filter.rkt
```#lang racket/base

(require (only-in racket pi)
racket/match
"rsound.rkt"
racket/flonum)

(provide (except-out (all-defined-out)
twopi i))

(define i (sqrt -1))
(define twopi (* 2 pi))

;; frequency response, given input frequency in Hz
(define (response/raw poly)
(define sr-inv (/ 1 (default-sample-rate)))
(lambda (omega)
(let ([z (exp (* i sr-inv twopi omega))])
(poly z))))

;; compute the magnitude of the response in decibels
(define (response/mag poly)
(compose
(lambda (x)
;; log-based, cap at -100 db, square to get power
#;(max -100 (* 10 (/ (log (expt (magnitude x) 2)) (log 10))))
;; equivalent to:
(* 10 (/ (log (max 1e-6 (magnitude x))) (/ (log 10) 2))))
(response/raw poly)))

;; given a set of poles, compute the corresponding
;; polynomial
(define (roots->poly iir-poles)
(coefficients->poly (roots->coefficients iir-poles)))

;; given a set of poles, compute the corresponding
;; IIR feedback coefficients.
(define (roots->coefficients iir-poles)
(let ([neg-poles (map - iir-poles)])
(reverse
(for/list ([exponent (in-range (add1 (length neg-poles)))])
(sum-of (map product-of (all-but-n exponent neg-poles)))))))

;; given a number, check that it's close to real, return the
;; real number
(define (tidy-imag i)
(define angl (angle i))
(define wrapped-angle (cond [(< angl (- (/ pi 2))) (+ angl (* 2 pi))]
[else angl]))
(cond [(< (abs wrapped-angle) angle-epsilon) (magnitude i)]
[(< (abs (- pi wrapped-angle)) angle-epsilon)
(- (magnitude i))]
[else (error 'tidy-imag "angle ~s of complex number ~s is not close to zero or pi." wrapped-angle i)]))
(define angle-epsilon 1e-5)

;; sum-of : (listof number) -> number
(define (sum-of l) (foldl + 0 l))

;; product-of : (listof number) -> number
(define (product-of l) (foldl * 1 l))

;; all-but-n : ways of choosing all but 'n' elements of the list
(define (all-but-n n l)
(cond [(= n 0) (list l)]
[(= n (length l)) (list '())]
[else (append (all-but-n (- n 1) (cdr l))
(map (lambda (x)
(cons (car l) x))
(all-but-n n (cdr l))))]))

;; given a set of polynomial coefficients, return
;; the corresponding polynomial
(define ((coefficients->poly coefficients) x)
(for/fold ([so-far 0])
([coefficient (in-list coefficients)])
(+ coefficient (* so-far x))))

;; given a list of poles and a list of zeros in z-space,
;; return the corresponding transfer function.
(define (poles&zeros->fun poles zeros)
(coefficient-sets->fun (roots->coefficients poles)
(roots->coefficients zeros)))

;; given a list of feedback coefficients and a list of feedforward
;; coefficients, return the corresponding transfer function
(define (coefficient-sets->fun fb-coefficients ff-coefficients)
(let ([feedback-poly (coefficients->poly fb-coefficients)]
[feedforward-poly (coefficients->poly ff-coefficients)])
(lambda (x)
(/ (feedforward-poly x)
(feedback-poly x)))))

;; constants in the 4-pole chebyshev low-pass filter:
(define chebyshev-s-poles
(let ()
;; how many poles (more poles is more computationally intensive)
(define num-poles 4)
;; higher epsilon gives sharper drop but more ripple in passband
(define epsilon 1.0)

;; the left half of the poles *in s-space*:
(define left-half
(for/list ([m (in-range num-poles)])
(* i (cos (+ (* (/ 1 num-poles)
(acos (/ i epsilon)))
(/ (* pi m) num-poles))))))
left-half))

;; convert s-space value to z-space value
(define (s-space->z-space pole) (exp pole))

;; given a scale, produce a 4-pole chebyshev low-pass filter
(define (lpf-coefficients scale)
(define s-poles (map (lambda (x) (* scale x)) chebyshev-s-poles))
(define z-poles (map s-space->z-space s-poles))
(map tidy-imag (cdr (roots->coefficients z-poles))))

;; FIR filters

;; fir-filter : (listof (list/c delay amplitude)) -> signal -> signal
;; filter the input signal using the delay values and amplitudes given for an FIR filter
(define (fir-filter params)
(match params
[`((,delays ,amplitudes) ...)
