Topics in..
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Chemical Instrumentation
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tdited by GALEN W. WING, Seton Hall University, So. Orange, N. J. 07079 These articles are intended to s e w the readers O ~ T H I JOURNAL S
by calling attention to new developments i n the theory, deuign, or availabililyp/ chemical laboratory instrumentation, or by preanting usejul ingights and ezplanations o j topics that are of practical imporlance to those who use, or teach the use of, modern instrumenlation and instrumenfa1 techniques. The ediror invites correspondence from prospective contributors.
LXXIV. Signal Averagers Robert L. Rowell.. Deoartment of Chemistry, University of Massachu. setts, Arnherst, M A 07002 Earlier articles (1.2) in this series have treated lock-in amplifiers. A lock-in amplifier is an instrument for the measurement of the amplitude of ac signals in the presence of noise. In operation the ac information-signal is amplified and then rectified (or demodulated) by a switching signal of the same frequency as the information signal so that a dc output is obtained. The dc output is proportional t o the ac amplitude of the information signal which is a t a single frequency and receives essentially no contribution from all other "noise" frequencies. Some signal averaging takes place in the process in that the dc output signal is low-pass filtered. In fact, a simple RC filter is the simplest kind of signal averager. The purpose of signal averaging is to improve on the reproducibility and precision of the measurement of a waveform. This is done by accumulating and superimposing a large number of repetitive measurements so that the signal increases linearly with the number of repetitions whereas random fluctuations will algebraically add to zero. It follows that in any signal-averaging application i t is necessary t o insure that the signal is as pure an additive component as possible and that the averaging is carried out over a sufficiently large number of repetitions that the fluctuations are randomly distributed. The signal to be averaged is generally a waveform or single sweep which is a measurement of some variable, usually as a function of time. However, a dc signal may also be averaged by making a waveform or sweep by a continuous recording with time and then averaging the waveform. Signal aueraging. The method of signal averaging is to sample and digitize a signal a t frequent intervals and store the array of measurements from a single sweep in a multichannel memory. The simplest approach to signal averaging is to merely accumulate successive repetitions of an input sweep in the multichannel memory. In this way, after a large number of sweeps, the signal or regularly occurring information will build up to a large value whereas random fluctuations will accumulate less rapidly and add to a small value in comparison to the signal. This last
point is crucial to the success of signal averaging. If there is a large coherent noise component present it will add along with the signal and there will be no net gain obtainable by signal averaging. Noise. If the signal S is the average value of a large number of measurements N then the noise n may be represented by mot-mean-square (rms) deviation from the mean
If enough measurements are taken to obtain a representative average signal then doubling the number of measurements would not change the average but it would double the accumulated signal. However, the rms noise varies as 1/\/10 so that doubling the number of measurements would lower the noise by \/XThis implies that the rms deviations remain constant as the number of measurements is doubled. Under these conditions the signal-to-noise ratio will be improved in proportion to
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Sign01 purity. The averaged signal can be no better than the best error free signal. Hence it is important to remove inherent additive systematic error contributions either by design of the apparatus configuration or by a separate backgraund or blank run. Such unwanted signals include drift, dc offset, dark current, background intensity, etc., which can be removed by signal averaging only if they can be separately measured or isolated from the measurement. If the unwanted dc component is unavoidably mixed with the signal it must be constant for the measurement and background runs or must show the same pattern far each. Gate and srueep. A given signal may he averaged by overlaying successive sweeps N times so that each paint on the waveform is measured N times. Each point, however, has same finite time period which is called the gate, and a single sampling of one point is really an average over the gating time or dwell time. One can also lower the noise by integrating during the dwell time which will lower the high frequency noise in proportion to \/;where r is the dwell time. This is seen by analogy with the \/m factor obtained above. The
