1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
|
module Basic where
import TypesettingTricks
--import Int( Num(fromInt) )
import Physical
--import GHC( (->) )
infixr 7 |>
class Signal s where
mapSignal:: (Physical a, Physical b) => (s a b) -> a -> b
mapSigList:: (Physical a, Physical b) => (s a b) -> [a] -> [b]
toSig:: (Physical a, Physical b) => (s a b) -> SignalRep a b
mapSignal = mapSignal . toSig
mapSigList = map . mapSignal
toSig = FunctionRep . mapSignal
instance Signal (->) where
mapSignal f = f
toSig = FunctionRep
data {- (Physical a, Physical b) => -} SignalRep a b =
FunctionRep (a -> b) |
PieceContRep (PieceCont a b)
instance Eq (SignalRep a b) where
(==) a b = error "No equality for SignalRep"
instance Show (SignalRep a b) where
show sr = error "No show for SignalRep"
instance Signal SignalRep where
mapSignal (FunctionRep f) = mapSignal f
mapSignal (PieceContRep f) = mapSignal f
mapSigList (FunctionRep f) = mapSigList f
mapSigList (PieceContRep f) = mapSigList f
toSig = id
instance (Physical a, Physical b) => Eq (a -> b) where
a == b = error "Attempt to apply equality to functions"
binop:: (Physical a, Physical b) => (Float -> Float -> Float) ->
(a -> b) -> (a -> b) -> a -> b
binop op f g t = toPhysical ((fromPhysical (f t)) `op` (fromPhysical (g t)))
unop:: (Physical a, Physical b ) => (Float -> Float) ->
(a -> b) -> a -> b
unop op f t = toPhysical (op (fromPhysical (f t)))
instance (Physical a, Physical b) => Num (SignalRep a b) where
f + g = FunctionRep (binop (+) (mapSignal f) (mapSignal g))
f * g = FunctionRep (binop (*) (mapSignal f) (mapSignal g))
negate f = FunctionRep (unop negate (mapSignal f))
abs f = FunctionRep (unop abs (mapSignal f))
signum f = FunctionRep (unop abs (mapSignal f))
fromInteger i = FunctionRep (\t -> toPhysical (fromInteger i))
--fromInt i = FunctionRep (\t -> toPhysical (fromInt i))
instance (Physical a, Physical b) =>
Fractional (SignalRep a b) where
f / g = FunctionRep (binop (/) (mapSignal f) (mapSignal g))
fromRational r = FunctionRep (\t -> (toPhysical (fromRational r)))
instance (Physical a, Physical b) =>
Floating (SignalRep a b) where
pi = FunctionRep (\t -> (toPhysical pi))
exp f = FunctionRep (unop exp (mapSignal f))
log f = FunctionRep (unop log (mapSignal f))
sin f = FunctionRep (unop sin (mapSignal f))
cos f = FunctionRep (unop cos (mapSignal f))
asin f = FunctionRep (unop asin (mapSignal f))
acos f = FunctionRep (unop acos (mapSignal f))
atan f = FunctionRep (unop atan (mapSignal f))
sinh f = FunctionRep (unop sinh (mapSignal f))
cosh f = FunctionRep (unop cosh (mapSignal f))
asinh f = FunctionRep (unop asinh (mapSignal f))
acosh f = FunctionRep (unop acosh (mapSignal f))
atanh f = FunctionRep (unop atanh (mapSignal f))
data Event =
TimeEvent Float |
FunctionEvent (Float -> Bool) |
BurstEvent Int Event
instance Show Event where
show (TimeEvent f) = "TimeEvent " ++ show f
show (FunctionEvent _) = "FunctionEvent"
show (BurstEvent i e) = "BurstEvent " ++ show i ++ " " ++ show e
instance Eq Event where
(TimeEvent x) == (TimeEvent y) = x == y
(BurstEvent i e) == (BurstEvent i' e') = (i' == i) && (e' == e)
eventOccurs:: Event -> Float -> Float
eventOccurs (TimeEvent t) x = if x < t then x else t
eventOccurs (FunctionEvent f) x = stepEval f x
eventOccurs (BurstEvent i e) x =
if i == 1 then
eventOccurs e x
else
eventOccurs (BurstEvent (i-1) e) ((eventOccurs e x) + eventEps x)
stepEval:: (Float -> Bool) -> Float -> Float
stepEval f x = if f x then x else stepEval f (x + eventEps x)
data ZeroIndicator = LocalZero | GlobalZero deriving (Eq, Show)
data {- (Physical a, Physical b) => -} FunctionWindow a b =
Window ZeroIndicator Event (SignalRep a b)
deriving (Eq, Show)
data PieceCont a b = Windows [FunctionWindow a b]
deriving (Eq, Show)
instance Signal PieceCont where
mapSignal (Windows []) t = toPhysical 0.0