(unless (andmap (lambda (d) (and (exact-integer? d) (<= 0 d))) delays)
(raise-type-error 'fir-filter "exact integer delays greater than zero" 0 params))
(unless (andmap real? amplitudes)
(raise-type-error 'fir-filter "real number amplitudes" 0 params))
(lambda (signal)
;; enough to hold delayed and current, rounded up to next power of 2:
(let* ([max-delay (up-to-power-of-two (+ 1 (apply max delays)))]
;; set up buffer to delay the signal
[delay-buf (make-vector max-delay 0.0)]
[next-idx 0]
;; ugh... we must be called sequentially:
[last-t -1])
(lambda (t)
(unless (= t (add1 last-t))
(error 'fir-filter "called with t=~s, expecting t=~s. Sorry about that limitation."
t
(let ([this-val (signal t)])
(begin
(vector-set! delay-buf next-idx this-val)
(define result
(for/fold ([sum 0])
([d (in-list delays)]
[a (in-list amplitudes)])
(+ sum (* a (vector-ref delay-buf (modulo (- next-idx d) max-delay))))))
(set! last-t (add1 last-t))
(set! next-idx (modulo (add1 next-idx) max-delay))
result)))))]
[other (raise-type-error 'fir-filter "(listof (list number number))" 0 params)]))

(define (up-to-power-of-two n)
(inexact->exact (expt 2 (ceiling (/ (log (max n 1)) (log 2))))))

;; IIR filters

;; iir-filter : (listof (list/c delay amplitude)) -> signal -> signal
;; filter the input signal using the delay values and amplitudes given for an IIR filter
;; the only difference here is that we put the final result in the delay line, rather than
;; the input signal.
(define (iir-filter params)
(match params
[`((,delays ,amplitudes) ...)
(unless (andmap (lambda (d) (and (exact-integer? d) (< 0 d))) delays)
(raise-type-error 'iir-filter "exact integer delays greater than zero" 0 params))
(unless (andmap real? amplitudes)
(raise-type-error 'iir-filter "real number amplitudes" 0 params))
(lambda (signal)
(let* ([max-delay (up-to-power-of-two (+ 1 (apply max delays)))]
;; set up buffer to delay the signal
[delay-buf (make-vector max-delay 0.0)]
[next-idx 0]
;; ugh... we must be called sequentially:
[last-t -1])
(lambda (t)
(unless (= t (add1 last-t))
(error 'fir-filter "called with t=~s, expecting t=~s. Sorry about that limitation."
t
(let* ([this-val (signal t)]
[new-val (for/fold ([sum this-val])
([d (in-list delays)]
[a (in-list amplitudes)])
(+ sum (* a (vector-ref delay-buf (modulo (- next-idx d) max-delay)))))])
(begin0
new-val
(vector-set! delay-buf next-idx new-val)
(set! last-t (add1 last-t))
(set! next-idx (modulo (add1 next-idx) max-delay)))))))]
[other (raise-type-error 'iir-filter "(listof (list number number))" 0 params)]))

;; lti-filter : rsound (listof (list/c number? number?)) (listof (list/c number? number?)) -> rsound
;; given coefficients for an FIR and an IIR filter, apply
;; the given filter to the sound.
#;(define (lti-filter gain fir-coefficients iir-coefficients)
(unless (real? gain)
(raise-type-error 'lti-filter "real number" 0 gain fir-coefficients
iir-coefficients))
(unless (and (list? fir-coefficients)
(andmap (lambda (x) (and (list? x)
(= (length x) 2)
(nonnegative-integer? (car x))
fir-coefficients))
(raise-type-error 'lti-filter "list of delays and coefficients" 1
snd fir-coefficients iir-coefficients))
(unless (and (list? iir-coefficients)
(andmap (lambda (x) (and (list? x)
(= (length x) 2)
(nonnegative-integer? (first x))
(real? (second x))))
iir-coefficients))
(raise-type-error 'lti-filter "list of delays and coefficients" 2
snd fir-coefficients iir-coefficients))
;; must normalize, include gain...