Dr. Robert L. Rowell is Associate Professor of Chemistry a t the University of Massachusetts, Amherst. He received a B.S. Ed. in scieneemath education from Bridgewater State College in 1954, an M.S. in physical chemistry from Boston College in 1956 and a Ph.D. in phpical chemistry from Indiana University in 1960. He was organizer and first Director of the University of Massachusetts Research Computing Center and an IBM Postdoctoral Fellow a t the M.I.T. Computation Center in 1963. He was co-chairman of the Second Interdisciplinary Conference on Electromagnetic Scattering in 1965 and Chairman of the 46th National Colloid Symposium in 1972. He has held offices in the Southern Indiana and Connecticut Valley Sections of the American Chemical Society and is currently National Secretary of the Division of Colloid and Surface Chemistry. He has authored numerous journal articles on light scattering and is co-editor of Electromagnetic Scattering, Gordon and Breach Science Pub., 1967. During 1973-74 he is on leave at the University of Bristal, England. under a Science Research Council Senior Visiting Fellowship, doing research in colloid chemistry and completing a chapter an "Particle Size Distribution" for Surface and Colloid Science to be published by Wiley-Interscience. His research interests include digital computers applied to chemical problems and laser light scattering from molecular and colloidal systems with current emphasis on determination of particle size, shape and concentration in growing systems in the polymer colloid range. total reduction of uniformly distributed broadband noise can be expected not to exceed a factor proportional to which is proportional to the square root of the total power level. Noise frequencies intermediate between the gate frequency and the sweep frequency tend to average out with (Continued on pogeA72) Volume 51, Number 2. February 1974
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Chemical Insfrun~entcrtion successive sweeps. However, noise frequencies lower than the sweep frequency will add to the base line of the sweep and in a long-time average approach a constant which may be eliminated by subtraction. Very low frequency noise has a power spectrum which is approximately proportional to l/f so that it is termed one-over-f noise or flicker noise. Flicker noise is common in most amplifiers and in almost all instrumental systems where i t is usually recognized as "drift." Superposition. Implied in the concept of signal averaging is the idea that the set of digital information to be averaged is not systematically modified in repetitive sweeps and that each set or sweep may he exactly superimposed on the previous set. This requires that a trigger link be available hetween the experiment and the measurement so that the measuring sweep is exactly phased to a given point on the signal cycle. The trigger may be internal in which case a pulse is available from the instrument to start the sweep and initiate the experiment cycle. Alternatively an external trigger pulse may be supplied by the experiment t o initiate the experiment cycle and start the measuringsweep. Data reduction. A true signal averager will not only accumulate sweeps but reduce the data by the number of sweeps so that a true average is obtained. The simplest signal averager is in effect a digital computer with a limited instruction set. Clearly any high speed general purpose digital computer can be programmed to signal average but the availability of a suitable interface t o the experiment may not be a trivial problem. Signal averagen may include additional simple data reduction features such as subtraction of one block of memory from another, integration over a memory block, differentiation aver a memory block, three-point smoothing and the like. Memory. One form of memory is the magnetic core memory which is usually available in blocks of 1024 storage locations or words. Word lengths are typically 12, 16, 18, 20 or 24 bits. Each bit is about the size of a period, a small doughnutshaped piece of ferrite called a magnetic mre. Wires passing through a core carry a current to magnetize the bit on or off (1 or 0) according to the direction of the eurrent. The 12 bits of a word have binary place value such as 2', Z1, Z2 etc. A 12-bit word can accumulate 212 or 4096 units whereas a 20-bit word can accumulate to ZZO or 1,048,576, If memory is fed, for example, with a 9-hit digitizer then the range in signal in a single sweep is limited t o 29 or 512. The ferrite magnetic-core memory has reigned supreme for two decades over similar magnetic devices such as plated wire, ferrite sheet and ribbon-like devices. A newer form of memory is the capacitor memory made possible by the fast gate and switch action of field effect transistors (FET). The range of the memory is dependent on the size of the capacitors and the increments accumulated in a single sweep are determined by RC time constants which may be varied by the user to optimize the data collection. A72
