• Math Channels (and Filters)
  • Math Channels
  • 'Default' Channels
    • Defining Default Channels
    • Applying Default Channels
  • Working with Functions
    • “As Default Folder“ Button
    • “Sub-Folder“ Option
    • “Make Available” Button
    • Report
  • Defining a Function
  • Formula & Computation Tab
    • Selecting a Channel
    • Selecting a Function
    • Compute Function
    • Include Relevant Timestamps
    • Computing Example
    • Format Tab
      • Numerical Format
      • Range of Values
  • Filter Functions
    • Bandpass, Lowpass, Highpass, and Stopband Functions
    • 'Filter' Function
    • BandpassFIR, LowpassFIR and HighpassFIR Functions
  • Mathematical Expressions
    • Constants
    • Arithmetic Operators
    • Comparisons
    • Logical operators
    • General functions
    • Math Functions
    • Scripting
    • Trace functions
    • IIR Filter Functions
      • bandpass
      • bandpassFIR
      • lowpass
      • lowpassFIR
      • highpass
      • highpassFIR
      • stopband
    • Lookup Function
  • Examples
    • Example with sigma and dt - Integration over time
    • Example with delta and dt - Derivation of a channel
    • Example with HOLD - Filtering measurement errors
    • Examples with sigma, lapsigma, dt, and delta - Calculating “highspeed”-duration for each lap
    • Example with DetectEvent - Brake Pressure
      • Detect Event Supports Multiple Overloads
    • Variables in Math Functions
    • Math Functions Support 'NoValue'
    • ValueAtDist
    • ValueAtTime
  • Conditions
    • Alternative to Conditions

In WinDarab it is possible to define filters or new channels with the help of math functions. WinDarab provides functions and filters that will help you to solve a great number of math and analytical problems.

• In a math function it is possible to use 'comment fields' — in addition to recorded channels — to include conditions that are specific to a particular file. Comment fields are included in the channel selection list and marked with “C”.
• Another approach is to use the 'Setupsheet' functionality to define outing dependant constants

A math channel calculates values based on other channels in a file. Which channels will be used is determined by the user entered expression.

If a math channel has been defined, it will be listed in the channel window. Much like internal channels, math channels can be used (in nearly all instances) as if they were logged data.

• If new a math channel is added, but another math channel with the same name already exists, the existing math channel is replaced by the new one. In case of a manual creation of the new math channel (Extras/Functions/New) a message box appears, informing the user about the duplicated math channel name.

WinDarab supports special functions that can be applied to any channel

Default channels are defined just like any other Math Function, just substitute {default} in your expression for a channel name:

Oscilloscope, define default function

Math functions can be saved in a folder in the File Explorer. In addition to the selected folder and its contents, the lower area of this window shows a summary of the most important information pertaining to a math function.

If you start the program WinDarab makes all functions saved to a specified folder available. To specify this folder select it from the directory and click on the “As Default Folder” button.

Activating this button makes all formulae contained in the default folder as well as those contained in the sub-folders available.

If you would like to make a math function available you will have to do this explicitly. This button is not active when the math function has already been made available.

This button enables you to create a report that contains all the settings for a math function. If you press this button, a dialog box for choosing a report template appears.

• WinDarab provides one template for each language it supports.
• If two functions with the same name exist WinDarab will only use the first one.

To define a new math function or to modify an existing one, follow these steps:

1. Use Tools → Mathematics → Functions to open the “Functions” dialog box.
2. Select the math function you want to edit and click on “Modify”
   • Or “New Function” if you want to create a new function.
3. The dialog box “Edit Function” appears. It contains three tabs in which you can make all entries pertaining to the math formula.
4. Once you have finished making your entries or modifications, click on “Save“ or “Save as”.

• When a math function is modified, WinDarab immediately function if it is displayed or in use in a window.
• You can also create a new function by right-clicking into the Channels window and select Math function → New. If you right-click on a function in the Channels window, you can chose to edit this function.
• Math formulas and channels with identical name are not allowed.
  If a user tries to save a math formula but at least one opened file contains a data channel with the same name, WinDarab asks the user to select a different name for the math formula.
• WinDarab shows a message, if a file contains data channels with the same name as already defined math formulas. The data channels are not available until the user changes the name of the math formula and reopens the file.

