
ForSyDe.Shallow.CTLib  Portability  portable  Stability  experimental  Maintainer  forsydedev@ict.kth.se 





Description 
This is the ForSyDe library for continuous time MoC (CTMoC).
Revision: $Revision: 1.7 $
Id: $Id: CTLib.hs,v 1.7 20070711 08:38:34 axel Exp $
It is still experimental.
Right now there are only constructors combCT, combCT2, delayCT,
shiftCT, mealyCT, mooreCT, scaleCT, addCT, multCT and absCT.
The main idea is to represent continuous time signals as functions
Real > a with a being a numerical type. This allows us to represent a
continuous time signal without loss of information because no sampling or
ADC is required. The sampling occurs only when a signal is evaluated,
for instance when it is plotted.
Thus, a signal is represented as a sequence of functions and intervals. For
instance a signal
s = <(sin,[0,100])> represents a sinus signal in the interval between 0 and 100. The signal
s2 = <(f1(x)=2x, [0,2]), (f2(x)=3+x,[2,4])> defines a signal that is defined by function f1 in the interval [0,2]
and by function f2 in the interval [2,4].
A process transforms the incoming functions into outgoing functions.
The approach is described in more detail in the ANDRES deliverable D1.1a.
Here we only briefly comment the main functions and constructors.


Synopsis 

data Num a => SubsigCT a = SubsigCT (Rational > a, (Rational, Rational))   timeStep :: Rational   combCT :: Num a => Rational > (Rational > a) > (Rational > a) > Signal (SubsigCT a) > Signal (SubsigCT a)   combCT2 :: Num a => Rational > (Rational > a) > (Rational > a) > (Rational > a) > Signal (SubsigCT a) > Signal (SubsigCT a) > Signal (SubsigCT a)   mooreCT :: (Num b, Num c) => a > Rational > a > (Rational > b) > a > a > (Rational > c) > a > Signal (SubsigCT b) > Signal (SubsigCT c)   mealyCT :: (Num b, Num c) => a > Rational > a > (Rational > b) > a > a > (Rational > b) > (Rational > c) > a > Signal (SubsigCT b) > Signal (SubsigCT c)   delayCT :: Num a => Rational > Signal (SubsigCT a) > Signal (SubsigCT a)   shiftCT :: Num a => Rational > Signal (SubsigCT a) > Signal (SubsigCT a)   initCT :: Num a => Signal (SubsigCT a) > Signal (SubsigCT a) > Signal (SubsigCT a)   scaleCT :: Num a => a > Signal (SubsigCT a) > Signal (SubsigCT a)   addCT :: Num a => Signal (SubsigCT a) > Signal (SubsigCT a) > Signal (SubsigCT a)   multCT :: Num a => Signal (SubsigCT a) > Signal (SubsigCT a) > Signal (SubsigCT a)   absCT :: (Num a, Ord a) => Signal (SubsigCT a) > Signal (SubsigCT a)   takeCT :: Num a => Rational > Signal (SubsigCT a) > Signal (SubsigCT a)   dropCT :: Num a => Rational > Signal (SubsigCT a) > Signal (SubsigCT a)   duration :: Num a => Signal (SubsigCT a) > Rational   startTime :: Num a => Signal (SubsigCT a) > Rational   sineWave :: Floating a => Rational > (Rational, Rational) > Signal (SubsigCT a)   constCT :: Num a => Rational > a > Signal (SubsigCT a)   zeroCT :: Num a => Rational > Signal (SubsigCT a)     a2dConverter :: Num a => Rational > Signal (SubsigCT a) > Signal a   d2aConverter :: Fractional a => DACMode > Rational > Signal a > Signal (SubsigCT a)   applyF1 :: (Num a, Num b) => ((Rational > a) > (Rational > b)) > Signal (SubsigCT a) > Signal (SubsigCT b)   applyF2 :: (Num a, Num b, Num c) => ((Rational > a) > (Rational > b) > (Rational > c)) > Signal (SubsigCT a) > Signal (SubsigCT b) > Signal (SubsigCT c)   applyG1 :: Num b => (a > (Rational > b) > a) > a > Signal (SubsigCT b) > a   cutEq :: (Num a, Num b) => Signal (SubsigCT a) > Signal (SubsigCT b) > (Signal (SubsigCT a), Signal (SubsigCT b))   plot :: Num a => Signal (SubsigCT a) > IO String   plotCT :: Num a => Rational > [Signal (SubsigCT a)] > IO String   plotCT' :: Num a => Rational > [(Signal (SubsigCT a), String)] > IO String   showParts :: Num a => Signal (SubsigCT a) > [(Double, Double)]   vcdGen :: Num a => Rational > [(Signal (SubsigCT a), String)] > IO String 



The signal data type



The type of a subsignal of a continuous signal. It consisits of the
function and the interval on which the function is defined.
The continuous time signal is then defined as a sequence of SubsigCT
elements: Signal SubsigCT
 Constructors   Instances  



This constant gives the default time step for sampling and plotting.
Its value is 10ns.


