The X-transform and its use in sampled data system analysis

✍ Scribed by Willie L. McDaniel Jr.; Charles L. Phillips

• Publisher: Elsevier Science
• Year: 1967
• Tongue: English
• Weight: 566 KB
• Volume: 284
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(67)90570-4

✦ Synopsis

This paper discusses the development of a new transform, called the x-transform, for a sampler-hold combination in open-loop and closed-loop sampled-data systems. The x-transform is a special form of the Laplace transform and is applicable to sampled-data systems which have all samplers followed by zero-order hold devices. The x-transform inherentl~f eliminates a special requirement of the z-transform which is that all samplers must be followec~ by a hold device in order to be assured of accurate results. The x-transform is developed utilizine$ the change of variable, x ~ --e-'r'/s, where T is the sampling period in seconds, s is the Laplace transform variable and n = O, 1, 2, .... The x-transform is defined as e(t) = E(s) I (e--r,/,)--~-. It is noted that the definition of x differs from that of z bya sign change in the exponential and an s in the denominator.