• Description
  • Enter a brief description that will be displayed in channel selection lists.
• Expression
  • Enter the math expression you want to calculate in this section.
• Data file to validate the math function
  • Select a file containing a list of channel names. This enables you to access the choice of available channels in the Insert channel area.
  • WinDarab will use this to test the syntax of the expression.
• Insert Math Function
  • This is a list of all available operators, filters, and functions

• Channel names should always be enclosed in braces. Alternatively, you can insert a channel in an expression by using the Insert Channel area
  • {default} is a wild-card that can be used. See Default Channels
• A formula is not limited to a single line. If a formula is too long or complex for one line, you can split it by using multiple lines.

A user can select a math function from the Insert Math Function section

• Information about each function can be found via intellisense or in Mathematical Expressions

This area is used to determine the sampling rate for calculating a math function.

Depending on the configuration for recording data, data is sampled at varying intervals. As a result, the number of samples per unit of time may vary.

Depending on the meaning of the variables in a math calculation, it may be necessary to vary the sampling rate. This setting determines the quality and speed of processing.

for every <x> sample:

This setting calculates the function independent of the samples that were recorded and which belong to channels included in the formula. Calculations are instead carried out for each <x>th sample of

• of all referenced channels: calculates every <x> sample point of all referenced channels
• of the fastest channel: calculates every <x> sample point of the fastest channel
• of the selected channel: calculates every <x> sample point of the selected channel
• of the slowest channel: calculates every <x> sample point of the slowest channel

Note: If WinDarab searches for the fastest channel it ignores standard channels such as xtime or xdist because they are included in every block and thus would always be the fastest channels. If you would indeed like to make a calculation for these samples, you must select the 'of the selected channel'.

Compute function with a period of <x> ms:

WinDarab calculates the function at a specified minimum time interval.

• WinDarab is able to perform a calculation only if sample positions are valid. As a result, WinDarab always searches for the sample separated from the previous sample by at least the specified value. It is therefore possible that the intervals vary – but they are always at least as big as the specified value.

Some math channels work better if relevant timestamps are included to the math function. E.g. functions like “LapSigma” reset their result if a laptrigger is passed. However, values can be incorrect at the laptrigger boundary if this timestamp (exactly at laptrigger) isn’t included in the selected timeline. This new option ensures that the timestamps of the laptriggers are included in the math channels timeline and the math channel has a value at these positions.

Note: The used math functions in a math formula control if relevant timestamps exist and which they are (an example is LapSigma which adds the timestamps of the laptriggers to the math channel).

Assume there are two channels (v_wheel_rb and v_wheel_rf) with different sampling rates (100ms and 130ms) and you want to create a math-channel to calculate the average of these channels.

You can create a math-channel with the expression “({v_wheel_rb} + {v_wheel_rf})/2”.

The Image below shows the two channels in the upper area and the math-channel with the computing-configurations “every sample from the fastest channel”, “every sample from the slowest channel”, “every 150ms” (from top to bottom in the bottom area).

As you can see, the blue math-channel has the same sample-points as the blue channel (fastest).

The red math-channel has the same sample-points as the red channel (slowest). The green math-channel has its own sample-points that are not in any way linked to the included channels sample-points.

The sample-points that are not on the channels-points are interpolated by the surrounding sample-points of the channel. As an example, the blue math-channel uses the exact values from the blue channel and interpolates (where the sample-points are not at the same point by a coincident) the red channel.

All the settings pertaining to the display of a math channel are made in the “Format” tab.

Make the settings for the numeric display of the channel values. You are able to choose either a “decimal”, “hexadecimal” or “binary” format. If you choose the decimal format, you are able to specify the width of the entry field as well as the number of decimal places.

Use this area to set the range of values (from - to) and the unit of measure to be used in the default channel display.

For this section, math foundations of filters are required. WinDarab provides a lot of math filters, such as:

• bandpass
• bandpassFIR
• filter
• lowpass
• lowpassFIR
• highpass
• highpassFIR
• stopband

They can all be found in the function window in the category “filter functions”

These Functions all have an editor, where you can insert the parameters for the function.

In the filtertype-list are up to six different filtertypes, that you can chose for your filter. Each of the filters have individual strengths and weaknesses regarding roll-off or phase response

The other lists supply the parameters for the order, the frequency and the sample frequency.

• Keep in mind, that the sample frequency has to be at least twice the filter frequency.

When all parameters are configured, you can go to the expression editor by clicking on Next.

In this dialog, you have to enter the expression you want to filter. The expression can be as complex as you require.

• It is also possible to define another filter within this expression by calling up the Assistant again.

Choosing 'Filter' from the filter funtions allows you to define your own coeffiients.

