-function to the result of the first application and the next element from
-the vector. This continues until the end of the vector is reached. The
-result of the \hs{foldl1} function is the result of the last application.
-As you can see, the \hs{zipWith (*)} function is just pairwise
-multiplication and the \hs{foldl1 (+)} function is just summation.
-
-Returning to the actual FIR filter, we will slightly change the
-equation belong to it, so as to make the translation to code more obvious.
-What we will do is change the definition of the vector of input samples.
-So, instead of having the input sample received at time
-$t$ stored in $x_t$, $x_0$ now always stores the current sample, and $x_i$
-stores the $ith$ previous sample. This changes the equation to the
-following (Note that this is completely equivalent to the original
-equation, just with a different definition of $x$ that will better suit
-the transformation to code):
+function to the result of the first application and the next element in the
+vector. This continues until the end of the vector is reached. The result of
+the \hs{foldl1} function is the result of the last application. It is obvious
+that the \hs{zipWith (*)} function is basically pairwise multiplication and
+that the \hs{foldl1 (+)} function is just summation.
+
+Returning to the actual FIR filter, we will slightly change the equation
+describing it, so as to make the translation to code more obvious and concise.
+What we do is change the definition of the vector of input samples and delay
+the computation by one sample. Instead of having the input sample received at
+time $t$ stored in $x_t$, $x_0$ now always stores the newest sample, and $x_i$
+stores the $ith$ previous sample. This changes the equation to the following
+(note that this is completely equivalent to the original equation, just with a
+different definition of $x$ that will better suit the transformation to code):