This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Lecture 2: Linear Transformations on the Independent Variable of Signals Tie Liu August 30, 2011 1 Transformation of signals in CT The are many ways of transforming a CT signal into another. For instance, we can scale it, shift it in time, differentiate it, or perform a combination of these actions. Later in this course, we will introduce the idea of transforming a signal as a system. To familiarize you with manipulating signals, well examine a particular type of transformation in this subsection: transformation on the independent variable of signals. More formally, let us for now restrict ourselves to transformations of the form: x ( t ) y ( t ) = x ( f ( t )) where x ( t ) is the starting signal given to us, y ( t ) is the signal we end up with after the transformation, and f ( t ) is a function of t . The arrow denotes the action and direction of transformation. The function f ( t ) can be any welldefined function, of course, but for the study of ECEN 314, we will look at the class of linear functions f ( t ) = at + b where a and b are arbitrary real constants. The resulting transformation of x ( t ) into y ( t ) is hence called linear transformations on the independent variable. All such transformations can be decomposed into just three fundamental types of signal transformations on the independent variable: time shift, time scaling, and time reversal. They involve a change of the variable t into something else: Time shift: f ( t ) = t t for some t R . Time scaling: f ( t ) = at for some a R + . Time reversal (or flip): f ( t ) = t ....
View
Full
Document
This document was uploaded on 02/14/2012.
 Fall '09

Click to edit the document details