MIT2_017JF09_p01

# MIT2_017JF09_p01 - 1 LINEAR TIME INVARIANCE 1 1 Linear Time...

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
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 LINEAR TIME INVARIANCE 1 1 Linear Time Invariance 1. For each system below, determine if it is linear or non-linear, and determine if it is time-invariant or not time-invariant (adapted from Siebert 1986). (a) y ( t ) = u ( t + 1) The system is linear time-invariant; the output is just a time-advanced version of the input- it is noncausal! (b) y ( t ) = 1 /u ( t ) Nonlinear, time-invariant. Replace u ( t ) with αu ( t ) – this does not get us to αy ( t ), which would be required for linearity. (c) 3¨ y + ˙ y ( t ) − y ( t ) = u ( t ) Linear time-invariant; an unstable second-order system. We have to assume y (0) = 0, and that we are talking about delays only if u ( t ) = 0 for t < = 0. (d) y ( t ) = sin( t ) u ( t ) Linear time-varying. The coeﬃcient sin( t ) is a function of time, so if a given input trajectory is played with different starting times, the outputs will be different- unless the initial times are off by a integer multiple of 2 π ....
View Full Document

{[ snackBarMessage ]}

### Page1 / 3

MIT2_017JF09_p01 - 1 LINEAR TIME INVARIANCE 1 1 Linear Time...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online