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Developments in solid-state technology have also resulted in the semiconductor random-access memory (RAM). In particular the emersine metal oxide semieonductor IMOS;' rerhnolc,gy provided the first cornpetitwe semwunductvr prudurt ~n a market that was served by magnetic core elements. The basic MOS memory stores information in binary form (1 or 0) in a flip-flop cell that consists of two semiconductor amplifiers, one in a n "on state" and one in an "off state." For example, some of the earliest configurations had 30,000 memory bits and associated access circuitry on a 30x40 cm board for an average density of 25 bits/em2. Bit densities and access time have improved enormously and are continuing to improve. In fact, there is a n active competition in the memory field which has already had impact in the minicomputer market and will continue to have impact there and in the developing field af signal averagers. For example, the latest forecast (3) is for a n eight-chip 32,768-bit memory module in a single 1.5-byd-inch package which amounts to s hit-density of 1600 hits/cm2. At the same hit-density it is also possible to provide 256 bits of a RAM/MOS array on a single chip measuring 0.146 in. by 0.164 in. Signal ouerager and computer. It should he clear from what has already been said that the application and development of signal averagers is closely related to the developing computer and minicomputer industry. In fact i t is becoming increasingh difficult to draw the line between signal &wagers and small laboratory computers. Some useful criteria for decisions along these lines have been reviewed elsewhere (4). In a broad sense, signal averaging is a simple kind of computational technique in which a correlation is made between successive repetitions of a waveform taken a t different times. Signal-to-noise enhancement and correlation techniques for achieving that end have received much consideration in the field of infomation theory. The problem has been recently reviewed from that standpoint with applications to analytical chemistry (5). Boxcar Integrator. The boxcar integrator has been called the "poor man's signal averager" (5). It is similar to the lock-in amplifier and the signal averager and may perform similar functions depending on its application. In essence, it is a single-channel signal averager with a sampling gate that can be opened for a variable and preselected time and synchronized to a particular portion of a repetitive waveform. At a fixed delay between synchronizing signal and sampling gate the same portion of a waveform is sampled for each sweep of the entire signal. The successive samples are then averaged by a low-pass filter to give signal-to-noise enhancement for that portion of the signal which is sampled. The idea of the technique is summarized nicely in its name. Imagine a railroad train made up of many cycles of boxcars each cycle of which includes a red car, a n orange car etc. throughout the spectrum. One can characterize the freight load by adding up the contents of all of the red boxcars. To complete the job however, one would have to add uo the contents of all of r h ~ or~11p.ecam. then the yellou cars etr. In the same way, a boxcar inlrgraror may be fitted uirh a rrnn r n d e so that the gate
can he slowly scanned across a repetitive signal. The total waveform can then be reproduced a t the output but clearly in a much longer time than the period of a single sweep. The signal averager is then a multi-channel boxcar integrator which, in terms of our analogy, is like having a counter for each colored box ear in simultaneous operation. If this analogy is not educational, it is certainly training. Other literature. It should now be clear that there is a spectrum of data-handling and computational techniques that range from the lock-in amplifier through the boxcar integrator, signal averager and mini-computer to the large scale computer that is directly interfaced to a Laboratory experiment. To the list of references which have been touched on above (1-5) we would add one more on signal averagers (6). In perspective, we would also point out that the signal averager is right in the middle of the hardware interface that is developing to link the large-scale computer to the laboratory experiment. In addition the signal averager stands on its awn as a link between scientist and experiment. Clearly, signal averagers have found numerous applications which could not adequately be covered here. Reference should be made however to the applications to sensitivity enhancement in magnetic resonance experiments (7) which lead one into the burgeoning field of Fourier transform spectroscopy. The reader who is interested further in the impact of semiconductor technology on memories should consult a recent article in this series giving an introduction to microelectronics (8).
COMMERCIAL EQUIPMENT Signal averaging can be done on a wide range of equipment from a boxcar integrator to a complex data pmessing system utilizing a minicomputer. Below we discuss a representative selection from a market that is undergoing rapid development spurred by scientific needs on anehand and advances in solid state technolow and the minicomputer field on the other. Hewlett-Paekord 5480B. In the 5480B Signal Analyzer the waveform is sampled a t 1000 points an each sweep using a 24-bit memory word for storage. Signal averaging may be carried out in three ways. In calibrated averaging the waveform is averaged as i t is gathered for a preset number of sweeps so that the display always remains the same size. Weighted averaging is similar to calibrated averaging but the averaging is continuous with a fixed weighting on new data after a selected sweep number count has been passed. In this mode the old data diminishes exponentially in weighting so that changing waveforms may be observed. This is useful when making adjustments on a source or when monitoring a source under test. Finally there is simple accumulation or summation averaging in which the display grows as the data is continuously summed for a preset number of sweeps. An additional feature allows selection of automatic scaling as each power-of-two sweep number is passed. In calibrated or weighted averaging a noise signal may be displayed. The noise for each point on the waveform is the (Continued on page A78)
