Calculation of individual spectral values

Block diagram

Program parameters

The table below shows a list of the important parameters for configuring the function blocks.

Configuration of the frequency bands

The GVL_Constants define the central parameters for initializing the algorithm and the properties of the generated signal.

VAR_GLOBAL CONSTANT
    cSampleRate   : LREAL := 10000;                                        // Sample rate of input signal.
    cWindowLength : UDINT := 2048;                                         // Internal buffer size with 50% overlapping
    cResolution   : LREAL := cSamplerate / cWindowLength;                  // Frequency resolution
    cBands        : UDINT := 2;                                            // Number of bands
    cSetFrequency : ARRAY[1..cBands] OF LREAL := [ 41*cResolution, 413 ];  // Frequency in Hz; [ exact, intermediate ]
    cSetAmplitude : ARRAY[1..cBands] OF LREAL := [ 1.0, 2.0 ];             // Peak amplitudes of sine signals
    cBandWidth    : UDINT := 5;                                            // Computed bins per frequency.
    cDFTBins      : UDINT := cBandWidth * cBands;                          // Number of spectral bins, cBandWidth bins per frequency
END_VAR

The generated signal (MAIN.aBuffer) consists of two frequency components. One is chosen with respect to the numerical resolution, i.e. it is a multiple of f = 10000 Hz/2048 = 4.8828125 Hz. The second is chosen such that the peak lies between two spectral values and thus cannot be precisely represented. In order to be able to illustrate the numerical effects, a further four values are calculated around the respectively sought spectral values. The configuration takes place in der MAIN_CM.

// Compute parameters, adjust if cDFTBins is changed.
FOR i := 1 TO cBands DO
    k := LREAL_TO_DINT(cSetFrequency[i] / cResolution);
    aDFTBins[(i-1) * cBandWidth + 1] := DINT_TO_UDINT(MAX(k-2,1));
    aDFTBins[(i-1) * cBandWidth + 2] := DINT_TO_UDINT(MAX(k-1,1));
    aDFTBins[(i-1) * cBandWidth + 3] := DINT_TO_UDINT(MIN(k+0,nyquist));
    aDFTBins[(i-1) * cBandWidth + 4] := DINT_TO_UDINT(MIN(k+1,nyquist));
    aDFTBins[(i-1) * cBandWidth + 5] := DINT_TO_UDINT(MIN(k+2,nyquist));
END_FOR

Visualization of the results

The sample includes an extensive TwinCAT measurement project in which the calculated spectral values from the function block FB_CMA_SparseSpectrum are compared with the reference algorithms (FB_CMA_RealFFT, FB_CMA_MagnitudeSpectrum, FB_CMA_PowerSpectrum). The difference between an excitation as a multiple of the numeric frequency resolution and a value between two such values is illustrated. The visualized frequency bands can be considered as a "zoom" of the corresponding area.

The following illustrations show the results from the comparison of the function blocks FB_CMA_RealFFT and FB_CMA_MagnitudeSpectrum.

Spectrum of the FB_RealFFT (top) and the spectral values of bands 1 (center) and 2 (bottom).

Magnitude spectrum of the function block FB_MagnitudeSpectrum (top) as well as the spectral values of bands 1 (center) and 2 (bottom).

Requirements