filter.rkt
```#lang racket/base

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

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

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

;; poly : a transfer function
;; coefficients : a list of coefficients to use in a transfer function
;; roots / zeros : places where the transfer function is zero
;; poles : places where the transfer function is infinite

;; FIR filters

;; fir-filter : (listof (list/c delay amplitude)) -> 1/1/network
;; 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))
;; enough to hold delayed and current, rounded up to next power of 2:
[define max-delay (up-to-power-of-two (+ 1 (apply max delays)))]
;; set up buffer to delay the signal
[define delay-buf (make-vector max-delay 0.0)]
[define next-idx 0]
(cond [(<= max-delay next) 0]
[else next]))
(lambda (this-val)
(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))))))
result)]
[other (raise-type-error 'fir-filter "(listof (list number number))" 0 params)]))

;; IIR filters

;; iir-filter : (listof (list/c delay amplitude)) -> 1/1/networkt
;; 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))
(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])
(lambda (this-val)
;; could be a lot faster:
(let* ([new-val (for/fold ([sum this-val])
([d (in-list delays)]
[a (in-list amplitudes)])
;; FIXME: get rid of this modulo:
(+ sum (* a (vector-ref delay-buf
(modulo (- next-idx d) max-delay)))))])
(begin0
new-val
(vector-set! delay-buf next-idx new-val)
(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 (rs-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...

;; (nat nat -> 2/1/network)
;; accepts a tap-length, produces
;; a network with two inputs: the parameter signal and the input
;; signal. The parameter signal must produce a vector of three
;; things: the input tap vector, the output tap vector, and the gain.
;; sadly, there's going to be some inevitable checking of vector
;; bounds here.
;; NB: requires input & output taps to be of the same length. This
;; is pretty normal.

;; this whole thing could be *way* more optimized.
(define (dynamic-lti-signal tap-len)
(unless (< 0 tap-len)
(raise-argument-error 'dynamic-lti-signal "number greater than zero" 0 tap-len))
(define saved-input-buf (make-flvector tap-len))
(define saved-output-buf (make-flvector tap-len))
(define (wraparound idx)
(cond [(<= tap-len idx) 0]
[else idx]))
(define next-idx 0)
(lambda (fir-terms iir-terms gain this-val)
;; don't want to do this check every time...
#;(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 vector of length ~s"
input-tap-len (flvector-length fir-terms)))
;; don't want to do this check every time....
#;(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 vector of length ~s"
output-tap-len (flvector-length iir-terms)))

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

;; A network that maps scale values into fir/iir vectors
(define lpf-sig
(lambda (scale)
(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 results
(match (vector-ref coefficient-table table-index)
[#f (define result-vec (lpf-tap-vectors scale))
(vector-set! coefficient-table table-index result-vec)
result-vec]
[other other]))
(values (vector-ref results 0)
(vector-ref results 1)
(vector-ref results 2))))

;; dynamic low-pass filter: the first argument is a signal that controls
;; the filter cutoff, the second is the signal being filtered.
(define lpf/dynamic

(network (lpf-control audio-sig)
[(fir-terms iir-terms gain) (lpf-sig lpf-control)]
[out ((dynamic-lti-signal 4) fir-terms iir-terms gain audio-sig)]))

(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

```