Anal. Chsm. l Q 8 2 , 54, 2590-2591
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50% and pyridine affected the amount of DCC required for the reaction, respectively. The present reaction needs only one reagent and proceeds under mild conditions, and so it is more simple than the two-reagent system of the pyridine-acetic anhydride method or o-aminothiophenol method, in which 125 OC and 15 h of heating are required. Moreover, in view of specificity, the present methods are excellent for citric and aconitic acids, because some polycarboxylic acids (especially,such as malonic acid) can fluoresce with tertiary amines in the presence of acetic anhydride (24, 25). Therefore, despite the similar sensitivity to that of pyridine-acetic anhydride method, the established methods are more amenable to specific routine work or automatic analysis. ACKNOWLEDGMENT The author thanks Zenzo Tamura and Hiroshi Nakamura, Faculty of Pharmaceutical Sciences, University of Tokyo, for their critical review of this manuscript and valuable suggestions. LITERATURE CITED Pellet, M. V.; Seigner, Ch.; Cohen, H. Pathol. Biol. 1989, 77, 909-914. Frohman, C. E.;Orthen, J. M. J . Biol. Chem. 1953, 205, 717-723. Yamamoto, D.; Kawamura, T. Me!//Dalgaku Ncgakubu Kenkyu Hokoku 1971, 26. 1-13. Hori, M.; Kometani, T.; Ueno, H.; Morimoto, H. Blochem. Med. 1974, 7 1 , 49-59.
(5) Massa, V.; Suspiugas, P.; Salabert, J. Trav. SOC.Pharm. Montpellier. 1974, 3 4 , 71-77. (6) Lang, H.; Lang, E. J . Chromatogr. 1972, 73, 290-291. (7) Chen, S . 4 . J . Chromatog. 1982, 238, 480-482. (8) Khorana, H. G. Chem. Rev. 1953, 5 3 , 145-166. (9) Mikolajczyk, M.; Kielbasinski, P. Tetrahedron 1981, 3 7 , 233-284. (10) Kasai, Y.; Tanimura, T.; Tamura, 2 . Anal. Chem. 1975, 47, 34-37. (11) Sheehan, J. C.; Hess, G. P. J . Am. Chem. SOC. 1955, 7 7 , 1067-1068. (12) Biout, E. R.; DesRoches, M. E. J . Am. Chem. SOC. 1959, 87, 370-372. (13) Albertson, N. F. "Organic Reactions"; Wlley: New York, 1962; Vol. 12, pp 205-213. (14) Khorana, H. G.; Todd, A. R. J . Chem. SOC. 1953, 2257-2260. (15) Khorana, H. G. J . Am. Chem. SOC. 1954, 7 6 , 3517-3522. (16) Decker, C. A.; Khorana, H. G. J . A m . Chem. SOC. 1954, 78, 3522-3527. (17) Corey, E. J.; Andersen, N. H.; Carbon, R. M.; Paust, J.; VedeJs, E.; Viattas, I.; Winter, R. E. K. J . Am. Chem. SOC. 1988, 9 0 , 3245-3247. (18) Aiexandre, C.; Rouessac, F. Bull. SOC.Chim. Fr. 1971, 1637-1840. (19) Alexandre, C.; Rouessac, F. C.R . Hebd. Seances Acad. Sci., Ser. C 1972, 274, 1585-1588. (20) Kllnman, J. P.; Rose, I . A. Biochemistry 1971, IO, 2259-2266. (21) Ambler, J. A.; Roberts, E. J. J . Org. Chem. 1948, 13, 399-402. (22) Pesez, M.; Bartos, J. Talanta 1989, 78, 331-336. (23) Moffatt, J. G.; Khorana, H. 0. J . A m . Chem. SOC. 1957, 79, 3741-3746. (24) Roeder, G. J . Am. Pharm. Assoc. 1941, 3 0 , 74-78. (25) Thomas, A. D. Talanta 1975, 2 2 , 865-889.
