Continuous-time signals

Digital computers can process only discrete-time signals, not continuous-time signals. For this reason, in Chapter 27 we will examine how to convert continuous- to discrete-time signals, and vice versa. In the same chapter we will also study the discretization of continuous systems. 

The control commands produced by the control program are digital and discrete-time signals. They are first converted to analog by a D/A converter and then to continuous-time signals by simple hold elements before they actuate the final control elements. 

In the development of the Fourier transform above we have assumed that the signal v t) was a continuous time signal defined for -oo < t < oo. These signals are also commonly called analogue signals. 

Discrete time signals may be generated by a discrete time process or may be the result of a sampling process on a continuous time signal. 

The common method to obtain a discrete representation of a continuous time signal is to take periodic samples of the signal, and create a sequence v[n] from the continuous time signal v t) defined by the equality... 

Measuring range between 10 17 M and saturated solutions with constant accuracy ° Delivery of a continuous electric signal with response times in the seconds range o Easy miniaturization... 

Probably the first instrument designed for reflectance studies was that described by Nutting [8], and improved by Taylor [9]. Since that time, a large number of instruments have been proposed, and numerous modifications suggested to continually improve signal-to-noise ratios [1,2]. 

A real sampler, as shown in Fig. 18.1, is closed for a finite period of time. This time of closure is usually small compared with the sampling period. Therefore the real sampler can be closely approximated by an impulse sampler. An impulse sampler is a device that converts a continuous input signal into a sequence of impulses or delta functions. Remember, these are impulses, not pulses. The height of each of these impulses is infinite. The width of each is zero. The area of the impulse or the strength of the impulse is equal to the magnitude of the input function at the sampling instant. 

Fig. 11.18 Arrival time spectra of the products of the collisional ionization of Xe 26f high Rydberg atoms by CH3I, and C6F6. As shown, collisions with CH3 lead only to r. Collisions with C F14 lead to both C7F14 and e, as shown by the large signal at early times due to electrons. C6F6 leads to the production of a long lived autodetaching state of QF6 which produces a nearly continuous electron signal at early times (from ref. 79).

C3] Bastiaans, Martin J., Gabor s Expansion and the Zak Transform for Continuous-Time and Discrete-Time Signals, w Josh Zeevi and Ronald Coifman (ed.), Signal and Image Representation in Combined Spaces, pp. 1—43, Academic Press, Inc., 1995... 

Insufficient removal of G6P, leading to a high intracellular free glucose. This blocks the muscle uptake, but as the whole-body uptake continues, at least in healthy people, it requires a yet unknown and precisely timed signal from the muscle to other organs. 

The development of the ultrafast streak camera (8) in the early 1970 s provided a continuous time base for the detection of transient photon signals within the picosecond timescale. Almost immediately the usefulness of image detectors became apparent. Instead of recording streak camera events on film, coupling of the streak camera through an image intensifier to an optical... 

The term Fourier transform usually refers to the continuous integration of any square-integrable function to re-express the function as a sum of complex exponentials. Due to the different types of functions to be transformed, many variations of this transform exist. Accordingly, Fourier transforms have scientific applications in many areas, including physics, chemical analysis, signal processing, and statistics. The continuous-time Fourier transforms are defined as follows [1-3] ... 

Given that flowstone and stalagmites may provide relatively continuously time lines that can be accurately calibrated by U/Th dating, it is possible to extract paleoclimatic signals beyond the bulk deposition of the calcite itself. This has been accomplished by tracking various isotope and trace element profiles. Samples can be drilled at sufficiently close intervals along a sawed slab of stalagmite or flowstone to provide profiles with a time resolution of a few tens to a few hundred years. 

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