• The Assistant supports up to 12 sampling points. If your filter requires more sampling points, you have to add these manually to the expression created by the assistant.

These functions don’t require an assistant. They all require as parameters the order of the filter, the channel to filter and at least one cut-off frequency (bandpass requires two).

All other parameters like the frequency are calculated.

The following sections list all operators and functions supported in WinDarab. WinDarab follows conventional mathematical rules for evaluating expressions.

*	Multiplication
+	Addition
-	Subtraction
/	Division
^	, Calculates the result of <x> raised to the power of <y>
<X> BitAnd <y>	Calculate the result of the bitwise AND-combination of <x> and <y>
<X> BitOr <y>	Calculate the result of the bitwise OR-combination of <x> and <y>
<X> BitXor <y>	Calculate the result of the bitwise XOR-combination of <x> and <y>

Abs(<x>)	Returns the positive absolute value of <x>.
arccos(<x>)	Calculates the radiant angle, the cosine of which equals the parameter <x>.
ArcCosH(<x>)	Calculates the radiant angle, the hyperbolic cosine of which equals the parameter <x>.
ArcSin(<x>)	Calculates the radiant angle, the sine of which equals the parameter <x>.
ArcTan(<x>)	Calculates the radiant angle, the tangent of which equals the parameter <x>.
ArcSinH(<x>)	Calculates the radiant angle, the hyperbolic sine of which equals the parameter <x>.
ArcTanH(<x>)	Calculates the radiant angle, the hyperbolic tangent of which equals the parameter <x>.
ceil(<x>)	Calculates the smallest integer greater than or equal to to <x>.
Cos(<x>)	Calculates the cosine of the radiant <x>.
CosH(<x>)	Calculates the hyperbolic cosine of the radiant <x>.
Exp(<x>)	Calculates the exponential value
floor(<x>)	Calculates the biggest integer smaller-equal to <x>.
frac(<x>)	Returns only the decimals from <x>.
HasValue(<value>)	True if the value is valid and False if the value is 'NoValue'
int(<x>)	Cuts all decimals from <x>.
lb(<x>)	Calculates the base-2 log of <x>.
lg(<x>)	Calculates the base-10 log of <x>.
ln(<x>)	Calculates the natural log of <x>.
round(<x>)	Rounds <x> to the nearest integer value.
sign(<x>)	Returns the sign of <x> (-1 or 1).
Sin(<x>)	Calculates the sinus of the radiant <x>.
SinH(<x>)	Calculates the hyperbolic sine of the radiant<x>.
sqr(<x>)	Calculates .
sqrt(<x>)	Calculates .
Tan(<x>)	Calculates the tangent of the radiant.
TanH(<x>)	Calculates the hyperbolic tangent of the radiant <x>.
BitInvert(<x>)	Calculates the bitwise Inversion of <x>.
Important	Due to limitations in precision of math results (because WinDarab is using 32-Bit IEEE-float values) there are problems, if the resulting value is too big. E.g. the result of BitInvert(128) is wrong, while the result of BitInvert(255) is correct. The precision problem occurs only, when saving the math result in memory. While evaluation the expression, there won’t be any precision issues. This means that the expression can evaluate a maximum of 32-Bit values, but the final result should be smaller.

WinDarab provides seven filter functions:

• bandpass
• bandpassFIR
• lowpass
• lowpassFIR
• highpass
• highpassFIR
• stopband

WinDarab supports a number of different approximation techniques and frequencies for each of these filters.

• Tip: Using the WinDarab Filter Assistant simplifies the assembly of filter functions considerably

Syntax:

• bandpass (<Technique>;<Order>;<Frequency Range>;<Expression>)

Parameters:

Syntax:

• bandpassFIR(<Order>, <lowerCutoff>, <upperCutoff>, <Channel>)

The channel is filtered using a FIR-bandpass-filter of the given order (>=4th order) and a cutoff frequency [Hz].

Syntax

• lowpass (<Technique>;<Order>;<Frequency>;<Expression>)

Parameters:

Syntax:

• lowpassFIR(Order, CutoffFreq, Channel)

The channel is filtered using a FIR-lowpass-filter of the given order (>=4th order) and cutoff frequency [Hz].

Syntax:

• highpass (<Technique>;<Order>;<Frequency>;<Expression>)

Parameters:

Syntax:

• highpassFIR (<Order>, <CutoffFreq>, <Channel>)

The channel is filtered using a FIR-highpass-filter of the given order (>=4th order) and cutoff frequency [Hz].

