FFT Based Filtering of Spectra

Command: Preprocessing > Filter > Spectral > FFT Based Filter

The command Preprocessing > Filter > Spectral > FFT Based Filter allows to filter the spectra by means of Fast Fourier Transform (FFT). The basic principle of this filter type uses an FFT to transform the spectrum into the corresponding frequency domain. In the frequency domain you can apply various cut-off functions to eliminate part of the lines. The reduced frequency domain signal is then transformed back into the original domain.

You can see the effect of the filter in the left pane of the window. The top chart in the left pane shows the spectrum selected by the image cursor in the image at the right. The middle chart shows the Fourier transform, and the bottom chart shows the inverse FFT for the spectrum displayed at the top. In order to configure the type of filtering you have to adjust the cut-off borders in the spectrum and the filter options.

How to:
  1. Select the spectral resolution.
  2. Select the weighting window.
  3. Select the type of clipping and the clipping range
  4. Select the padding mode (only necessary if the signal is shorter than the selected spectral resolution)
  5. Select the borders of the processed spectral range
  6. In multimodal datasets select the spetra to be processed
  7. Click "Apply" to process all pixels of the image.

Following is a short explanation of the filter options:

  • Spectral resolution: the spectral resolution determines the number of data points used for the FFT. It should always be greater than the number of data points (number of layers of the hyperspectral cube) of the spectrum. If you use a spectral resolution which is too low then only the lower part of the spectral data is processed.
  • Spectrum Type: this option has no effect on the filtering, it only determines which kind of spectral information is displayed in the spectral chart.
  • Weighting Window: this option determines the weigting of the data in the FFT. Note that using weighting windows other than a rectangle may require to increase the spectral resolution in order to reduce edge effects.
  • Padding: The padding mode controls how the data points outside the actual data range are filled. "zero padding" fills the unused range with zeroes, "level padding" fills it with the first/last data value of the signal and "mirrored signal" mirrors the signal along the time axis (this mode is sometimes mentioned in the literature, but is not recommended).
  • Type of Spectral Clipping: determines whether the clipping of the spectral lines is done smoothly or abruptly.
  • Clipping Range: you can select to cut the range either inside the border cursors or outside of it (i.e. band stopp vs. band pass filter)
  • Destination: you can either replace the original data or append the filtered data to the hypercube (a maximum of four spectral groups is allowed)