This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: CHAPTER FIVE SIGNALS
AND NOISE CHEM 4369 Two components of analytical measurement: 0 SIGNAL: carries information (qualitative and
quantitative) about the analyte that is of interest to the
chemist 9 NOISE: an unwanted signal (always present) due to
the random fluctuations observed whenever replicate
measurements are made on signals that are monitored
continuously. 055 lt is unwanted because it degrades the accuracy and
precision of an analysis and also places a lower limit
on the amount of analyte that can be detected. ﬁlm» 5'. @rzmng; CHEM 4369 Signal Magnitude Two ways of determining the magnitude of S: 0 The signal is characterized
by its mean value, which
can be estimated by drawing _ a line through the center of “If,” "
the fluctuations as shown 1:92?" Figures1 Eﬁectofnmseonacurrentmeasurement: (a) experimental stripchart recording of a 09:4015 A
direct current, (b) mean of the ﬂuctuations C‘LIJ'rcnl. '\ X It!" 9 Alternatively, n independent
measurements x, can be made "
during the observation period, and _ E1 If
the arithmetic mean calculated x =
from 12 ﬁlm» 5'. @rzmyw; cH EM 4369 Noise Magnitude
.3;:,:;«, Noise (N) is characterized by its magnitude, frequency,
phase, and character. Hr Noise magnitudes are typically expressed as 0 root
meansquare (rms) or 9 as peaktopeak (p—p) values. 0 The rms noise (average power content of the noise) is
the standard deviation of the signal (S) derived from
n independent measurements. rms noise = s ﬁrm» 5'. @rzmyw; CHEM 4369 Noise Magnitude (contd.) 9 The peaktopeak noise (Ep_p)
can be extracted from a
recorder tracing as shown in
the Figure. it If n discrete measurements of
the signal are made, Ep_,, is the
range or the difference between
the maximum and minimum Recorder tracing of dc voltage
values of discrete signal with “0158
measurements. Time car The rms noise (3) is approximately onefifth of the peaktopeak noise (EM) for normally distributed
noise. ﬁlm» 5'. ggumym; CHEM 4369 Sources of Noise in Instrumental Analysis Two types of noise: 0 Chemical noise arises from a host of uncontrollable
variables (e.g., fluctuations in temperature, pressure,
humidity, vibrations, laboratory fumes, light intensity) that
affect the chemistry of the system being analyzed. 9 Instrumental noise is associated with each
component of an instrument—that is, with the source,
the input transducer, all signalprocessing elements, and the output transducer. The recognizable kinds
include:  thermal or Jonhson noise
' shot noise
' flicker Ol‘ 1/f noise ] pink noise  interference or environmental noise ﬁmu S. @rzmyw; } white noise CHEM 4369 Noise Power Spectrum (NPS) car The magnitude and frequency of the noise can be more
fully described by a noise power spectrum (N PS), Le,
a plot of the meansquare noise (variance, $2) per unit
frequency interval, P(e) in V2 H24, vs. the frequency in Hz. The three types of noise 9 obvious in the NPS are: Interference
 "Oise 0 White noise: /
P(e) is independent of 1‘ White noise 9 Pink or 1/fnoise:
P(e) increases as fdecreases Frequency (Hz) —) 9 Interference noise:
P(e) is frequency dependent and finite at specific frequencies am» 5'. @ezmgrw; CHEM 4369 Thermal Noise, or Johnson Noise Thermal noise is caused by random thermal agitation of
charged particles (electrons, etc.) in the resistive elements
(resistors, capacitors, radiation transducers, eiectrochemicat
cells, etc.) of an instrument. Tim“ 2 rootrmeanrsquare noise voltage
— ? 1 ion in a fre uenc bandwidth ot‘Af Hz
1/. = warmth Y a ‘1 Y
""5 ( ) k 2 Boltzman constant (].38><10_23 JiK')
T 2 temperature in kclvin
A f : (3:1. )—1 R : resistance in ohms
1,. : rise time of an instrument in seconds Thus, thermal noise can be reduced by:
as narrowing the frequency bandwidth
E3” lowering the electrical resistance of instrument circuits as lowering the temperature of instrument components
(e.g., by coating transducers) ﬁlm» 5'. @rzmyw; CHEM 4369 Shot Noise Shot noise (or quantum noise) is a fundamental noise
(a noise arising from the particle nature of light and matter)
that is observed whenever electrons or other charged
particles cross a junction, like the pn interfaces in typical
electronic circuits and the vacuum space between the
anode and cathode in photocells and vacuum tubes. in,“ : rootelncanrsquare current associated with the average direct current, i
c 2 charge on the electron {l .60xl(}_w C)
Af= bandwidth of frequencies being considered Thus, shot noise can be reduced by: I35 narrowing the frequency bandwidth ﬁlm» 5. @rzmym; CHEM 4369 Pink or 1lfNoise, Flicker Noise use Flicker noise (also called proportional noise,
multiplicative noise, or fluctuation noise) is another
name for nonfundamental or excess noise (a noise due
to imperfect components and instrumentaion) for which
the rms noise in the signal is directly proportional to the
magnitude of the signal. use It is a random noise with a frequency—dependent NPS,