Chemical Instrumentation
Figure 1. Hewlett-Packard Model 54808 Signal Analyzer: up to four different signals may be averaged simuitaneously. (Courtesy 01 HewleftPackard)
difference between the input signal and the average for that point. A variance circuit provides an output derived from the noise signal which is proportional to the square of the noise signal over a selected memory segment. Memory may be selected in quarter or half segments so that four different waveforms may be stared sequentially or alternatively up to four different
1000 pbint resolutionas well as waveform recoverv bv sveraeine. Cross-correlation of
ing, output connectors are provided for a plotter, teleprinter, tape punch or, under options, magnetic tape and telephone data terminal interface. The 5480B may he interfaced to a n onsite minicomputer as in the 5481A Signal Analyzer System. An averaged signal may then he fast Fourier transformed by the minicomputer and the frequency data may be displayed in half or quarter segments of memory permitting comparison of up to four sets of data. Honeywell. The Honeywell SAICOR SAI-43A Correlation and Probability Analyzer provides real-time computation in three primary operating modes: Correlation (auto and cross), Enhancement (signal recovery) and Probability (density and diitribution). A 400-paint analysis is accomplished in all three modes with a minimum gate of 0.2 ps or a 5 MHz sampling rate. In autocorrelation a signal is compared with a time shifted version of itself. In cross correlation the similarity between two signals is determined as a function of the time shift between them. In enhancement or signal averaging the waveform is
divided into 400 successive pulses that can be linearly averaged or exponentially averaged in addition to the continuous aperation (accumulation) mode. An internal or external synchronization pulse starts the sweep and an 800-point precomputatian delay may be inserted between the sync pulse and the start of the waveform to be averaged. The all digital MOS FET memory consists of 400 29-bit words. Exponential rRC) averaging is accomplished with a sliding time base which constantly updates the memory with new information while dropping off old information. Two identical independent channels are provided for signal input with 8-bit quantization. Tape punches, digital printers, teletype machines as well as the corresponding interfaces are available for output. There are two probability modes of operation, In Probability Density mode of the A/D converter (9 bits1 digitizes the amplitude of each sample a t the input to one part in four hundred. The converted amplitude corresponds to the bin number into which a single count is inserted. In the Probability Distribution mode counts are inserted into all bins equal to or greater than the digitized amplitude value. Nicolet 1020A. The model 1020A time averaging system, Niealet Instrument Corporation, has been developed for use with nmr and epr magnetie/resonance speetrorneters. It has been specifically de' signed for use with Bruker, Hitachi, JEOL, Perkin-Elmer and Varian spectrometers and has built-in interfaces for those units. The 1020A has a normalized signal feature so that the signal does not grow but the noise decreases. This allows up to 8192 sweeps with a 24-bit word length. The digitizer resolution is 12-bits (1 part in 4096) for sweep times over 1 second and 9 hits ( 1 part in 512) far sweep times less than 1 second. Sweep times range from 60 ms to 1999 ms in 1 ms inerements or from 1 to 1999 s in 1 s inerements. The sweep can also be controlled by a n external clock signal which can be reduced by any integer from 1 to 1999 by panel thumb-wheel switches. Two 1024word memory blocks are used with a third 1024-word block available far storage in the data-transfer mode. The 1020A can also supply the sweep current to the spectrometer in widths of 25, 50, 100, 250, 500, or 1000 Hz or optional 30, 60, 120, 300, 600 or 1200. An unwanted de level shift may be subtracted from the display and the
ur Figure 2. Haneyweil SAICOR Model SAi-43A Correlation and Probability Analyzer: three principal modes are enhancement. correlation and probability distribution. (Courtesy of Honeywell)
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Figure 3. Nicolet 1020A S g n a Averaging System: specifically designed for use with a broad range of nmr and epr spectrometers. (Courtesy of Nicole: lnsfrurnen: Corporafion)
Figure 4. Nicolet 1070 Series Instrument Computer (formerly Fabri-Tek Instruments. inc.): special features include push-button 3-point smoothing, add +K, integrate X D and differentiate. (Courtesy of Nicole! Inslrurnent Corporation)
