  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 .

;; ANSWER ------------------------------------------------------------

(define dx 0.001)

(define (smooth f)
  (lambda (x)
    (/ (+ (f x)
          (f (+ x dx))
          (f (- x dx)))
       3.0)))

 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
 ANSWER ------------------------------------------------------------
  SICP 1.44

  Exercise 1.44 .   The idea of smoothing a function is an important
  exercise 1.43 .


(define dx 0.001)

(define (smooth f)
  (lambda (x)
    (/ (+ (f x)
          (f (+ x dx))
          (f (- x dx)))
       3.0)))
