This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: Cauley Jan 23, 2009 EE602 Homework #1 Solutions Note: Most of the solutions provided below are terse. Your work is expected to be much more complete. 1. Determine if the following systems are linear, time-invariant, and causal: (a) y ( t ) = ( t, if | u ( t ) | ≤ 1 , if | u ( t ) | > 1 . Solution: Nonlinear, time-varying, causal. [ Nonlinear ] For example, for u ( t ) = 0 for all t , the output is y ( t ) = t (whereas a linear system produces zero output for zero input). [ Time-varying ] Shifting the above input does not cause the output to be shifted. [ Causal ] Output does not depend on future input. (Actually, the output at time t does not depend on the past input either, it just depends on the input at time t ; systems such as this are sometimes called “instantaneous” systems.) By the way, it is a good exercise to formally verify causality using the definition given in the class notes. You don’t have to do this in an exam, however (unless I explicitly require that). (b) y ( t ) = ( 3 u ( t ) , if t ≥ , if t < . Solution: Linear, time-varying, causal. [ Linear ] Easily checked using the definition. [ Time-varying ] When the input is an impulse function u ( t ) = δ ( t ), the output is y ( t ) = 3 δ ( t ). However, the output to the shifted input...
View Full Document
This note was uploaded on 04/08/2009 for the course ECE 602 taught by Professor Staff during the Spring '08 term at Purdue.
- Spring '08