+15), yhat[1:320], col="red", lwd=2)
+lines(1:320, y, lwd=2, lty=3)
+
+#############
+

From fcbd90dac9448fce034a44065628d58c41edc9a3 Mon Sep 17 00:00:00 2001
From: aaaakshat <33050725+aaaakshat@users.noreply.github.com>
Date: Tue, 16 Nov 2021 20:37:22 -0500
Subject: [PATCH 13/13] Rename ch07.R -> ch07.r

---
 ch07.R => ch07.r | 0
 1 file changed, 0 insertions(+), 0 deletions(-)
 rename ch07.R => ch07.r (100%)

diff --git a/ch07.R b/ch07.r
similarity index 100%
rename from ch07.R
rename to ch07.r