spectrum may be integrated with 12 normalization constants ranging from 2' t o 2-" with preservation of the original spectrum. The complete spectrum or expanded portions of it are continuously shown on a 5-in. CRT display throughout the averaging process. Nicolet 1070. The 1070 series. Nicolet Instrument Corporation, has a number of computer-like features beyond that of simple signal accumulation. The basic 1024 18-bit-word memory may be upgraded to 4096 words and has a full cycle time (readadd-write) of 2.5 ps. Versatility is achieved with a wide range of plug-ins: there are. 1, 2 or 4 input signal digitizers, digitizers with up to 12 bit resolution and others with time resolution down to 1 ps. There are also plug-ins for auto- or erosscorrelation work, pulse height analysis, multichannel scaling and for a variety of time interval measurements. The 1070 series may be interfaced with mast minicomputers or the NIC-80 series 20-bit word length processor offered by the manufacturer. In addition to data accumulation and additive transfer the following data reduction operations can be performed: 3point smoothing, add *K, integrate XD and differentiate. Nicolet 1080. The 1080 System was designed with the special requirements of Fourier transform nmr in mind. In addition to being a signal averager it is also a completely general purpose stored program computer. It has a 20-bit word length that allows the identification of peaks ranging over five orders of magnitude and the accumulation of several hundred thousand sweeps without memory overflow. Timing responses are accurate to 100 ns with a sampling interval and delay time adjustable from 0 to 99.99 s in one microsecond steps with 4 digit accuracy. Hard-wired data acquisition circuitry allows viewing of the input signal and the entire averaged signal. Time domain signals may be sampled a t rates up to 100 kHz which permits averaging and transformation of signal frequencies up to 50 kHz with 12 bits of vertical resolution. Interfaces to highspeed analog-to-digital converters and buffers are available to extend the sampling rates to 1W MHz. Memory may be expanded in 4k increments to 40k with an additional 6Wk disk system available for spectra and program storage. The system comes with a Fast Fourier Transform nmr program including routines for baseline (Continued onpageA82)
Chemical Instrumentation
.. Figure 6. P.A.R. Boxcar Integrator Model CW-I; gate width is adjustable from 1 microsecond to 110 milliseconds. (Courtesy of Princeton Appiied Research Corporation)
Figure 5. Nicolet 1060 Data Acquisition and Processing System; designed with the special requirements of fast Fourier transform in mind. (Courtesy of Nicolet Instrument Corpoialian)
correction, digital filtering, Fourier transformation, semi-automatic phase correction, integration, peak printout, display expansion and constant speed plotting. Training in use of the program is part of the on-site installation. P.A.R. Boxcar Integrators. The boxcar integrator is a single channel device which allows recovery of very short pulses or waveforms from noise. It has a variable width integrator with variahle delay between integration periods so that any point on a repetitive signal may he examined. There is also a scan mode which allaws the integration gate ta be slowly scanned across the input waveform giving in effect a multichannel equivalent a t the expense of a longer measuring time. Two models are available from Princeton Applied Research Corporation, model CW-1
and model 160. The gate width of the CW-I is adjustable from 1 ps to 110 ms. The model 160 is for faster signals so that the gate width may be as small as 10 ns or as long as 0.55 s and offers additional features such as digital storage for experiments involving long information holding times. Repetition in either instrument is governed by the frequency of an external trigger pulse whieh initiates the time base. Further details regarding the operation and applications of the Waveform Eductor and boxcar integrators are available from the Princeton Applied Research Corru.--.--.
P.A.R. Woueform Eduetor TDH-9. The Waveform Eductor (trademark) introduced by Princeton Applied Research Cororation is a good approximation to a true analog signal averager. The input waveform is divided into one hundred time segments by field effect transistor (FET) gates which control one hundred channels of capacitor memory. The memory bank can he continuously monitored an an oscilloseape and it can be read out through a smoothing circuit a t slow speed on to a recorder. Both internal and external synchronization are available. The FET gates
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Figure 7. P.A.R. Boxcar integrator Model 160: gate width may be as small as 10 nanoseconds or as long as 0.55 seconds. (Courtesy 01 Princeton Applied Research Corporation)
