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2 'Zero-order' Hold Element Many digital devices such as analogue/digital and digital/analogue converters operate in such a way that the converted quantity remains constant between sampling intervals. This action may be represented by means of a sampler and a 'zero-order hold' element, as shown in Fig. 4. r - - S;;;;pUng "7n t-:-rv:l l --- --, I I I {ut} I deal 'ampler ~. \ T 0 ! ·I 2 Figure 4. I I "H ltl Z. H. 3 4 {Vt} I ·I ~~ ! (j ( ' l -----n Action of 'Zero Order Hold' Element The 'transfer function' of such an ele•ent has the form UH(s) lJ\sT"' 1_e -sT s ( 10) and the pulse transfer of a linear system preceded by a sampler and zero-order hold element (with synchronously sampled output) is ( 11) where H(s) is the transfer function of the system whose input is derived from the zero-order hold, and h{H(s)/s} means 'Take the z-transform of the time function whose Laplace transform is H(s)/s'.

Hughes 1• INTRODUCTION This section outlines some basic concepts and techniques of matrix analysis. Some of these will be employed in later lectures. The intention here is to provide a guide to further study for those who are unfamiliar v1ith the subject, and to introduce the notation which will be employed subsequently in the vacation school. 2. ELEMENTARY DEFINITIONS 1•4 Am x n matrix is defined here as an array of numbers arranged in m rows and n columns, thus; a 11 a 12 ......... a 1n ( 1) A tie note that individual elements are identified by ordered subscripts, thus aij is the element in the i'th row and j'th column.

McGraw Hill, 1983). D. R. Cooper, "Continuous and Discrete Signal and System Analysis" (Holt, Rinehart and Winston, 1974). T. Kai lath, "Linear Systems". (Prentice Hall, 1980). On Frequency Domain Concepts: See the notes for Lecture LB. S. G. Piersol, "Random Data: Analysis and Measurement Procedures". (Wiley, 1971 ). S. G. Piersol, "Engineering Applications of Correlation and Spectral Analysis". (Wiley, 1980). F. D. Powell, "Digital Control of Dynamic Systems". (Addison- Wesley, 1980). L. T. Nagle, "Digital Control System Analysis and Design".

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