Digital Processing for EELS DataDigital Processing for EELS Data

Xiang YangXiang Yang

WATLABS, Univeristy of WaterlooWATLABS, Univeristy of Waterloo

Signals and NoiseSignals and Noise --1 --1

Signal: any Signal: any usefuluseful

informationinformation

Noise: any Noise: any unwatedunwated

informationinformation

Signals and NoiseSignals and Noise --2 --2

SSignalignal:: what you are measuring that is the result of what you are measuring that is the result of

the presence of your analytethe presence of your analyte

NoiseNoise: : extraneous information that can interfere with extraneous information that can interfere with

or alter the signal. or alter the signal.

Types of NoiseTypes of Noise --1 --1

Random Noise: sign & magnitude --unpredictableRandom Noise: sign & magnitude --unpredictable

Non-RandomNon-Random Noise Noise: :

sign & magnitude – correlated with some eventsign & magnitude – correlated with some event

Types of NoiseTypes of Noise --2 --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-FundamentalNon-Fundamental Noise Noise: : ------- Mostly due to instrumentation------- Mostly due to instrumentation ------- can be eliminated (theoretically)------- can be eliminated (theoretically)

sX

deviation standardmean

NoiseSignal

Signal to Noise Ratio

(SNR)

Noise SourcesNoise Sources

Signal Source

Detector

Analog Treatments

Analog to DigitalConversion

Non-monochromate light source

Detector’s Dark Current, electromagnetic interference, etc.

Circuit noise, baseline, electromagnetic interference, etc.

Quantization effects

SNR EnhancementSNR Enhancement HardwareHardware

Dwell Time v.s. SNRDwell Time v.s. SNR

Communication Communication between Computer & between Computer & MachineMachine

Ensemble AveragingEnsemble Averaging Collect multiple signals over Collect multiple signals over

the same time or wavelength the same time or wavelength ((x-axisx-axis) domain) domain

Calculate the mean signal at Calculate the mean signal at each point in the domaineach point in the domain

Re-plot the averaged signalRe-plot the averaged signal

Since noise is random (some Since noise is random (some +/ some -), this helps reduce +/ some -), this helps reduce the overall noise by the overall noise by cancellation!cancellation!

Boxcar AveragingBoxcar Averaging

– Take an average of Take an average of 2 or more signals in 2 or more signals in some domainsome domain

– Plot these points as Plot these points as the average signal in the average signal in the same domainthe same domain

– Can be done with Can be done with just one set of datajust one set of data

– You lose some detail You lose some detail in the overall signalin the overall signal

Digital FilteringDigital Filtering

Weighted Digital FilteringWeighted Digital Filtering

Fast Fourier Transform Digital FilteringFast Fourier Transform Digital Filtering

Weighted FilteringWeighted Filtering

Fast Fourier Transformation FilteringFast Fourier Transformation Filtering

Main Point: Noise is of a higher

frequency than the information

FFT FilteringFFT Filtering

Noisy Data(Time Domain)

Tranformed Data(Frequency Domain)

FT

Modified Data

(Freq. Domain)

Low Pass Filter

Filtered Signal

FT

FTFT

Filtering

FFT ---- Real SampleFFT ---- Real Sample

First Fourier Tranform

Cut off Frequency (0.003 Hz)

Thank You !