simple noise level digitizer
TRANSCRIPT
Simple noise level digitizerDon J. Latham Citation: Review of Scientific Instruments 51, 148 (1980); doi: 10.1063/1.1136043 View online: http://dx.doi.org/10.1063/1.1136043 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/51/1?ver=pdfcov Published by the AIP Publishing Articles you may be interested in A simple method for estimating the noise level in a signal region of an MR image Med. Phys. 37, 5072 (2010); 10.1118/1.3480511 Investigation of basic imaging properties in digital radiography. 13. Effect of simple structured noise on thedetectability of simulated stenotic lesions Med. Phys. 16, 14 (1989); 10.1118/1.596391 Simple fast transient digitizer Rev. Sci. Instrum. 52, 297 (1981); 10.1063/1.1136554 Simple digital waveform synthesizer Am. J. Phys. 44, 710 (1976); 10.1119/1.10170 Simple Digital Correlator Rev. Sci. Instrum. 29, 487 (1958); 10.1063/1.1716232
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Simple noise level digitizer
Don J. Latham
Forest Service. u.s. Department of Agriculture. Intermountain Forest and Range Experiment Station. Northern Forest Fire Laboratory. Missoula. Montana 59806
(Received 2 August 1979; accepted for publication 11 September 1979)
A simple, high-precision technique for measuring the rms value of noise signals is described. The technique is based on a statistical theory relating the number of threshold crossings of a noise signal to its variance.
During the course of an experiment to study radio noise from thunderstorm clouds, we developed a simple highprecision technique for measuring the rms value of noise signals from our radiometer. This technique does not use a conventional digital-to-analog (DI A) converter, but enables low-cost acquisition of the digital data value by microcomputer or minicomputer.
The optimum detector for Gaussian noise imbedded in Gaussian noise, i.e., a noise signal added to the system noise, can be shown to be an assessment of the variance of the signaI. 1
-:l This is usually found by smoothing the
output of the square law detected signal with simple, low-pass filtering; this method is easily accomplished and commonly used in radiometric measurements. 4
We wanted to have the signal in digital form for data processing; so rather than digitizing the output of a conventional radiometer system, we applied a statistical theory relating the number of crossings of a noise signal through an arbitrary threshold value to the variance of the signal. We replaced the square-law detector with a multiplier and second local oscillator, followed by a low-pass filter. This procedure gives a low-passed zeromean Gaussian noise signal.
Rice" showed that the number of positive-going signal crossings per unit time (n) of a threshold value (v) is related to the number of positive-going zero crossings per unit time (N) and the variance (or the square of the rms value) of the noise signal (0):
11 = N exp( ~v2/20) (1)
(Fig. 1). N is a function of the bandwidth of the filter placed between the noise input (broadband) to the system and the threshold detector.
Our implementation of this relationship is shown in Fig. 2. It consists of a comparator, a DI A converter for
THRESHOLD EXCEEDED
ZERO VOLTS fA-j~f.IA ..... -+-I~f-f4,...--f-If-:-++-:,..----
FI(;. I. A representative input signal.
setting the threshold (8-bit resolution), and a counter. The counter and DI A converter were interfaced to a small microcomputer and treated as memory locations. The microcomputer was programed to handle the DI A converter and counter either in BASIC or FOCAL as needed. There is nothing extraordinary about any of the components used and there may be better choices for some of them.
The technique was tested by replacing the output of the radiometer system with a random noise generator. A sample of the results is shown in Fig. 3. The number of zero crossings per second in the positive direction (N) is not simple to calculate from the characteristics of the generator. We can only compare the curve shape for the theoretical crossing rate with the experimental points. In doing so, we must consider that: (l) the meter on the noise generator is only good to 3% of full scale at best, (2) the generator output is "white" noise only from 20 Hz to 20 kHz, and (3) the comparator exhibits some hysteresis. Even so, the agreement is good enough to justify use of the technique.
The chief advantage of this technique is that a very high precision measurement is possible without the expense of a precise AID converter. In addition, changes in configuration are made by software changes in a highlevel language. Note that the D/A converter need not have even 8-bit precision, but must be very stable. If accuracy is required, the DI A converter voltage steps must be carefully calibrated and the comparator hys-
FIG. 2. Adjustable threshold microcomputer/counter interface.
148 Rev. Sci. Instrum. 51(1), Jan. 1980 0034-6748/80/010148-02$00.60 © 1980 American Institute of Physics 148
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N I £ Q)
3000
2500
2000
20 kHz lo-pass noise 1V RMS
x -experimental - -theory
t;; ex: Ol c
FIG. 3. Sample output of the test.
iii If)
e u
1500
1000
5.00
0.00 20 .40
Threshold Voltage (Volts)
.60 .00 1.00 1.20
teresis should be very smalL Of primary importance is the comparator response time, which obviously must be faster than the highest frequency component in the noise.
We are still investigating the relative sampling times necessary to reach the same confidence levels in the rms value using the AID converter and our technique. Even if a longer sampling time is necessary for our technique, its simplicity remains attractive.
140
x
1.60 1.00
1 C. w. Helstrom, Statistical Theory of Signal Detection (Pergamon, New York, 1968).
21. C. Hancock, and P. A. Wintz, SiRnal Detection Theory (McGraw-Hili, New York, 1966).
3 D. Middleton, An Introduction to Statistical Communication Theory (McGraw-Hili, New York, 1960).
4 R. S. Colvin, ., A study of radio-astronomy receivers," Report 18A, Stanford Radio Astronomy Institute (1961).
, S. O. Rice, Bell System Tech. 1. 27, 109 (1948).
DeSign, description, and application of a micromanipulator suitable for use in closed systemsa
)
C. van Netten and P. Belton
Department of Biological Sciences, Simon Fraser University, Burnaby, British Columbia, Canada
(Received 21 August 1979; accepted for publication 8 October 1979)
A design for a compact micromanipulator is presented. The range and sensltlVlty of movements it provides are comparable with large, benchmounted instruments, yet several of these micromanipulators can be mounted in a small chamber holding an electrophysiological preparation. With the use of such a chamber the environment of its contents can be closely controlled yet access is maintained at all times.
Commercially available micro manipulators cannot be used in restricted areas or in a closed system so that, for example, radioactive solutions can be passed over a preparation without leakage with the system in any position. Attempts to make a closed system have been made, for instance, by floating a layer of paraffin oil over the saline covering the preparation for the measurement of exchange of radioactive potassium in crab nerve.!
Several micromanipulators were built and tested for use in experiments designed to correlate electrical activity of living cells with other physical parameters. Some of these experiments must be carried out in extremely restricted areas such as chambers of scintillating counters or spectrophotometers. A further requirement is that the electrodes are inserted into cells under the dissecting microscope and then the pre para-
149 Rev_ Sci_ Instrum. 51(1), Jan. 1980 0034-6748/80/010149-02$00_60 © 1980 American Institute ()f Physics 149
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