Matching of initial behavior in time domain approximation

✍ Scribed by Bede Liu

• Publisher: Elsevier Science
• Year: 1964
• Tongue: English
• Weight: 694 KB
• Volume: 277
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(64)90061-4

✦ Synopsis

The purpose of this paper is to present an extension of the method of leastsquares as applied to time domain approximation. A technique is developed by which one is able to match the initial time domain behavior of the desired impulse response while performing the usual least-squares approximation. The method begins with the construction of a set of junctions, all with proper initial behavior, through linear combination of exponentials. Then the desired impulse response is expanded in terms of this set of

junctions. The closure property of sets of exponential junctions is studied to show that, if the error of approximation without the matching of initial behavior can be made arbitrarily small by using more and more terms, then the 'same is true when the initial behavior is matched. An example is included to illustrate the method.