mapSignal (Windows wl) t = (mapSignal s) (toPhysical t')
where (t', (Window z e s), wl') = getWindow 0.0 (fromPhysical t) wl
toSig = PieceContRep
getWindow:: (Physical a, Physical b) =>
Float -> Float -> [ FunctionWindow a b ] ->
(Float, FunctionWindow a b, [ FunctionWindow a b ])
getWindow st t [] = (t, Window LocalZero e f, [])
where e = TimeEvent (realmul 2 t)
f = FunctionRep (\t -> toPhysical 0.0)
getWindow st t (w:wl) = if t' <= wt then (t',w,w:wl)
else getWindow (st+wt) t wl
where wt = eventOccurs e t'
(Window z e s) = w
t' = if z == LocalZero then t-st else t
(|>) :: (Physical a, Physical b) => FunctionWindow a b ->
PieceCont a b -> PieceCont a b
w |> (Windows wl) = Windows (w:wl)
nullWindow = Windows []
cycleWindows:: (Physical a, Physical b) =>
PieceCont a b -> PieceCont a b
cycleWindows (Windows wl) = Windows (cycle wl)
constant:: (Physical a, Physical b) => b -> SignalRep a b
constant x = FunctionRep (\t -> x)
linear:: (Physical a, Physical b) => Float -> b -> SignalRep a b
linear m b = FunctionRep (\x -> toPhysical (realmul m (fromPhysical x) + (fromPhysical b)))
sine:: (Physical a, Physical b) =>
b -> Frequency -> Float -> SignalRep a b
sine mag omeg phase = FunctionRep (\x -> toPhysical (realmul (fromPhysical mag) (sin (realmul (realmul (realmul 2 pi) (fromPhysical omeg)) (fromPhysical x) + phase))))
waveform:: (Physical a, Physical b) => a -> [b] -> SignalRep a b
waveform samp ampls =
let stepSlope y y' = realdiv ((fromPhysical y') - (fromPhysical y)) (fromPhysical samp)
makeWin (v,v') = Window LocalZero (TimeEvent (fromPhysical samp))
(linear (stepSlope v v') v)
points = cycle ampls
in PieceContRep (Windows (map makeWin (zip points (tail points))))
random:: (Physical a, Physical b) =>
Integer -> a -> SignalRep a b
random i s = waveform s (map toPhysical (rand i))
ramp:: (Physical a, Physical b) => a -> b -> SignalRep a b
ramp per v =
let sig = linear (realdiv (fromPhysical v) (fromPhysical per)) (toPhysical 0.0)
in PieceContRep (Windows (cycle ([Window LocalZero (TimeEvent (fromPhysical per)) sig ])))
triangle:: (Physical a, Physical b) => a -> b -> SignalRep a b
triangle per v =
let sl = realmul 2.0 (realdiv (fromPhysical v) (fromPhysical per))
qper = realdiv (fromPhysical v) 4.0
wins = (Window LocalZero (TimeEvent qper) (linear sl (toPhysical 0.0))) |>
(Window LocalZero (TimeEvent (realmul 2.0 qper)) (linear (- sl) v)) |>
(Window LocalZero (TimeEvent qper) (linear sl (toPhysical (- (fromPhysical v))))) |>
nullWindow
in PieceContRep (cycleWindows wins)
step:: (Physical a, Physical b) => a -> b -> SignalRep a b
step tr lvl = FunctionRep (\t -> if (fromPhysical t) < (fromPhysical tr) then (toPhysical 0.0) else lvl)
square:: (Physical a, Physical b) => a -> b -> SignalRep a b
square per lvl =
let trans = realdiv (fromPhysical per) 2.0
nlvl = asTypeOf (toPhysical (- (fromPhysical lvl))) lvl
f t = if (fromPhysical t) < trans then lvl else nlvl
wins = Windows [Window LocalZero (TimeEvent (fromPhysical per)) (FunctionRep f)]
in PieceContRep (cycleWindows wins)
pulse:: (Physical a, Physical b) => a -> a -> b -> SignalRep a b
pulse st wid lvl =
let tr = (fromPhysical st) + (fromPhysical wid)
f t = if (fromPhysical t) < (fromPhysical st) then (toPhysical 0.0)
else if (fromPhysical t) < tr then lvl else (toPhysical 0.0)
in FunctionRep f
trap:: (Physical a, Physical b) => a -> a -> a -> a -> b ->
SignalRep a b
trap st r wid f lvl =
let stepSlope y y' t = realdiv (y' - y) (fromPhysical t)
bigwin = realmul 10000000 ((fromPhysical st) + (fromPhysical wid))
wins = Window LocalZero (TimeEvent (fromPhysical st)) (constant (toPhysical 0.0)) |>
Window LocalZero (TimeEvent (fromPhysical r)) (linear (stepSlope 0.0 (fromPhysical lvl) r) (toPhysical 0.0)) |>
Window LocalZero (TimeEvent (fromPhysical wid)) (constant lvl) |>
