Low Pass Fourier Transform Spectral Analysis
Features:
Performs FFT of the spectrum and removes high-frequency data.
The Low Pass FFT of the spectrum from the region of interest is performed in several steps automatically after several inputs from the user. First, the function averages the spectra from the region of interest. Second, the algorithm performs a Fourier transform of the spectrum, converting the mean spectrum into its corresponding frequency domain spectrum. Third, the algorithm executes a low pass filter with a specified user cut-off frequency. In the final step, the inverted Fourier transform algorithm is performed to generate a new dataset with only low frequencies remaining.
Steps:
1. Optimize and visualize the performance of FFT on an individual spectrum from the selected region of interest using Fourier Transform.
a. Load the file.
b. Select Spectra Mathematics.
c. Select Low Pass Fourier Transform.
2. Click Select 1st Spectrum and draw a region of interest. A spectrum corresponding to the region will appear in the SPECTRAL ANALYSIS window.
3. Press Generate and enter a Cutoff value number in the pop-up dialog. The number reflects the % of Nyquist frequency in the range between 0 and 1.
4. Press Visualize Spectra.
Observe a new window that shows the following spectra: the original spectrum, FFT transformed spectrum, and a reconstructed spectrum as shown in the figure below. From top to bottom: i) original spectrum, ii) frequency domain spectrum, with red dots showing the frequencies that are preserved for subsequent inverse Fourier transform, iii) the spectrum after the inverse Fourier transform.
Note: the intensity scale of the reconstructed spectra automatically changes and ranges from 0 to 1. The results of these transformations can be also seen in the SPECTRAL ANALYSIS panel. Multiple reconstructed spectra from several cutoffs can be visualized.
(Optional) After the cutoff value of the FFT filter is optimized, press Apply to Image to visualize the resulting filtered image.
References:
The algorithm is built using part of the fftl library developed by Shmuel Ben-Ezra in 2009:
