Ensemble signal-averaging

Figure 23.38. Ensemble signal averaging. In this example, the signal-to-noise ratio increases from about 25 to about 800 with averaging. From S. P. Perone and D. O. Jones, Digital Computers in Scientific Instrumentation, New York McGraw-Hill, 1973, by permission of the publisher. Copyright 9Ti by McGraw-Hill, Inc.

Figure C3.5.4. Ensemble-averaged loss of energy from vibrationally excited I2 created by photodissociation and subsequent recombination in solid Kr, from 1811. The inset shows calculated transient absorjDtion (pump-probe) signals for inner turning points at 3.5, 3.4 or 3.3 A.

The polarization dependencies in the signal were reduced to an ensemble average in the quadrupole alignment term which was dependent on... 

Here we have introduced N(a>) as the Fourier transform of the noise n(x). Frieden assumed a simple triangular form for t(co) and constant noise-to-signal ratio for all frequencies. Goldman (1953) provides an appropriate discussion of ensemble averages and the like. 

In order to describe the signal observed, it is necessary to average over the canonic ensemble of N identical particles j, or, in other words, to pass over to the density matrix Jmm [73]. The oscillatory term does not disappear after such a procedure, because at pulsed excitation all excitation moments are synchronized. 

The signal to noise ratio for an individual spectrum is given in Table II. The methods of acquisition were either A (single spectrum acquisition) or B (ensemble averaged spectrum). 

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