Sampling Continuous Signals

Feature extraction and data reduction. A sampled continuous signal can frequently be well described in terms of a few low-frequency components of its discrete Fourier transform. This enables us to study, store and compare relatively short vectors in large data bases. 

Modem signal processing in analytical chemistry is usually performed by computer. Therefore, signals are digitized by taking uniformly spaced samples from the continuous signal, which is measured over a finite time. 

Reference inlets serve equally well for the analysis of gases, solvents, and similar volatile samples. They are especially convenient when a continuous signal is desired for instrument tuning or long-lasting MS/MS experiments in ion chemistry. In addition, the components of a mixture are admitted to the ion source without fractionation, i.e., without affecting their partial pressures. This property of reservior inlets has extensively been used in the petroleum industry. 

Many of the apphcations described in the hterature do httle more than reduce the volume of sample taken. However, Perkin Elmer introduced a product particularly designed to use the flow-injection approach. At present this seems httle more than a marketing ploy to gain advantages over competitors. However, in reahty, many ICP systems, and indeed some AA systems, do not make it easy to hnk to FIA systems because the data-processing side of these instruments cannot cope with a transient rather than a continuous signal. 

In the EBES electron beam mask-maker, the beam is electronically scanned in one direction only, and the sample continuously moved in the other direction (55). Chips are written strip by strip, the same strip on every chip being written before proceeding to the next strip. The position of the beam is checked initially with a direct beam to sample measurement, but after this a laser interferometer keeps track of the sample. Errors in position are corrected by feeding signals to the electron beam deflection coils. 

Fig. 7.88. Sampling a continous signal (a) sampler switch (b) continuous signal—input to sampler (c) sampled signal—output from sampler...

However, the z-transform f(z) represents a sampled data signal of which f(0 is the continuous form. Thus the inverse of f(z) is the sampled data signal f (t) corresponding to f(f), where, from equation 7.206 ... 

Many industrial applications employ discrete time controllers. These operate on the basis of discrete signals rather than on a continuous signal as with analog controllers. They are ideally suited to the digital environment produced by computer control and/or sampled data systems. 

Symbols with bar represent the Laplace transform of the variable (e.g. is the Laplace transform of 0). Starred symbols represent a sampled output (e.g. f (t) is the sampled data equivalent of the continuous signal f(0). 

Continuous functions and signals in the time domain are denoted by lower case letters with the argument in parentheses, e.g. x(t). Sampling at constant intervals A t produces a discrete approximation x[n] to the continuous signal, defined at times f = n A t, n = 0,1,2. Square brackets are used for the arguments of discrete functions. The Fourier transform establishes the connection between the time and frequency domains [76] ... 

With pneumatic nebulizers the samples can be taken up continuously. Then after a few seconds of aspiration a continuous signal is obtained and it can be integrated for a certain time. However, small sample aliquots can also be injected directly into the nebulizer [125-128] or into a continuous flow of liquid. The latter... 

Fig. 2.3.9 [Deri] Digital sampling of analog signals. The continuous signal is digitized at an adequate sampling rate, the broken signal is not. After sampling it appears at the frequency of the continuously drawn signal.

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