(define the-fir (fir-filter fir-coefficients))
(define the-iir (iir-filter iir-coefficients))
(signals->rsound (rsound-frames snd)
(the-iir (the-fir (rsound->signal/left snd)))
(the-iir (the-fir (rsound->signal/right snd)))))

(define filter-param-update-interval 32)

;; we want to be able to change the filter dynamically...
(define (dynamic-lti-signal param-signal input-tap-len output-tap-len
input-signal)
(define input-buf-len (max 1 input-tap-len))
(define output-buf-len (max 1 output-tap-len))
;; enough to hold delayed and current, rounded up to next power of 2:
(define saved-input-buf (make-flvector input-buf-len))
(define saved-output-buf (make-flvector output-buf-len))
(define next-idx 0)
;; ugh... we must be called sequentially:
(define last-t -1)
(define saved-fir-terms #f)
(define saved-iir-terms #f)
(define saved-gain #f)
(lambda (t)
(unless (= t (add1 last-t))
(error 'fir-filter "called with t=~s, expecting t=~s. Sorry about that limitation."
t
;; only update the filter parameters every 32 samples
(when (= (modulo t filter-param-update-interval) 0)
(define-values (fir-terms iir-terms gain) (param-signal t))
(unless (and (flvector? fir-terms)
(= (flvector-length fir-terms)
input-tap-len))
(error 'dynamic-lti-signal
"expected vector of length ~s for fir-terms, got ~s"
input-tap-len fir-terms))
(unless (and (flvector? iir-terms)
(= (flvector-length iir-terms)
output-tap-len))
(error 'dynamic-lti-signal
"expected vector of length ~s for iir-terms, got ~s"
output-tap-len iir-terms))
(set! saved-fir-terms fir-terms)
(set! saved-iir-terms iir-terms)
(set! saved-gain gain))

(define fir-sum
(for/fold ([sum 0.0])
([i (in-range input-tap-len)])
(fl+ sum
(fl* (flvector-ref saved-fir-terms i)
(flvector-ref saved-input-buf
(modulo (- t i 1) input-buf-len))))))
(define iir-sum
(for/fold ([sum 0.0])
([i (in-range output-tap-len)])
(fl+ sum
(fl* (flvector-ref saved-iir-terms i)
(flvector-ref saved-output-buf
(modulo (- t i 1) output-buf-len))))))
(define next-val (fl* saved-gain (exact->inexact (input-signal t))))
(flvector-set! saved-input-buf (modulo t input-buf-len) next-val)
(define output-val (fl+ next-val (fl+ fir-sum iir-sum)))
(flvector-set! saved-output-buf (modulo t output-buf-len) output-val)
(set! last-t (add1 last-t))
output-val))

(define max-scale-val 3.0)
(define min-scale-val 0.00)
(define perceptible-interval 0.01)
(define coefficient-table (make-vector (inexact->exact
(floor
(/ (- max-scale-val
min-scale-val)
perceptible-interval)))
#f))

(define (lpf/dynamic scale-signal input-signal)
(dynamic-lti-signal
(lambda (t)
(define scale (scale-signal t))
(when (not (<= min-scale-val scale max-scale-val))
(error 'dynamic-lpf "scale value ~s not between ~s and ~s"
scale
min-scale-val
max-scale-val))
(define table-index (inexact->exact
(round
(/ (- scale min-scale-val)
perceptible-interval))))
(define tap-mults
(match (vector-ref coefficient-table table-index)
[#f (define coefficients (lpf-coefficients scale))
(define new-table-entry
(apply flvector
(map (lambda (x) (* x -1.0))
coefficients)))
(vector-set! coefficient-table table-index new-table-entry)
new-table-entry]
[other other]))
(define gain (+ 1.0 (fl- 0.0 (flvector-sum tap-mults))))
(values (flvector)
tap-mults
gain))
0 4
input-signal))

(define (flvector-sum vec)
(for/fold ([sum 0.0]) ([f (in-flvector vec)]) (fl+ sum f)))

;; it looks like 1/100 is close enough not to notice. This
;; is totally a guess on my part

```