MIT6_003S10_assn06

MIT6_003S10_assn06 - 6.003 Homework 6 Due at the beginning...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 6.003 Homework 6 Due at the beginning of recitation on Wednesday, March 17, 2010 . Problems 1. Second-order systems The impulse response of a second-order CT system has the form h ( t ) = e t cos( d t + ) u ( t ) where the parameters , d , and are related to the parameters of the characteristic polynomial for the system: s 2 + Bs + C . a. Determine expressions for and d (not ) in terms of B and C . b. Determine the time required for the envelope e t of h ( t ) to diminish by a factor of e , the period of the oscillations in h ( t ), and the number of periods of oscillation before h ( t ) diminishes by a factor of e . Express your results as functions of B and C only. c. