test/test-frequency-response.rkt
```#lang racket

(require "../frequency-response.rkt"
rackunit)

(define (complex-within a b tolerance)
(< (magnitude (- a b)) tolerance))

(define (complex-check a b tolerance)
(unless (complex-within a b tolerance)
(error 'complex-check "expected ~a, got ~a, difference ~a is greater than tolerance ~a\n"
b a (magnitude (- a b)) tolerance)))

(define (1-zero z)
(+ 1 (expt z -1)))

(complex-check ((response/raw 1-zero) 0) 2.0 1e-4)
(complex-check ((response/raw 1-zero) 22050) 0.0 1e-4)

(check-equal? (all-but-n 3 '(1 2 3 4 5))
'((4 5) (3 5) (3 4) (2 5) (2 4)
(2 3) (1 5) (1 4) (1 3) (1 2)))

(check-true (andmap = (roots->coefficients '(0.5 0.5+i 0.5-i))
(list 1.0 -1.5 1.75 -0.625)))

(check-= (product-of '(1 2 3 4)) 24 0.0)
(check-= (sum-of '(1 2 3 4)) 10 0.0)

(check-= ((coefficients->poly '(3 1 9)) 6)
123
1e-7)

;; EXAMPLES

;; 100-pole comb
(define (poly1 z)
(/ 1 (- 1 (* 0.95 (expt z -100)))))

;; show the whole range:
(response-plot poly1
30
0      ; min-freq
22050) ; max-freq

;; show the range from 10K to 11K:
(response-plot poly1
30
10000  ; min-freq
11000) ; max-freq

;; a single zero at 1:
(response-plot (lambda (z) (- 1 (expt z -1))) 6 0 22050)

;; the same thing, using poles&zeros:
(response-plot (poles&zeros->fun '() '(1)) 6 0 22050)

;; modeling a single pole and two zeros.
(response-plot (lambda (z)
(let ([a -0.28]
[b 0.57])
(/ (- 1 (expt z -2))
1
(+ 1
(* -2 a (expt z -1))
(* (+ (* a a) (* b b)) (expt z -2))))))
11
0
22050)

;; the same thing, using poles&zeros:
(response-plot (poles&zeros->fun '(-0.28+0.57i -0.28-0.57i) '(1 -1))
11
0
22050)

(response-plot (poles&zeros->fun '(0.5 0.5+0.5i 0.5-0.5i) '(0+i 0-i))
40
0
22050)

(response-plot (coefficient-sets->fun
'(1.0 -3.826392 5.516636 -3.5511127 0.861025)
'(8.697132e-06 3.478853e-05 5.2182793e-05 3.478853e-05
8.697132e-06))
0
0
22050)

```