Smoothing a Signal

A procedure smooth that takes as input a procedure that computes f and returns a procedure that computes the smoothed f.

Also implemented is a procedure that computes the n-fold smoothed function.

	(define (cube x) (* x x x))
	(define dx 0.00001)
	(define (compose f g)
	(lambda (x)
	(f (g x))))
	(define (repeated f n)
	(if
	(= n 1)
	(lambda (x) (f x))
	(compose f (repeated f (- n 1)))))
	(define (smooth-once f)
	(lambda (x)
	(/
	(+
	(f (- x dx))
	(f x)
	(f (+ x dx)))
	3)))
	(define (smooth f n)
	(repeated (smooth-once f) n))

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