1. Digital Processing for EELS Data Xiang Yang WATLABS, Univeristy of Waterloo

2. Signals and Noise --1 Signal: any useful information information Noise: any unwated information information

3. Signals and Noise --2 Signal: Signal: what you are measuring that is the result of the presence of your analyte what you are measuring that is the result of the presence of your analyte Noise: Noise: extraneous information that can interfere with or alter the signal. extraneous information that can interfere with or alter the signal.

4. Types of Noise --1 Random Noise: sign & magnitude --unpredictable Random Noise: sign & magnitude --unpredictable Non-Random Noise: Non-Random Noise: sign & magnitude – correlated with some event sign & magnitude – correlated with some event

5. Types of Noise --2 Fundamental Noise: Fundamental Noise: ------- Due to the nature of light and matter ------- Due to the nature of light and matter ------- Cannot be totally eliminated ------- Cannot be totally eliminated Non-Fundamental Noise: Non-Fundamental Noise: ------- Mostly due to instrumentation ------- Mostly due to instrumentation ------- can be eliminated (theoretically) ------- can be eliminated (theoretically)

6. Signal to Noise Ratio (SNR)

8. Noise Sources Signal Source Detector Analog Treatments Analog to Digital Conversion Non-monochromate light source Detector’s Dark Current, electromagnetic interference, etc. Circuit noise, baseline, electromagnetic interference, etc. Quantization effects

9. SNR Enhancement Hardware Hardware

10. Dwell Time v.s. SNR Communication between Computer & Machine Communication between Computer & Machine

11. Ensemble Averaging Collect multiple signals over the same time or wavelength (x-axis) domain Collect multiple signals over the same time or wavelength (x-axis) domain Calculate the mean signal at each point in the domain Calculate the mean signal at each point in the domain Re-plot the averaged signal Re-plot the averaged signal Since noise is random (some +/ some -), this helps reduce the overall noise by cancellation! Since noise is random (some +/ some -), this helps reduce the overall noise by cancellation!

13. Boxcar Averaging –Take an average of 2 or more signals in some domain –Plot these points as the average signal in the same domain –Can be done with just one set of data –You lose some detail in the overall signal

16. Digital Filtering Weighted Digital Filtering Weighted Digital Filtering Fast Fourier Transform Digital Filtering Fast Fourier Transform Digital Filtering

17. Weighted Filtering

19. Fast Fourier Transformation Filtering Main Point: Noise is of a higher frequency than the information

20. FFT Filtering Noisy Data (Time Domain) Tranformed Data (Frequency Domain) FT Modified Data (Freq. Domain) Low Pass Filter Filtered Signal FT

21. Filtering

22. FFT ---- Real Sample

23. First Fourier Tranform Cut off Frequency (0.003 Hz)

25. Thank You !