FB_CMA_SlidingDFT

Online calculation of spectral values for real-valued input signals

The function block FB_CMA_SlidingDFT provides a configurable number of individual spectral values that are conform to the function block FB_CMA_RealFFT. The DFT coefficients are calculated

FB_CMA_SlidingDFT 1:

approximately with the attenuation parameter r, 0<r<1, by means of the recursion rule

FB_CMA_SlidingDFT 2:

The calculation is done by using a sliding window, so that the spectral values are updated with each new sample. The advantages of the online calculation of selected spectral values compared to the FFT consist on the one hand of the constant utilization of the processor (no block processing) as well as the independence of the window length with respect to powers of two. The highest frequency of a component in the input signal should be at the most around half of the sampling rate of the input signal so that aliasing effects are avoided.

Memory properties

Due to the use of the last nWindowLength (N) samples for the calculation of the spectral values, jumps in the time series can lead in the frequency analysis to incorrect results in the spectral range. In a call with smaller input buffer size, fewer values can be transferred. In this case, the configured spectral values are updated for all newly transferred values.

NaN occurrence

If the input vector contains one or more NaN (Not a Number) values, the entire output sector is filled with NaN. See separate section for further information on NaN values.

FB_CMA_SlidingDFT 3:

Handling of NaN values

If the situations described above, which lead to NaN values, cannot be ruled out or safely neglected, the application program must be able to handle these error values.

Behavior when processing multi-channel input data

When processing several channels (nChannels > 1), there is a possibility of each channel having different return values. In this case, return values can be queried separately on the function block. If the results from one or more channels are impermissible, but not all channels, the value on the function block corresponds to eCM_InfRTime_AmbiguousChannelResults. If the results of all channels are impermissible, then the value on the function block corresponds to eCM_ErrRTime_ErrornousChannelResults.

A list of return values of all channels can be queried using the method GetChannelErrors().

Sample implementation

A sample implementation showing the possible uses of the function block and its configuration is available under the following link: Sliding DFT

Inputs and outputs

The input and output buffers correspond to one of the following definitions (input / output shape). The variable parameters are part of the function block input stInitPars.

Versions

Input buffer (MultiArray input stream)
element type, number of dimensions, dimension sizes

Output buffer (MultiArray output stream)
element type, number of dimensions, dimension sizes

Standard variant
(nChannels = 1)

LREAL, 1,
not specified*

LCOMPLEX, 1,
nBins

Multichannel variant
(nChannels > 1)

LREAL, 2,
nChannels x 
not specified*

LCOMPLEX, 2,
nChannels x nBins

VAR_INPUT
    stInitPars       : ST_CM_SlidingDFT_InitPars;        // init parameter
    nOwnID           : UDINT;                            // ID for this FB instance
    aDestIDs         : ARRAY[1..cCMA_MaxDest] OF UDINT;  // IDs of destinations for output
    nResultBuffers   : UDINT := 4;                       // number of MultiArrays which should be initialized for results (0 for no initialization)
    tTransferTimeout : LTIME := LTIME#500US;              // timeout checking off during access to inter-task FIFOs
END_VAR

Input parameters

The input parameters of this function block represent initialization parameters and must already be assigned in the declaration of the FB instance! (Alternatively: Init() method). They may only be assigned once. A change at runtime is not possible.

Output parameters

VAR_OUTPUT
    bError         : BOOL;                           // TRUE if an error occurs. Reset by next method call.
    hrErrorCode    : HRESULT;                        // '< 0' = error; '> 0' = info; '0' = no error/info
    ipErrorMessage : I_TcMessage := fbErrorMessage;  // Shows detailed information about occurred errors, warnings and more.
    nCntResults    : ULINT;                          // Counts outgoing results (MultiArrays were calculated and sent to transfer tray).
END_VAR
  • bError: The output is TRUE if an error occurs.
  • hrErrorCode: If an error occurs, a corresponding error code of the type HRESULT is output. Possible values are described in the List of error codes.
  • ipErrorMessage: Contains more detailed information on the current return value. Refer here to the section Error description and information. This special interface pointer is internally secured so that it is always valid/assigned.

Methods

Call():

The method is called each cycle in order to apply the algorithm to the current input data. The function block waits for input data if the method indicates neither new results nor an error. This is a regular behavior in the process of the analysis chain.