often having 1/f character in its NPS. as: it exhibits larger magnitudes at low frequencies and
becomes especially significant at f < ~100 Hz. ﬁlm» 5'. @rzmgrmz; CHEM 4369 Pink or 1lfNoise, Flicker Noise A few general sources of flicker noise include: as: Slow drifts (lowfrequency fluctuations) that are abserved
in dc amplifiers, meters, and galvanometers. Ear Source flicker noise, which is caused by variations in
experimental variables that control the excitation source
radiance, such as electrical power, temperature, or
mechanical vibrations. Es Transmission or convection flicker noise, which is
caused by fluctuations in the transmission characteristics
of the sample container (independent of the analyte). as: Analyte flicker noise, which is caused by fluctuations in
the sample presentation system. QM» 5'. @rzmyw; CHEM 4369 Interference or Environmental Noise Interference or environmental noise is frequency dependent,
nonfundamental noise that often appears at discrete
frequencies due to pickup from and parasitic coupling to other
signal sources. Examples include: [is (SO—Hz noise from ac power
lines in the USA; the NPS has
Spikes at 60 Hz and its harmonics
(8.9., 120, 180 Hz) ‘ noise spikes generated by
turning instruments on and off radiofrequency noise from Spark gaps in lasers I In" in " ilniu‘ m4 It:’ i In" In" Ill“
I'Icquvnt‘y. ll: — — noise at frequencies generated by oscillators in
instruments and computers
or by other timing devices Figure 53 Some sources of environmental noise in a
university laboratory. Note the frequency dependence and
regions where various types of interference occur. arm» 5'. @rzmng; CHEM 4369 The SignaltoNoise Ratio (S/N) The signaltonoise ratio (SIN) is the inverse of the relative
noise and is given by: where:
S is the mean value of the analytical signal (f) and
N is the rootmeansquare, or rms, noise (5) in the analytical signal, i.e., standard deviation of the signal derived from :1
measurements i iii92;.Invmv'ar‘” ’" . Note: if noise is what causes
w /  the uncertainty in the signal,
“=43  the signal—tonoise ratio is
the reciprocal of the relative
standard deviation \ , _~"‘r"‘;r.;.—rr."" . . .‘r'n " ll It'll} Itll'l Silt] Jiltl
liclﬂlL‘llL}. I'll.
Figure 52 Effect of signalto—noise on the NMR
spectrum of progesterone Ch513 ﬁrms» 5'. @ezmyw; CHEM 4369 SignaltoNoise Enhancement Two methods for improving the S l N ratio of an insrumental
method: 0 HARDWARE DEVICES and TECHNIQUES, in which noise
reduction is accomplished by incorporating into the instrument
design components such as filters, choppers, shields,
modulators, and synchronous detectors. 9 SOFTWARE METHODS, which are based upon various computer algorithms that permit extraction of signals from
noisy data collected digitally. These includes:  ensemble averaging  boxcar averaging  digital filtering  Fourier transformation
 smoothing  correlation techniques QM“ S. gfczmyw; CHEM 4369 Ensemble Averaging Digilnl llleI hui'mc pronminty. b) cliscm Ia]: titcragu 0 successive sets of data stored in
memory as arrays are collected and
summed point by point (coaddition) 9 the data are then averaged by dividing ‘ ‘ '
the sum for each point by the number I ' " ' “““"”'”‘
of scans (n) performed 1H _________ "it 1 l i '“h I‘llf:il;ti (lulu llllt‘l’ pruwnvugr It} unwmhlc .ncrnp: .\ \‘cmgr sinLinn” Havelcligili — Figure 59 Ensemble averaging of a spectrum. NOTE: The signalto—noise ratio is
proportional to the square root of the number of data collected to determine the ensemble average. Ch515 ﬁned“ @rzmym; CHEM 4359 Example: Signal Averaging ofthe NMR Spectrum (a) ‘  “an r I ‘t:n‘l_l'1_l._"II.$.I'A\Il mu. Rt! “1"” '11.. R has d h .6. “l'\L_.‘. Hr.M.‘JITJ;I,I Random fluctuations in the noise
tend to cancel as the number of
scans increases, but the signal
accumulates; thus, S / N increases. Problem 511 (SIN)50
(SIN)1 In progressing from (a) to (c)
the SIN ratio improved 7.1 times % after 50 scans, and 14.1 times
(S/N)1 after 200 scans. Figure 510 Effect of signal averaging. ﬁrm» 5'. gfczmyw; CHEM 4369 Problem 58: Calculating (a) SIN and (b) n to Improve S /N The following data were obtained for a voltage measurement, in mV,
on a noisy system: 1.37. 1.84. 1.35. 1.47. 1.10. 1.73. 1.54. 1.08.
(a) Assuming the noise is random, what is the signaltonoise ratio? (b) How many measurements would have to be averaged to increase
S/N to 10? B (a) 2 x. The mean for the data is: 36 = ' ‘ t The standard deviation is: .‘ — arm» 5'. @rzmng; CHEM 4369 Problem 58: Calculating (a) SIN and (b) n to Improve S /N The following data were obtained for a voltage measurement, in mV,
onanoisy system: 1.37. 1.84. 1.35. 1.47. 1.10. 1.73, 1.54. 1.08.
(a) Assuming the noise is random, what is the signaltonoise ratio? (b) How many measurements would have to be averaged to increase
S/N to 10? (b) ﬁma 5'. @rzmgww; CHEM 4369 ...
View
Full Document
 Spring '08
 asshole
 NPS, Johnson noise

Click to edit the document details