Signal Processing and Linear Systems-B.P.Lathi copy

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Unformatted text preview: ta (Hybrid) Systems r elate t he samples of t he o utput t o those of the input. But, this procedure yields information a bout t he o utput only a t sampling instants. We c an overcome this difficulty by taking t he samples a t i nstants in between samples using t he m odified z -transform as explained later. In sampled-data systems, t he discrete-time signals are often o btained as a result o f sampling continuous-time signals. These samples are narrow pulses, which may be considered as impulses, provided t he pulse width is small compared t o t he s ystem time constant. Thus, in t he following discussion, a discrete-time signal, when i t a ppears in conjunction with a continuous-time system, is a sequence o f impulses r ather t han a sequence o f numbers. Hence, a discrete-time signal I [k] c an also be considered as continuous-time signal I (t), where (b) I (t) = L /[k]6(t - kT) k y (t) (c) F ig. 1 1.9 Typical sampled-data systems. i tself a t a c ertain position a nd fires. Another example is attitude-control problem in a spacecraft, where t he i nformation a bout t he a ctual s pacecraft a ttitude is fed b ack t o a d igital processor, which generates corrective i nput t o b e applied t o t he s pacecraft, which is a c ontinuous-time system. I n a utomatic periodic quality check in production line, t he d iscrete-data obtained from t he p eriodic check, after some digital processing, generates t he corrective i nput t o b e a pplied t o a continuous-time p lant. I n complex control systems, use o f d igital processor as a controller or a c ompensator for continuous-time plants is growing rapidly. I n t ime-sharing systems, where, for economic reasons, certain facilities are s hared by several systems, t he signals are, by nature, discrete-time o r sampled. I n r egulator t ype control systems, where a n o utput v ariable m ust b e maintained a t a c onstant value, t he e xternal disturbance a nd p lant p arameters v ariations are usually so slow t hat c ontinuous monitoring (or feedback) is unnecessary. I t is adequate t o s ample t he o utput periodically a nd t hen feed back this discrete-data. In s uch cases, feedback transducers, data-processing facilities a nd possibly long a nd e xpensive feedback communication facilities c an b e s hared a mong several control systems. Figure 11.9 shows some typical sampled-data systems. Figure 11.9a contains a digital processor, whereas in Fig. 11.9b, t he s ampled signal is directly applied t o D j A converter (the hold circuit) without further digital processing. Figure 11.9c shows a practical system, where t he i nput signal itself is a d iscrete-time signal J[kJ, a nd t he s ampler is in t he feedback path. T his s ystem is equivalent t o t hat i n Fig. 11.9b. How do we analyze such hybrid systems, where continuous-time and discrete-time signals intermingle? An effective s trategy in such a situation is t o Observe a n i nteresting fact: in this representation a discrete-time u nit impulse 6[k] is t he c...
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This note was uploaded on 04/14/2013 for the course ENG 350 taught by Professor Bayliss during the Spring '13 term at Northwestern.

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