From 9ac9c6f724c16a172ecb923a0360bc9a9ffc3806 Mon Sep 17 00:00:00 2001
From: wukong <wukong@longaeva>
Date: Tue, 25 Dec 2018 14:44:46 -0800
Subject: began merging windowing scripts; swapped std_dev and std_err in mean
 and mean_avg;

---
 fib.awk      |  4 +++-
 gaussian.awk | 19 ++++++++++++++-----
 hamming.awk  | 48 +++++++++++++++++++++++++++++++++---------------
 lpf.awk      |  5 +++--
 mean.awk     |  4 ++--
 mean_avg.awk |  6 +++---
 6 files changed, 58 insertions(+), 28 deletions(-)

diff --git a/fib.awk b/fib.awk
index 654921c..0d46479 100644
--- a/fib.awk
+++ b/fib.awk
@@ -6,6 +6,8 @@
 BEGIN {
     ARGV[1] ? n = ARGV[1] : n = 0
     ARGV[2] ? OFMT = "%." ARGV[2] "g" : OFMT = "%g"
-    print (1/sqrt(5))*(0.5*(1 + sqrt(5)))^n - (1/sqrt(5))*(0.5*(1 - sqrt(5)))^n
+    C1 = 1.0/sqrt(5)
+    C2 = -1.0/sqrt(5)
+    print C1*(0.5*(1 + sqrt(5)))^n + C2*(0.5*(1 - sqrt(5)))^n
 }
 
diff --git a/gaussian.awk b/gaussian.awk
index 48c3f9a..dfb5fb4 100644
--- a/gaussian.awk
+++ b/gaussian.awk
@@ -4,19 +4,28 @@
 # generate a Gaussian window
 # https://en.wikipedia.org/wiki/Window_function
 
+
+### Gaussian
+function gaussian(n) {
+    # sigma <= 0.5
+    sigma = 0.4
+    en[n] = (n - M)/(sigma*M)
+    return exp(-0.5*e[n]*e[n])
+}
+
+
 BEGIN {
 
     ARGV[1] ? N = ARGV[1] : N = 0
     ARGV[2] ? OFMT = "%." ARGV[2] "g" : OFMT = "%g"
-    M = 0.5*(N - 1)
 
-    # sigma <= 0.5
-    sigma = 0.4
+    # window interval goes from -M to M
+    M = 0.5*(N - 1)
+    pi = 4*atan2(1,1)
 
     for (n=0; n<N; n++) {
         if (N > 1 && M > 0) {
-            e[n] = (n - M)/(sigma*M)
-            w[n] = exp(-0.5*e[n]*e[n])
+            w[n] = gaussian(n)
             print n, w[n]/M
         }
         else {
diff --git a/hamming.awk b/hamming.awk
index f7ff9f7..acfde97 100644
--- a/hamming.awk
+++ b/hamming.awk
@@ -2,35 +2,52 @@
 
 ### hamming.awk
 # generate a Hamming window
+# R.W. Hamming, 'Digital Filters': H = '0.23 0.54 0.23'
 # https://en.wikipedia.org/wiki/Window_function provides a few values for the
 # 'a0' and 'a1' parameters of the raised cosine.
 
-BEGIN {
 
-    ARGV[1] ? N = ARGV[1] : N = 0
-    ARGV[2] ? OFMT = "%." ARGV[2] "g" : OFMT = "%g"
+### Gaussian
+function gaussian(n) {
+    # sigma <= 0.5
+    sigma = 0.4
+    e[n] = (n)/(sigma*M)
+    return exp(-0.5*e[n]*e[n])
+}
 
-    # window interval goes from -M to M
-    M = 0.5*(N - 1)
-    pi = 4*atan2(1,1)
 
-    ### R.W. Hamming, "Digital Filters"
-    # H = "0.23 0.54 0.23"
+### Hamming, raised cosine
+function hamming(n) {
+    ### optimal values for equal-ripple
+    #a0 = 0.53836
+    #a1 = 0.46164
 
     a0 = (25.0/46.0)
     a1 = (21.0/46.0)
+    return a0 + a1*cos((pi*n)/M)
+}
 
-    ### optimal values for equal-ripple
-    #a0 = 0.53836
-    #a1 = 0.46164
 
-    ### VonHann
-    #a0 = 0.5
-    #a1 = 0.5
+### vonHann, raised cosine
+function vonhann(n) {
+    a0 = 0.5
+    a1 = 0.5
+    return a0 + a1*cos((pi*n)/M)
+}
+
+
+BEGIN {
+
+    ARGV[1] ? N = ARGV[1] : N = 0
+    ARGV[2] ? OFMT = "%." ARGV[2] "g" : OFMT = "%g"
+
+    # window interval goes from -M to M
+    M = 0.5*(N - 1)
+    pi = 4*atan2(1,1)
 
     for (n=-M; n<=M; n++) {
         if (N > 1 && M > 0) {
-            w[n] = a0 + a1*cos((pi*n)/M)
+            w[n] = hamming(n)
             print n + M, w[n]/M
         }
         else {
@@ -39,3 +56,4 @@ BEGIN {
     }
 
 }
+
diff --git a/lpf.awk b/lpf.awk
index 814020f..aba92e1 100644
--- a/lpf.awk
+++ b/lpf.awk
@@ -5,6 +5,7 @@
 
 BEGIN {
     OFS = FS
+    ARGV[1] ? OFMT = "%." ARGV[1] "g" : OFMT = "%g"
     sign = "[+-]?"
     decimal = "[0-9]+[.]?[0-9]*"
     fraction = "[.][0-9]*"
@@ -28,7 +29,7 @@ NF > 0 {
     if (NF > nf_max)
         nf_max = NF
 
-    input_size = window_size 
+    input_size = window_size
     output_size = (input_size + window_size - 1)
 
     ### columns
@@ -72,7 +73,7 @@ NF > 0 {
             printf(OFS)
         else
             printf(ORS)
-        
+
     }
 
 
diff --git a/mean.awk b/mean.awk
index b509473..816208c 100644
--- a/mean.awk
+++ b/mean.awk
@@ -30,7 +30,7 @@ NF > 0 {
 }
 
 END {
-    print "mean", "std_dev", "std_err", "count"
-    print mean, sqrt(var), sqrt(var/count), count
+    print "mean", "std_err", "std_dev", "count"
+    print mean, sqrt(var/count), sqrt(var), count
 }
 
diff --git a/mean_avg.awk b/mean_avg.awk
index 8a5a3c5..ed6f81a 100644
--- a/mean_avg.awk
+++ b/mean_avg.awk
@@ -34,12 +34,12 @@ NF > 0 {
 }
 
 END {
-    print "col", "mean", "std_dev", "std_err", "count"
+    print "col", "mean", "std_err", "std_dev", "count"
     for (n=1; n<=max_nf; n++) {
         if (header[n])
-            print header[n], mean[n], sqrt(var[n]), sqrt(var[n]/count[n]), count[n]
+            print header[n], mean[n], sqrt(var[n]/count[n]), sqrt(var[n]), count[n]
         else
-            print "col" n, mean[n], sqrt(var[n]), sqrt(var[n]/count[n]), count[n]
+            print "col" n, mean[n], sqrt(var[n]/count[n]), sqrt(var[n]), count[n]
     }
 }
 
-- 
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