N-fold smoothed function
The idea of smoothing a function is an important concept in signal processing. If
f
is a function and
dx
is some small number, then the smoothed version of
f
is the function whose value at a point
x
is the average of
f(x − dx)
,
f(x)
, and
f(x + dx)
. Write a procedure
smooth
that takes as input a procedure that computes
f
and returns a procedure that computes the smoothed
f
. It is sometimes valuable to repeatedly smooth a function (that is, smooth the smoothed function, and so on) to obtained the
n
-fold smoothed function. Show how to generate the
n
-fold smoothed function of any given function using
smooth
and
repeated
from exercise
1.43
.