allow very low leakage from the memory capacitors (typically 1% in 30 minutes). The instrument is designed t o provide full scale output with an input noise/signal ratio of 411 and a t reduced signal output can be used to extract meaningful data from noise/signal input levels in the range of 4011 to lM)/l. The principal limitations are internal instrument noise and drift specification whieh is 0.2% full scale per hour a t a constant ambient temperature. Sweep time may be as short as 100 ps (1 ps per channel) or as long as 11 s with a variable delay between sweeps of 10 ps to 11 s. Recorder readout sweep is fixed a t 100 s. OMA 1205. SSR Instruments Ca., a suhsidiary of Princeton Applied Research Corp., has developed an optical multichannel analyzer which may he used to collect and signal average optical signals so that with suitable input optics one has an "electronic photographic plate." Input is a silicon vidicon target area 0.5 X 0.2 in. on a television camera tube. The target is divided into 500 channels, each 0.001 X 0.2 in., that are sequentially and completely scanned in 32 ms. An equivalent target area is used for dark current. and stray light subtraction. The amplified vidicon signal is digitized and recorded in one of two MOS shift register memories with a work length of 5 BCD digits or lo5 counts. The contents of each 500-word memory may be displayed directly or a digital suhtraction of one memory from the other may he performed prior to display. Tektronix P7001. The Tektronix PI001 digital processing oscilloscope can digitize any signal displayable on a 200-MHz general purpose oscilloscope using 4000 words of 10 bit core memory. It can store up to four digitized waveforms, associated parameters and messages. Thirteen user-definable program call buttons permit the operator to call prestored computer-measurement programs from an associated minicomputer. At the push of a button a waveform buried in noise will be automatically averaged and rescaled for display. Similarly the derivative of a waveform may be ohtained or a fast Fourier transform (FFT) program may be called to give
Figure 8. P.A.R. Waveform Eductor Model TDH-9: very nearly a true analog signal averager with a sweep time that may be as short as l o o microseconds (1 microsecond per channel) or as long as 1 1 seconds. (Courtesy of Princeton Applied Research Corporation1
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Figure 9. SSR Instruments Co. Model 1205 Optical Multichannel Analyzer: the dispersion optics and silicon vidicon input provide in effect an "electronic photographic plate" for signal averaging of spectra. (Courtesy of Princeloo Applied Research Corporation)
a display of frequency distribution. The system includes a Tektronix Type 7704A oscilloscope and a Digital Equipment Corporation PDP-11 general purpose minicomputer. A wide range of plug-ins are available for the oscilloscope. All signals are routed through a Processor that cantains 4k words of 10-bit care memory. A waveform occupies 512 words of storage and a new sample may be processed every 6.5 ps. Thirteen push buttons on the Pracessor can be set up by the operator t o execute calculations using the included software. The software is a modified BASIC computer language available in one form for the 8k minicomputer and another form for the 16k minicomputer. JEOL. The JEOL EC-100 is advertised a s a real-time data processing system and as such it is far more than a signal averager. It was designed with Fourier transform and other analytical tasks in mind. It is currently being used with all models of the JEOL Fourier transform NMR systems. It has a basic 4k 16-bit wordlength MOS memory with hardware double precision in the central processing unit. It is really a computer system and signal averaging is
Figure 10. Tektronix P7001 Digital Processing OSCilloSCope System; a combination at general purpose o ~ ~ i i l o s ~ o with p e a wide range of plugins and a general purpose minicomputer linked through a push-bufton Operated processor. (Courtesy of Tektronix, Inc.)
only one function that can be done under software control. Thus it may he interfaced with auxilliary processing devices and high speed peripherals. It is mentioned here primarily for comparison with the larger systems such as the Nicolet 1080, the Tektronix PI001 or the H P 5481A and to illustrate the hardware developments resulting from advances in MOS technology and the minicomputer field.
REFERENCES (1) T. C. O'Haver. "Lack-in Amplifien-Part Chem Edue.. 49,A13L (19721. (21 T. C. O'Haver. "Loek-in Amplifiers-Part Cham. Educ.. 49, A211 119721.
I," J. 11,'' J.
Figure 11. JEOL EC-100 Real-Time Data Reduction System: designed with fast Fourier transform NMR and other anaiyticai tasks in mind. (Courtesy 01 JEOL) I31 P. Ransan. "Core Memories Am Still On Top." Elecimnics. 46 (No. 31. 69 119131. I41 J. W. Cooper. "The Computer and Signsi Average, in the Laborstory," Amwicon Lobomlow. 4 (No. 91 10(1S721 ,~~ -, ~~
I51 G. M. Hiaftjc, "Signal-fo~Noias Enhancement Thmugh Instrumental Techniques." A~llytical Chemlsfw, 44 (No. 6) 81A lL972): ibid. Pf. n.. 44 (No. 71, 69A (19721. (61 C. A. Nittrouer, "Signal Averagers." Princeton Ap. plied Research Cow. Tech. NofsT-162A (19681. I71 R. R. Emst. "Sensitivity Enhancement in Magnetic k n a n e e , " pp. 1-135 in Advoncrs in Magnetic Resononce. J. S. Waugh. Ed., Academic press. Now York, 1966. IS1 E. M. Winkler and M. van Swaay. "An Introduction t o Micmoioctmnics." J Chem. Edue. 50, A325. W63.A394 (19731.
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