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diff --git a/hamming.sh b/hamming.sh
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+#!/bin/bash
+
+### hamming.sh
+# Convolve input vector with 3-element Hamming window [0.23, 0.54, 0.23]
+# note: bash built-in $(( )) constructs only support integer arithmetic
+# floating point operation will require another language such as awk, perl, or
+# python.
+
+### input vector as array
+X=($1)
+echo ${#X[@]}
+
+### Hamming window vector
+H=(0.23 0.54 0.23)
+echo ${#H[@]}
+
+### length of output
+L=$(( ${#X[@]} + ${#H[@]} - 1 ))
+
+### iterate over both vectors
+for N in $( seq 0 1 $L ) ; do
+    for M in $( seq 0 1 $(( ${#H[@]} - 1 )) ) ; do
+        if [ $(( $N >= $M )) ] ; then
+            printf "N=$N\tM=$M\tN-M=$(( $N - $M ))\n"
+        else
+            continue
+        fi
+    done
+done
+