sicp 1.44

Exercise 1.44.  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 .
 

(define (smooth-n f n)
  ((repeated smooth n) f))

(define (smooth f)
  (lambda (x)
    (/ (+ (f (- x dx))
          (f x)
          (f (+ x dx)))
       3)))

(define (repeated f n)
  (if (= n 1)
      f
      (composed f (repeated f (- n 1)))))

(define (composed f g)
  (lambda (x) (f (g x))))

(define dx 0.00001)