Window LocalZero (TimeEvent (fromPhysical f)) (linear (stepSlope (fromPhysical lvl) 0.0 f) lvl) |>
Window LocalZero (TimeEvent bigwin) (constant (toPhysical 0.0)) |>
nullWindow
in PieceContRep wins
expc:: (Physical a, Physical b) => Float -> SignalRep a b
expc damp = FunctionRep (\t -> toPhysical (exp (- (realmul (fromPhysical t) damp))))
data {- (Physical indep, Physical dep) => -} BasicSignal indep dep =
Overshoot {start_delay::indep,
pulse_width::indep,
ringing::dep,
oscillation::Frequency,
damp_fac::Float}
| Pulse_dc {start_delay::indep,
pulse_width::indep,
rise_time::indep,
fall_time::indep,
period::indep,
dc_offset::dep,
amplitude::dep,
over::BasicSignal indep dep,
under::BasicSignal indep dep}
| Pulse_ac {start_delay::indep,
pulse_width::indep,
period::indep,
dc_offset::dep,
amplitude::dep,
frequency::Frequency,
phase::Float}
deriving (Eq, Show)
data {- (Eq a, Eq b) => -} Foo a b = Foo { x :: a, y :: b}
foo :: (Eq a, Eq b) => Foo a b
foo = Foo{}
{-
overshoot:: (Physical a, Physical b) => BasicSignal a b
overshoot = Overshoot{}
pulse_dc:: (Physical a, Physical b) => BasicSignal a b
pulse_dc = Pulse_dc {over = Overshoot{start_delay=toPhysical 0.0,
ringing=(toPhysical 0.0),
oscillation=toPhysical 1.0,
damp_fac=1.0},
under = Overshoot{start_delay=toPhysical 0.0,
ringing=(toPhysical 0.0),
oscillation=toPhysical 1.0,
damp_fac=1.0},
start_delay = toPhysical 0.0,
dc_offset = toPhysical 0.0}
pulse_ac:: (Physical a, Physical b) => BasicSignal a b
pulse_ac = Pulse_ac {dc_offset = toPhysical 0.0,
amplitude = toPhysical 0.0}
-}
makeWin:: (Physical a, Physical b) => a -> a ->
SignalRep a b -> SignalRep a b
makeWin st wid sig =
let wins = Window LocalZero (TimeEvent (fromPhysical st)) (constant (toPhysical 0.0)) |>
Window LocalZero (TimeEvent (fromPhysical wid)) sig |>
nullWindow
in PieceContRep wins
instance Signal BasicSignal where
toSig (Overshoot start_delay pulse_width ringing oscillation damp_fac) =
let ring = sine ringing oscillation 0.0
cond = asTypeOf (expc damp_fac) ring
sig = temp ring cond
temp:: (Physical a, Physical b) => SignalRep a b ->
SignalRep a b -> SignalRep a b
temp f g = FunctionRep (binop (*) (mapSignal f) (mapSignal g))
-- temp f g = f * g
-- temp f g = asTypeOf (f * g) ring
wins = Window LocalZero (TimeEvent (fromPhysical start_delay)) (constant (toPhysical 0.0)) |>
Window LocalZero (TimeEvent (fromPhysical pulse_width)) sig |>
nullWindow
in PieceContRep wins
toSig Pulse_dc{ start_delay = start_delay
, rise_time = rise_time
, pulse_width = pulse_width
, fall_time = fall_time
, dc_offset = dc_offset
, period = period
, amplitude = amplitude
, over = over
, under = under
} =
let pul = trap start_delay rise_time pulse_width fall_time amplitude
so = toPhysical ((fromPhysical start_delay) + (fromPhysical rise_time))
su = toPhysical ((fromPhysical so) + (fromPhysical pulse_width) + (fromPhysical fall_time))
oversh = toSig over{start_delay=so}
undersh = toSig under{start_delay=su}
off = constant dc_offset
temp:: (Physical a, Physical b) => SignalRep a b ->
SignalRep a b -> SignalRep a b
temp f g = FunctionRep (binop (+) (mapSignal f) (mapSignal g))
sig = temp (temp (temp pul oversh) undersh) off
wins = (Window LocalZero (TimeEvent (fromPhysical period)) sig) |>
nullWindow
in PieceContRep (cycleWindows wins)
sumSig:: (Physical a, Physical b, Signal s, Signal s') =>
(s a b) -> (s' a b) -> SignalRep a b
sumSig f f' =
let s1 t = fromPhysical (mapSignal f t)
s2 t = fromPhysical (mapSignal f' t)
in FunctionRep (\t -> toPhysical ((s1 t) + (s2 t)))
mulSig:: (Physical a, Physical b, Signal s, Signal s') =>
(s a b) -> (s' a b) -> SignalRep a b
mulSig f f' =
let f1 t = fromPhysical (mapSignal f t)
f2 t = fromPhysical (mapSignal f' t)
in FunctionRep (\t -> toPhysical ((f1 t) * (f2 t)))
eventEps:: Float -> Float
eventEps x = let eps = realdiv x 1000 in if 0.01 < eps then 0.01 else eps
|