RECEIVED for review April 6, 1982. Accepted September 10, 1982. Presented at the Annual Meeting of the Pharmaceutical Society of the Republic of China, Taipei, Dec 1981.
CORRESPONDENCE Effect of Analog-to-Digital Converter Resolution on Absorbance Measurements Sir: The wide use of digital data acquisition in chemical instrumentation has led to an appreciation of the effects of amplitude quantization of signal-to-noise ratio. It has been shown theoretically that, under most experimental conditions, the effect of quantization is to add white or uncorrelated noise to the total signal noise and that the root mean square magnitude of the quantization is q/121/2, where q is the quantization interval (I,2). The derivation of this expression is given in ref 2 and will not be repeated here. It is of interest to inquire whether these theoretical predictions can be verified experimentally under practical laboratory conditions. We report here a method for measuring quantitatively the effect of quantization noise in experimental signals and demonstrate its application to absorbance measurements made with a continuum-source atomic absorption spectrometer. The method requires the acceptance of four basic assumptions. First, one must assume that noises add quadratically P=Q2+N2
(') where T is the total noise, Q is the quantization noise, and N represents all other noise sources such as photon noise, flicker noise, etc. Second, quantization noise must be assumed to be directly proportional to the Size of the quantization interval (2) Qs = 4Q10 = 16Q12 where Qs, Ql0, and QI2are the quantization noises for the 8-,
lo-, and 12-bit resolutions, respectively. Third, we must assume that all other noises are not a function of resolution. Fourth, it is necessary to assume that the quantization noise is smaller than other noise sources. On the basis of these four assumptions one can write equations for the total noise T with 8-bit and 12-bit quantization Ta2= Qa2 IF' = (16Q12)2 N2 (3)
+
+
T122= QlZ2+ IF' (4) where Taand T12represent the total noise for an 8- and 12-bit quantization, respectively. Both Ta and T12can be measured from one set of 12-bit data by masking the four least significant bits to get 8-bit data. Solving eq 3 and 4 simultaneously for Qlz yields
Values of Q for 10- and 8-bit quantization may be obtained from eq 2.
EXPERIMENTAL SECTION Measurements were made on a continuum-source atomic absorption spectrometer (3) which utilizes a 300-w sc source, a wavelength modulation spectrometer with a photomultiplier detector, and a 12-bit analog-to-digital(ADC) converter interfaced to a minicomputer. Intensities are measured directly by the ADC and are converted into absorbances by the minicomputer. Two types of noise measurements were performed:
0003-2700/82/0354-2590$01.25/00 1982 American Chemlcai Society
Anal. Chem. 1982, 5 4 , 2591-2593
Table I. Quantization Noise (mV) resolution
theoretical
exptl
8-bit
11.6
11.7 2.9
10-bit
12-bit
2.9 0.72
0.73
intensity noise and absorbance noise. Intensity noise is taken as the standard deviation of the intensity of the unabsorbed primary light beam, Io, sampled at a 1120 Hz rate for 10 s. Absorbance is calculated as the log of the ratio of the unabsorbed intensity, I,, to the absorbed intensity, I , where each of these intensities is the sum of IO successive samples, taken also at a 1120 Hz rate. Thus, absorbances are calculated at a 56 Hz rate. Absorbance noise is taken as the standard deviation of 1120 such absorbances measured over a 20-s interval. [n the measurements reported here, only base line absorbance noise is measured; thus Io and I are effectively equal, except for noise. A computer program, written in Fortran, acquires 12-bit intensity data, masks the two or four least-signifkant bits to simulate 10- and 8-bit data, and computes standard deviations for each case.