Syntax:

• stopband (<Technique>;<Order>;<Frequency Range>;<Expression>)

Parameters:

Syntax:

• Lookup(<LookupTable>;<param1>[;<param2>…])

Parameters:

• LookupTable: The base table for the lookup-value.
  • For more information on lookup tables see LookupTables.
• param1-x: The input parameters for the first (x) dimension of the lookup table
• param2-y: The input parameters for the second (y) dimension of the lookup table

Note: The number of the dimensional-parameters has to match the dimension of the lookup table.

The following examples use a few channels and functions which are:

• speed: The speed of the car in km/h
• lapctr: The current lapnumber
• HOLD: The last value calculated by this math-channel
• dt: Time past since the last calculated sample of this math-channel
• sigma: Sums up the expression inside for the whole file up to the current sample

There is no function for integrating a channel over time. No matter, integration over time is simply the sum of a channel multiplied with the delta-time:

In this example the speed is integrated over the file. The result is the distance driven (assuming the unit of speed is km/h, we have to divide by 3.6 to receive the distance in meters)

sigma(speed*dt) / 3.6

To derivate a channel by time, you have to divide the change of the channel by the change of time:

delta(channel)/dt

Assuming the speed of a car is between 0 and 400 km/h. If we want to clean the speed-channel from all measurement errors (values outside the valid speed-range) we have to find the error values.

If (speed <0 OR speed >400;0;speed)

Now every wrong value is set to 0. Instead of using this static value, you may want to keep the latest reasonable value. This can be accomplished by inserting the HOLD-function: HOLD returns the previous result of the math channel.

If(speed < 0 OR speed > 400; HOLD; speed)

In this example you are shown how to use these functions to generate a math channel that calculates the duration driven with more than 200km/h for each lap. First thing to do is to sum up the time, the car is faster than 200km/h.

sigma(if(speed > 200; dt; 0))

The if-function returns the time since the last sample when speed is greater 200 and 0 if not. Sigma sums up the results of the if-function to get the time past driving faster than 200km/h.

Note:

• This current function sums up the time for the whole file.

If you want the time being calculated for each lap individual, you have to reset the sum at the each laptrigger.

Unfortunately the sigma-function works on the whole file by default, so you need to reset the function after each lap. For that matter, the sigma-function has an optional reset condition.

Sigma(if(speed > 200; dt; 0); delta(lapctr) <> 0)

The new part in this function does exactly that. If the lap number changed (delta(lapctr) <> 0) sigma resets the sum back to zero and starts again.

Note:

• Instead of delta(lapctr) you can also use {laptrig} <> 0.
  Whatever your choice is, take care of the calculation period of your math channel. Especially {laptrig} is a single peak at the lap trigger and can be easily missed, if the calculation period is set to “Slowest channel”. Therefore using the lap counter is better, but again: If the period is “slowest channel” and your speed is measured faster, you have to select “fastest channel”!
  For more information see also “Computing Tab”.

There is a faster way to get the same results as well. Use LapSigma for resetting the sum at the beginning of a new lap.

LapSigma(if(speed > 200; dt; 0))

A Simple math function:

DetectEvent({pbrake_fl} > 10)

This generates an output with a non-zero value while the condition is true, in this case the front brake pressure is greater than 10 bar. For one braking event, this looks like:

1. Rising Edge: The output is equal to a value of '1' for exactly one sample.
2. Event True: The output is equal to a value of '2' while the event is true (between the rising and falling edge)
3. Falling Edge: The output is equal to a value of '-1' for exactly one sample.

• Two additional arguments “BeginDelay” and “EndDelay” were added to DetectEvent. With these arguments DetectEvent delays state changes by the given amount of time.
• The two arguments are optional and don’t change the signature of the “old” DetectEvent:

DetectEvent(Inactive|Rising|Active|Falling; <BeginCondition>; <BeginDuration>; <BeginDelay>; <EndCondition>; <EndDuration>; <EndDelay>)

• The kind of the arguments are actually controlled by the given number of arguments. Hereby the first keyword argument (Inactive/Rising|Active|Falling) is always optional and is NOT counted as an argument!