Primary process constructors



:: Num a   => Rational  The partitioning of the input signal. In other words
this gives the time period which is consumed by the
process during each evaluation cycle.
 > (Rational > a) > (Rational > a)  The function that
defines the process
behaviour
 > Signal (SubsigCT a)  The input signal
 > Signal (SubsigCT a)  The output signal of the process.
 combCT is a process constructor with one input and one output signal.
It instantiates a combinatorial, stateless process.







:: (Num b, Num c)   => a > Rational  The gamma function which defines
the partitioning of the input
signal.
 > a > (Rational > b) > a  The next state function g
 > a > (Rational > c)  The output encoding function f
 > a  The initial state
 > Signal (SubsigCT b)  The input signal
 > Signal (SubsigCT c)  The output signal
 The statefull constructor mooreCT resembles a Moore machine.




:: (Num b, Num c)   => a > Rational  The gamma function which defines
the partitioning of the input
signal.
 > a > (Rational > b) > a  The next state function g
 > a > (Rational > b) > (Rational > c)  The output encoding function f
 > a  The initial state
 > Signal (SubsigCT b)  The input signal
 > Signal (SubsigCT c)  The output signal
 The statefull constructor mealyCT resembles a Mealy machine.




:: Num a   => Rational  The delay
 > Signal (SubsigCT a)  The input signal
 > Signal (SubsigCT a)  The output signal
 delayCT is a delay process which simply delays the
output but does not buffer it. The value at each time t is the same as
for the input signal, after the initial delay.







:: Num a   => Signal (SubsigCT a)  The initial signal output first.
 > Signal (SubsigCT a)  Then this signal is output, but delayed.
 > Signal (SubsigCT a)  The concatation of the two inputs.
 initCT takes an initial signal, outputs it and then copies its second
input signal, which is delayed by the duration of the initial signal.
The delay is realized by delayCT



Derived process constructors


These constructors instantiate very useful processes.
They could be defined in terms of the basic constructors
but are typically defined in a more direct way for
the sake of efficieny.














Convenient functions and processes


Several helper functions are available to obtain parts
of a signal, the duration, the start time of a signal, and
to generate a sine wave and constant signals.














:: Num a   => Rational  The time duration of the generated signal.
 > a  The constant value of the signal.
 > Signal (SubsigCT a)  The resulting signal.
 constCT generates a constant signal for a given time duration.




:: Num a   => Rational  The time duration
 > Signal (SubsigCT a)  The generated signal.
 zeroCT generates a constant 0 signal for the given time duration.



AD and DA converters



For the digitalanalog conversion we have two different possibilities
which is determined by this data type DACMode.
 Constructors  DAlinear  linear interpolation
 DAhold  the last digital value is frozen

 Instances  



:: Num a   => Rational  Sampling Period
 > Signal (SubsigCT a)  Input signal (continuous time)
 > Signal a  Output signal (untimed)
 The process a2dConverter converts a continuous time signal to
an untimed or synchronous signal. The first parameter gives the
sampling period of the converter.
Note, that the process a2dConverter is an ideal component,
i.e. there are no losses due to a limited resolution due to a fixed
number of bits.




:: Fractional a   => DACMode  Mode of conversion
 > Rational  Duration of input signal
 > Signal a  Input signal (untimed MoC)
 > Signal (SubsigCT a)  Output signal (continuous time MoC)
 d2aConverter converts an untimes or synchronous signal into a
continuous time signal.
The process d2aConverter converts a signal of the digital domain
into a continuous time signal. There are two modes, DAlinear,
which makes a smooth transition between adjacent digital values and
DAhold, where the analog value directly follows the digital
value. This means that in DAholdmode a staircase function
remains a staircase function, while in DAlinear the staircase
function would resemble at least partially a saw toothcurve.
The resolution of the converter is given by the parameter
timeStep.
Note, that the process d2aConverter is an ideal component, i.e. there
are no losses due to a limited resolution due to a fixed number of bits.