  • Return value: If an error occurs, a corresponding error code of the type HRESULT is output. Possible values are described in the List of error codes.
METHOD Call : HRESULT
VAR_OUTPUT
    bNewResult   : BOOL;       // TRUE every time when outgoing MultiArray was calculated and sent to transfer tray.
    bError       : BOOL;       // TRUE if an error occurs.
    hrErrorCode  : HRESULT;    // '< 0' = error; '> 0' = info; '0' = no error/info
END_VAR
  • bError: The output is TRUE if an error occurs.
  • hrErrorCode: If an error occurs, a corresponding error code of the type HRESULT is output. Possible values are described in the List of error codes. This output is identical to the return value of the method.
FB_CMA_SlidingDFT 4:

If a timeout occurs or no MultiArray buffer is available for the result, then neither the input data nor the result data are lost. They are forwarded on the next call.

Configure():

On calling this method, the spectral values must be configured at the beginning. The DFT index is calculated for the frequency f to k = f * fSampleRate / nWindowLength. If f is not an integer multiple of the frequency resolution fSampleRate / nWindowLength, the spectral portions are distributed to two consecutive spectral values.

The corresponding PLC array must be defined as follows. The Configure() method can also be used for a new configuration with a different set of arguments.

METHOD Configure : HRESULT
VAR_INPUT
    pArg     : PVOID;    // pointer to array of arguments
    nArgSize : UDINT;    // size of arguments buffer in bytes 
END_VAR

The input buffers correspond to one of the following definitions (input shape). The variable parameters are part of the function block input stInitPars.

Versions

Input buffer (MultiArray input stream)
element type, number of dimensions, dimension sizes

Identical configuration of all channels

UDINT, 1,
nBins

Channel-specific configuration
(nChannels > 1)

UDINT, 2,
nChannels x nBins

METHOD Init : HRESULT
VAR_INPUT
    stInitPars     : ST_CM_SlidingDFT_InitPars;        // init parameter
    nOwnID         : UDINT;                            // ID for this FB instance
    aDestIDs       : ARRAY[1..cCMA_MaxDest] OF UDINT;  // IDs of destinations for output
    nResultBuffers : UDINT := 4;                       // number of MultiArrays which should be initialized for results (0 for no initialization)
END_VAR

Init():

This method is not usually necessary in a Condition Monitoring application. It offers an alternative to the function block initialization. The Init() method may only be called during the initialization phase of the PLC. It cannot be used at runtime. You are referred to the use of an FB_init method or the attribute 'call_after_init' (see TwinCAT PLC reference). In addition, this facilitates the function block encapsulation.

The input parameters of the function block instance may not be assigned in the declaration if the initialization is to take place using the Init() method.

  • Return value: If an error occurs, a corresponding error code of the type HRESULT is output. Possible values are described in the List of error codes.

ResetData():

The method deletes all data records that have already been added, see Memory property of the function block. If the Call() method is called again after a ResetData(), the internal memory must be replenished in order to calculate a valid result.

  • Return value: If an error occurs, a corresponding error code of the type HRESULT is output. Possible values are described in the List of error codes.
METHOD ResetData : HRESULT
VAR_INPUT
END_VAR

PassInputs():

As long as an FB_CMA_Source instance is called and signal data are thus transferred to a target block, all further function blocks of the analysis chain have to be called cyclically as explained in the API PLC Reference.
Sometimes it is useful not to execute an algorithm for a certain time. For example, some algorithms should be executed only after prior training or configuration. The function block must be called cyclically, but it is sufficient for the data arriving at the function block to be forwarded in the communication ring. This is done using the PassInputs() method in place of the Call() method. The algorithm itself is not called here, and accordingly no result is calculated and no output buffer generated.

  • Return value: If an error occurs, a corresponding error code of the type HRESULT is output. Possible values are described in the List of error codes.
METHOD PassInputs : HRESULT
VAR_INPUT
END_VAR

GetChannelErrors():

The method enables the querying of a list of the channel-specific return values when processing several channels (nChannels > 1). A call is useful in the case that the return value of the function block corresponds to one of the values eCM_InfRTime_AmbiguousChannelResults or eCM_ErrRTime_ErrornousChannelResults.

  • Return value: Information on the reading process of the list of error codes. The value is set to TRUE if the query was successful, otherwise to FALSE.

    METHOD GetChannelErrors : BOOL
VAR_IN_OUT
    aChannelErrors : ARRAY[*] OF HRESULT;
END_VAR
  • aChannelErrors: Error list of the type HRESULT of the length nChannels.

Similar function blocks

The function block FB_CMA_RealFFT calculates the Fast Fourier Transform for real-valued input signals.

The function block ST_CM_SparseSpectrum_InitPars calculates individual, configurable magnitude and spectral values.

Requirements

Development environment

Target platform

PLC libraries to include

TwinCAT v3.1.4022.25

PC or CX (x86, x64)

Tc3_CM, Tc3_CM_Base