DetectEvent with 6 Arguments

DetectEvent(
    Inactive|Rising|Active|Falling;
    <BeginCondition>; <BeginDuration>; <BeginDelay>;  
    <EndCondition>; <EndDuration>; <EndDelay>
)

DetectEvent with 5 Arguments

DetectEvent(
    Inactive|Rising|Active|Falling;
    <BeginCondition>; <BeginDuration>; <BeginDelay>;
    <EndCondition>; <EndDuration>; <EndDelay>
)

DetectEvent with 4 Arguments

DetectEvent(
    Inactive|Rising|Active|Falling;
    <BeginCondition>; <BeginDuration>; <BeginDelay>;
    <EndCondition>; <EndDuration>; <EndDelay>
)

DetectEvent with 3 Arguments

DetectEvent(
    Inactive|Rising|Active|Falling;
    <BeginCondition>; <BeginDuration>; <BeginDelay>;
    <EndCondition>; <EndDuration>; <EndDelay>
)

DetectEvent with 2 Arguments

DetectEvent(
    Inactive|Rising|Active|Falling;
    <BeginCondition>; <BeginDuration>; <BeginDelay>; 
    <EndCondition>; <EndDuration>; <EndDelay>
)

DetectEvent with 1 Arguments

DetectEvent(
    Inactive|Rising|Active|Falling;
    <BeginCondition>; <BeginDuration>; <BeginDelay>; 
    <EndCondition>; <EndDuration>; <EndDelay>
)

Math functions support var & local variables

• var declared variables keep their values between the calculation of one sample to the next. They are initialized once when evaluation the value of the first sample and can be used to “transfer” intermediate results to the next calculation cycle.
• local declared variables are always initialized when calculating a sample. They can be used to calculate intermediate values – e.g. if an intermediate result is required multiple times in the same expression.

Calculate the average wheel speed over a file

var wheelSpeedSum
var wheelSpeedCount
Local wheelSpeedAve := (vwheel_fl + vwheel_fr) / 2
wheelSpeedSum := wheelSpeedSum + wheelSpeedAve
wheelSpeedCount := wheelSpeedCount + 1
wheelSpeedSum / WheelSpeedCount

You can even use script blocks within any other function argument. Simple put your expressions within “begin” and “end”

var wheelSpeedSum
var  wheelSpeedCount
If (nmot >= 5000;
  begin
    Local wheelSpeedAve := (vwheel_fl + vwheel_fr) / 2
    wheelSpeedSum := wheelSpeedSum + wheelSpeedAve
    wheelSpeedCount := wheelSpeedCount + 1
  end; 0)
wheelSpeedSum / WheelSpeedCount

• In math channels you can use “NoValue” to supress any output in WinDarab (e.g. the oscilloscope signal is interrupted).
• A math function “IsValue” was added to checka input value for “NoValue”.
• Also all analysis windows (should) work correctly, if they meet a “NoValue”.
• Note: All comparisions with NoValue will returns false (NoValue is internally a NaN double value)
• Here’s a sample math function:

if (nmot > 6000; nmot; NoValue)

This channel will show only a signal, if nmot is larger than 6000 – anywhere else there’s nothing!

ValueAtDist(<channel>; <dist> [; <LapIndex>])

• If <LapIndex> is omitted, <dist> is the absolute distance value within the file.

ValueAtDist(<channel>; <xdist>-10)
returns the value 10m before the current position.

• If <LapIndex> is given, the <dist> argument is a lap distance value.

ValueAtDist(<channel>; 100; LapIndex)
returns the value at position 100m of the current lap.

ValueAtDist(<channel>; lapdist; LapIndex-1)
returns the value at the lap position but in the previous lap

ValueAtTime(<channel>; <time> [; <LapIndex>])

• If <LapIndex> is omitted, <time> is the absolute time value within the file.

ValueAtTime(<channel>; <xtime>-10)
returns the value 10sec before the current position.

• If <LapIndex> is given, the <time> argument is a lap time value.

ValueAtDist(<channel>; 10; LapIndex)
returns the value at position 10sec of the current lap.

ValueAtDist(<channel>; laptime; LapIndex-1)
returns the value at the same laptime position but in the previous lap

Conditions are a smaller size datatype that is meant to represent a boolean value. To access the dialog, from the ribbon: Tools → Mathematics → Conditions

Conditions are stored on disk in the Settings.Ini file. This is located at %WinDarab Install%/Config/Settings.ini.

• We recommend not using Conditions, as this functionality is nearing end of life and will be removed in a later version.

Throughout WinDarab, any dialog box where a 'Condition' is specified, you can instead select a Math function where and value not equal to 0 is true.

• Alternatively, you can enter a condition manually in any of these dialogs