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Analytical figures of merit, noise, and S/N ratio. Chemistry 243. Noise. A signal is only of analytical value if it can be definitively attributed to the species/system of interest in the presence of noise . Probably noise, or not very useful; a hint of a signal. Looks like a real signal.

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noise
Noise
  • A signal is only of analytical value if it can be definitively attributed to the species/system of interest in the presence of noise.

Probably noise, or not very useful;

a hint of a signal

Looks like a real signal

signal to noise ratio s n
Signal-to-noise ratio (S/N) is a measure of the quality of an instrumental measurement

Ratio of the mean of the analyte signal to the standard deviation of the noise signal

High value of S/N : easier to distinguish analyte signal from the noise signal

Signal-to-Noise Ratio (S/N)

Mostly

Signal

signal

Std. Dev.

Mostly

Noise

Rev. Sci. Inst., 1966, 37, 93-102.

where does noise come from
Where does noise come from?
  • Chemical noise
    • Temperature, pressure, humidity, fumes, etc.
  • Instrumental noise
detector and post detector noise
Detector and post-detector noise
  • Thermal (Johnson) noise
  • Shot noise
  • Flicker (1/f) noise
  • Environmental noise
  • Popcorn (burst) noise
  • Microphonic noise
thermal johnson noise
Thermal (Johnson) noise
  • Random motions of charge carriers (electrons or holes) that accompany thermal motions of solid lattice of atoms.
  • Lead to thermal current fluctuations that create voltage fluctuations in the presence of a resistive element
    • Resistor, capacitor, etc.

nrms = root-mean-square noise voltage

k = Boltzman’s constant

T = temperature

R = resistance of element (W)

Df = bandwith (Hz) = 1/(3tr)

tr = rise time

thermal johnson noise continued
Thermal (Johnson) noise continued
  • Dependent upon bandwidth (Df) but not f itself
    • white noise
  • Can be reduced by narrowing bandwidth
    • Slows instrument response time
    • More time required for measurement
  • Reduced by lowering T
    • Common to cool detectors
      • 298K77K lowers thermal noise by factor of ~2

N2(l): bp=77K

nrms = root-mean-square noise voltage

k = Boltzman’s constant

T = temperature

R = resistance of element (W)

Df = bandwith (Hz) = 1/(3tr)

tr = rise time

shot noise

11 e-/s

10.5 e-/s

10 e-/s

Shot noise
  • Arises from statistical fluctuations in quantized behaviors
    • Electrons crossing junctions or surfaces
  • Independent of frequency
  • Example: current

irms = root-mean-square noise current

I = average direct current

e = electron charge

Df = bandwidth (Hz)

flicker 1 f noise
Flicker (1/f) noise
  • Magnitude is inversely proportional to the frequency of the signal
  • Significant at frequencies lower than 100 Hz
    • Long-term drift
  • Origin is not well understood
    • Dependent upon materials and device shape
      • Metallic resistors have 10-fold less flicker noise than carbon-based resistors.
    • Referred to as “pink” noise—more red (low frequency) components
environmental noise
Environmental noise
  • Comes from the surroundings
  • Biggest source is “antenna” effect of instrument cabling

J. Chem. Educ., 1968, 45, A533-542.

noise contributions in different frequency regimes
Noise contributions in different frequency regimes

Frequency independent

Supposedly 1/f—mostly at low frequencies

Occurs at discrete frequencies

enhancing signal to noise
Hardware methods

Grounding and shielding

Difference and Instrumentation Amplifiers

Analog Filtering

Lock-In Amplifiers

Modulation and Synchronous Demodulation

Software methods

Ensemble averaging

Boxcar averaging

Digital filtering

Correlation methods

Enhancing signal-to-noise
grounding and shielding
Grounding and shielding
  • Surround circuits (most critical conductors) with conducting material that is connected to ground
    • Noise will be picked up by shield and not by circuit
  • Faraday cage

http://www.autom8.com/images_product/table_farady_benchtop.jpg

http://farm2.static.flickr.com/1227/578199978_17e8133c7c_o.jpg

analog filtering
Analog filtering
  • Low pass filter removes high frequency noise
    • Thermal and shot noise
  • High pass filter removes low frequency noise
    • Drift and flicker noise
  • Narrow-band electronic filters

High freq removed.

Low freq preserved

(passed).

Example of low-pass filter

lock in amplifiers
Lock-in amplifiers
  • Modulation
    • Translate low frequency signal (prone to 1/f noise) to a high frequency signal which can amplified and then filtered to remove 1/f noise

Mechanical chopper

lock in amplifiers continued
Lock-in amplifierscontinued
  • Synchronous demodulation
    • Converts AC signal to DC signal synchronous with chopper—follows reference
  • Low-pass filtering
    • Back converts high frequency DC signal to return filtered, low frequency output.
ensemble averaging to increase s n
Ensemble averaging to increase S/N
  • Averaging multiple data sets taken in succession
    • Divide sum of data sets by number of data sets

J. Chem. Educ., 1979, 56, 148-153.

ensemble averaging continued
Ensemble averagingcontinued
  • Signal-to-noise improves with increasing number of data sets

N = rms noise

n = number of replicate scans

i = number of replicate scans

in other data set

# Scans, n Relative S/N

1 1

4 2

16 4

64 8

boxcar averaging
Boxcar averaging
  • Smoothing irregularities and increasing S/N
  • Assumes signal varies slowly in time
  • Multiple points are averaged to give a single value
  • Often performed in real time
  • Detail is lost and utility limited for rapidly changing samples
  • Boxcar integrators commonly used in fast (pico- to microsecond) measurements using pulsed lasers.
moving average smooth
Moving average smooth
  • Similar to a boxcar average, but changes in time
digital filtering
Digital filtering
  • Fourier transform
    • Convert data from time- to frequency-domain, manipulate to remove higher frequency noise components, regenerate time-domain signal
  • Polynomial data smoothing
    • Moving average smooth
    • Least-squares polynomial smoothing
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