Some helper functions



applyF1 applies a function on a subsignal, which means the function of
the subsignal is transformed to another function:



applyF2 works just like applyF1 but operates on two incoming signals.



applyG1 is used to apply a nextstate function. A very interesting
question is, what should be an argument to the nextstate function:
the incoming function, defining the value of the input signal?
or the incoming function and the incoming interval?
or the value of the incoming signal at a particular point, e.g. at the
left most point of the interval?
To give the nextstate function the interval itself as argument, would mean
that the process becomes time variant process, i.e. its behaviour is
dependent on the absolute time values. This is not a good thing to have!
Another possibility may be to give a subsignal that is relative to the
current evaluation, i.e. the left most point is always 0. Would that make
sense?



cutEq partitions the two signals such that the partitioning are identical
in both result signals, but only up to the duration of the shorter of the
two signals:


Sampling, printing and plotting


Several functions are available to display a signal in textual or
graphics form. All displaying of signals is based on sampling and
evaluation the signal at regular sampling points.
The function sample evaluates the signal and returns a list of
(time,value) pairs, which can be displayed as text or used in any other way.
showParts does not evaluate the signal; it only shows how it is
partitioned. Hence, it returns a sequence of intervals.
plot, plotCT and plotCT' can plot a signal or a list of signals
in a graph. They use gnuplot for doing the actual work.
They are in the IO monad because they write to the file system.
plot is defined in terms of plotCT but it uses the default sampling
period timeStep and it can plot only one signal in a plot.
plotCT can plot a list of signals in the same plot.
plotCT is defined in terms of plotCT' but uses
default label names for the plot.
vcdGen writes the values of signals in Value Change Dump (VCD) format to
a file. There are public domain wave viewers which understand this format
and can display the signals.



:: Num a   => Signal (SubsigCT a)  The signal to be plotted.
 > IO String  A reporting message.
 plot plots one signal in a graph with the default sampling period
of 1/200 of the duration of the signal.




:: Num a   => Rational  The sampling period
 > [Signal (SubsigCT a)]  The list of signals to be ploted
in the same graph
 > IO String  A messeage reporting what has been done.
 plotCT plots a list of signals in the same graph. The sampling period
has to be given as argument. In the graph default label names are used
to identify the signals.




:: Num a   => Rational  Sampling period
 > [(Signal (SubsigCT a), String)]  A list of (signal,label) pairs. The signals are plotted and
denoted by the corresponding labels in the plot.
 > IO String  A simple message to report completion
 plotCT' is the work horse for plotting and the functions plot and
plotCT use it with specialising arguments.
plotCT' plots all the signals in the list in one graph. If a label is
given for a signal, this label appears in the graph. If the label string is
"", a default label like "sig1" is used.
In addition to displaying the graph on the screen, the following files
are created in directory ./fig:
 ctmocgraph.eps
 an eps file of the complete graph
 ctmocgraph.pdf
 A pdf file of the complete graph
 ctmocgraphlatex.eps
 included by ctmocgraphlatex.tex
 ctmocgraphlatex.tex
 This is the tex file that should be included
by your latex document. It in turn includes
the file ctmocgraphlatex.eps.
These two files have to be used together;
the .eps file contains only the graphics,
while the .tex file contains the labels and
text.




:: Num a   => Signal (SubsigCT a)  The partitioned signal
 > [(Double, Double)]  The sequence of intervals
 showParts allows to see how a signal is partitioned into subsignals.
It returns the sequence of intervals.




:: Num a   => Rational  Sampling period; defines for what
time stamps the values are written.
 > [(Signal (SubsigCT a), String)]  A list of (signal,label) pairs. The signal values written and
denoted by the corresponding labels.
 > IO String  A simple message to report completion
 vcdGen dumps the values of a list of signal in VCD (Value Change Dump) format
(IEEE Std 13642001), which is part of the Verilog standard
(http://en.wikipedia.org/wiki/Value_change_dump).
There are public domain tools to view VCD files. For instance,
GTKWave (http://home.nc.rr.com/gtkwave/) is a popular viewer available for
Windows and Linux.
The values are written to the file .figctmoc.vcd. If the file exists, it
is overwritten. If the directory does not exist, it is created.



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