Instrument Components

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Instrument Components
Signal Generator (Energy Source) Analytical
Signal Transducer Signal Processor Display

• Can you identify these components in the
  following instruments?
• UV-Vis spectrophotometer
• pH meter
• NMR spectrometer

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Signal - the net response when a measurement is
performed. It consists of several components
(baseline, blank, noise) that must be subtracted
from the response to determine the true
analytical signal.
Noise - the random excursion of the signal about
some average value. If there is a lot of noise,
then the signal becomes harder to measure.
Signal-to-noise ratio (SNR) is frequently the
most important parameter to optimize in any
measurement system.
3
Types of noise Shot and thermal noise are
consequences of properties of matter and cannot
be avoided. They are distributed evenly at ALL
frequencies and are referred to as white noise.
Flicker noise is more intense at low frequencies
than high frequencies, varying approximately as
1/f and is only appreciable below 1 KHz.
Environmental noise is usually the dominant
source arising primarily from 60 Hz transmission
lines (and higher harmonics). Other sources of
environmental noise include vibrations and
electrical interactions between instruments.
4
Intuitively, the relative amounts of signal and
noise will influence the precision associated
with the measurement. Our confidence in a
measurement performed in a high-noise environment
differs from that in a low-noise environment.
In the lab, if the results of an experiment are
noisy, one typically replicates the experiment
and reports the mean or average result. In fact,
the mean of many measurements will more
accurately estimate the true signal.
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Boxcar Averaging
The average (or sum) of a set of points replaces
the individual values over a narrow portion of
the data set. This operation is repeated over
the entire domain of data.
interval

Original data set

Boxcar averaged data set
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Boxcar Averaging
Number of points in interval ? Nbox 1
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Boxcar Averaging
Nbox 3
8
Boxcar Averaging
Nbox 5
9
Boxcar Averaging
Nbox 7
10
Boxcar Averaging
Nbox 11
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Boxcar Averaging

• Limitations of boxcar averaging
• Analysis time increases.
• Resolution decreases.
• Distortion increases.
• Number of points per data set reduced by a
  factor of N.

Time-dependent information is maintained.
12
Moving Average (Moving Window)
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Moving Average
Number of points in moving window ? Nmov box 1
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Moving Average
Nmov box 3
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Moving Average
Nmov box 5
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Moving Average
Nmov box 7
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Moving Average
Nmov box 9
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Moving Average
Nmov box 15
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Moving Average
Nmov box 25
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Moving Average

• Limitations of moving average
• Analysis time increases.
• Resolution decreases.
• Distortion increases.

Time-dependent information is maintained.
21
Savitsky-Golay Smoothing
A polynomial is fit to the data in each window.
The center value is replaced by the calculated
value from the model. The window is shifted and
the fitting process is repeated. Savitsky and
Golay developed a set of weighting factors
(integers) that, when used in a convolution
process, and achieve the same effect as as a
least squares fit to a polynomial equation, but
in a faster, neater, and more elegant manner.
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Savitsky-Golay Smoothing
Number of points in moving window ? Nmov box 1
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Savitsky-Golay Smoothing
Nmov box 5
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Savitsky-Golay Smoothing
Nmov box 7
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Savitsky-Golay Smoothing
Nmov box 9
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Savitsky-Golay Smoothing
Nmov box 13
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Savitsky-Golay Smoothing
Nmov box 17
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Savitsky-Golay Smoothing
Nmov box 19
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Savitsky-Golay Smoothing

• Limitations of Savitsky-Golay smoothing
• Analysis time increases.
• Resolution decreases.
• Distortion increases.

Time-dependent information is maintained.
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Moving Average
Savitsky-Golay Smoothing
Nmov box 19
Nmov box 15
Which method yields the better SNR? Which
provides lower distortion?
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Ensemble Averaging
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Ensemble Averaging
Number of averaged data sets ? Ne.a. 1
Point by point ensemble averaging should increase
the SNR by the square root of N. Lets check it
out.
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Ensemble Averaging
Ne.a. 10
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Ensemble Averaging
Ne.a. 20
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Ensemble Averaging
Ne.a. 50
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Ensemble Averaging
Ne.a. 100
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Ensemble Averaging
Ne.a. 200
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Ensemble Averaging
Ne.a. 1000
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Ensemble Averaging

• Limitations of ensemble averaging
• Repetitive measurement of the same sample is
  required.
• Time per experiment increases by a factor of N.
• Time-dependent information is lost. You can not
  tell if there is a drift, or systematic error in
  the data with only the average.

SNR is dramatically improved with minimal
distortion.
40
Digital Filtering
To remove interference noise, the following
process is employed 1. Time-domain data is
transformed into frequency-domain data with the
Fourier transform. 2. Selected frequencies are
deleted (or multiplied by filtering function) 3.
The digitally filtered frequency-domain data
back to the time-domain using the inverse Fourier
transform.