Enhancement of Signal-to-Noise Ratio by Continuous Averaging: Application to Magnetic Resonance

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Abstract
Spectroscopic investigations commonly involve a measurement of power as a function of some external parameters. It is usual, for improvement of signal‐to‐noise, to modulate the interaction between the radiation and sample and to apply the resulting signal to a synchronous detector followed by an integrating filter and a chart recorder. An extended search for a weak signal may require slow scanning rates and long time constants. Such a combination imposes severe requirements on the stability of the equipment, for any nonstochastic noise can frustrate a single scan by exceeding the dynamic range of the chart recorder. An alternative approach to the problem is to accumulate many relatively rapid scans of the full spectrum so that the signals add coherently whereas the noise adds randomly. The first approach may be termed frequency domain filtering while the latter is termed time domain filtering. Here we report an example of the latter approach employing a multichannel pulse‐height analyzer as a storage device. The voltage from the output terminals of a spectrometer (nuclear magnetic resonance or electron paramagnetic resonance) is converted to pulses, the pulse rate being proportional to the voltage. The channels are opened successively in synchronism with the progress of the magnetic field. Thus each channel corresponds to a finite region of the field while the number of counts in each channel is proportional to the time integral of voltage corresponding to that field. In such an arrangement the signal increases directly as the number of scans while the noise increases as the square root of the number. In effect the average response is computed continuously. The great dynamic range, 106 pulses/channel, precludes overloading or saturation effects. Since no long time constants are employed, low‐frequency noise is no longer the limiting factor in equipment performance. We present spectra, resulting from many thousands of scans, which demonstrate that signal‐to‐noise ratios may be enhanced by one to two orders of magnitude without sacrifice of bandwidth.

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