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
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.
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.
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.
Detector Response
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Detector Response
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.
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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
}
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Original data set
Boxcar averaged data set
Boxcar Averaging
Number of points in interval  Nbox = 1
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Boxcar Averaging
Nbox = 3
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Boxcar Averaging
Nbox = 5
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Boxcar Averaging
Nbox = 7
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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.
Moving Average (Moving Window)
Moving Average
Number of points in moving window  Nmov box = 1
Moving Average
Nmov box = 3
Moving Average
Nmov box = 5
Moving Average
Nmov box = 7
Moving Average
Nmov box = 9
Moving Average
Nmov box = 15
Moving Average
Nmov box = 25
Moving Average
Limitations of moving average:
• Analysis time increases.
• Resolution decreases. *
• Distortion increases. *
Time-dependent information is maintained.
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.
Savitsky-Golay Smoothing
Number of points in moving window  Nmov box = 1
Savitsky-Golay Smoothing
Nmov box = 5
Savitsky-Golay Smoothing
Nmov box = 7
Savitsky-Golay Smoothing
Nmov box = 9
Savitsky-Golay Smoothing
Nmov box = 13
Savitsky-Golay Smoothing
Nmov box = 17
Savitsky-Golay Smoothing
Nmov box = 19
Savitsky-Golay Smoothing
Limitations of Savitsky-Golay smoothing:
• Analysis time increases.
• Resolution decreases. *
• Distortion increases. *
Time-dependent information is maintained.
Moving Average
Nmov box = 15
Savitsky-Golay Smoothing
Nmov box = 19
Which method yields the better SNR?
Which provides lower distortion?
Ensemble Averaging
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. Let’s check it out….
Ensemble Averaging
Ne.a. = 10
Ensemble Averaging
Ne.a. = 20
Ensemble Averaging
Ne.a. = 50
Ensemble Averaging
Ne.a. = 100
Ensemble Averaging
Ne.a. = 200
Ensemble Averaging
Ne.a. = 1000
Ensemble Averaging
Limitations of ensemble averaging:
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Repetitive measurement of the same sample is required.
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Time per experiment increases by a factor of N.
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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.
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.