chap5 instr - CHAPTER FIVE SIGNALS AND NOISE CHEM 4369 Two...

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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. 0-55- 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?" Figures-1 Efiectofnmseonacurrentmeasurement: (a) experimental strip-chart recording of a 09:40-15 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- mean-square (rms) or 9 as peak-to-peak (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 peak-to-peak 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 one-fifth of the peak-to-peak 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 signal-processing 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 mean-square 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 (low-frequency 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 radio-frequency 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 5-3 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 Signal-to-Noise Ratio (S/N) The signal-to-noise 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 root-mean-square, or rms, noise (5) in the analytical signal, i.e., standard deviation of the signal derived from :1 measurements i iii-92;.Invmv'ar‘” -’" . Note: if noise is what causes w / - the uncertainty in the signal, “=43 - the signal—to-noise 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 5-2 Effect of signal-to—noise on the NMR spectrum of progesterone Ch5-13 firms» 5'. @ezmyw; CHEM 4369 Signal-to-Noise 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 pron-minty. b) cliscm Ia]: tit-cragu 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 sin-Linn” Havelcligili —- Figure 5-9 Ensemble averaging of a spectrum. NOTE: The signal-to—noise ratio is proportional to the square root of the number of data collected to determine the ensemble average. Ch5-15 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 5-11 (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 5-10 Effect of signal averaging. firm» 5'. gfczmyw; CHEM 4369 Problem 5-8: 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 signal-to-noise 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 5-8: 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 signal-to-noise ratio? (b) How many measurements would have to be averaged to increase S/N to 10? (b) fima 5'. @rzmgww; CHEM 4369 ...
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This note was uploaded on 12/12/2008 for the course WHO CARES 23948 taught by Professor Asshole during the Spring '08 term at University of Houston.

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chap5 instr - CHAPTER FIVE SIGNALS AND NOISE CHEM 4369 Two...

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