RESULTS AND DISCUSSION Direct Measurement of Quantization Noise. For a 12-bit ADC with a range of 0-10 V the theoretical quantization noise is 0.722 mV. Average raw intensity data obtained experimentally at 324.7 nm showed Tl, = 63.355 mV and TS = 64.420 mV. This provided a 12-bit quantization noise value of 0.730 mV using eq 5. Table I contains a comparison of theoretical and experimiental values. The agreement is excellent, in spite of the fact that the quantization noise is in this case a very small fraction of the total noise. Reduction of Quantization Noise by Averaging. The effect of averaging on the reduction of quantization noise was determined by averaging 2 to 50 successive intensity values and computing the quantization noise from the standard deviation of the means. The experimental values are in good agreement with the theoretical prediction. Base Line Absorbance Quantization Noise. All previously reported quantization noise measurements in this work were obtained by using intensity noise measurements (in mV). It is possible to predict absorbance quantization noise values in absorbance units by using the following expression:
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Table 11. Double Beam Absorbance Base Line Quantization Noise no. of
quantization levels 3850 1540 530
abs std dev theoretical exptl 0.000 015 0.000 037 0.000 11
0,000 017
0.000 0 5 0.000 1 2
absorbance quantization noises agree fairly well with the theoretically predicted values. The relative contribution of quantization noise to the total system noise obviously depends on the magnitude of the other (nonquantization) noises. The base line absorbance noise of UV-visible and atomic absorption spectrometers is typically greater than 0.0001 a. Thus, if 12-bit intensity resolution is utilized, quantization noise will typically be a small fraction of the total noise. However, if the effective intensity resolution is reduced, as for example by low reference energy in UVvisible absorption or by background absorption in atomic absorption, then, of course quantization noise becomes more significant. We have found that on our continuum-source atomic absorption system which uses a 12-bit analog-to-digital converter, quantization noise accounts for less than 7% of the total base line noise when the background absorption is 1.8, corresponding to an intensity resolution of one part in 530. It should be noted that in some types of spectrometers digitization occurs after log conversion. Clearly in that case the effect of quantization would be different. The present treatment is meant to apply only to those instruments in which log conversion occurs after quantization. Finally, the opportunity usually exists to reduce quantization noise (and other noise sources as well) by averaging. If low-frequency (flicker or l/f) noise is a significant part of the total base line noise, then averaging the intensity data may reduce the relative contribution of quantization noise, because quantization noise will be reduced by averaging like any white noise, while l / f noise is not much reduced by averaging.
LITERATURE CITED (1) Horiick G.Anal. Chem. 1975, 47, 353. (2) Kelly, P. C.; Horlick, G. Anal. Chem. 1973, 45, 518. (3) Harnly, J. M.; OHaver, T. C.; Golden, B.; Wolf, W. R. Anal. Cbem. 1979, 57, 2007.
N. J. Miller-Ihli T. C. O'Haver* where Q is the quantization noise in absorbance units, S is the number of quantization levels in the intensity measurements, & refers to the dlouble beam nature of the absorbance measurement, and dz refers to the fact that ten intensities were averaged to obtain both Io and I. By use of various incident intensity (Io)values, the base line absorbance quantization noise at 324.754 mm was measured. These results appear in 'Table I1 along with the theoretical results. In general, the experimentally determined base line
University of Maryland Department of Chemistry College Park, Maryland 20742
J. M. Harnly Nutrient Composition Laboratory United States Department of Agriculture Beltsville, Maryland 20705
RECEIWDfor review June 7, 1982. Accepted August 31,1982.
Optimal Experimental Parameters for Quantitative Pulse Fourier Transform Proton Nuclear Magnetic Resonance Spectrometry Sir: In pulse Fourier transform lH NMR spectrometry, the achievement of quantitative results and/or good spectral signal to noise ratios ( S I N ) is influenced by the choice of pulse flip angle (6) and the time between consecutive pulses (T) in 0003-2700/82/0354-2591$01.25/0
relation to the lH spin-lattice relaxation time ( T l ) . It is routine practice to optimize SIN by using a small pulse flip angle and a short time T , though such a procedure will not in general (see below) yield quantitative results. Further, 0 1982 American Chemical Soclety
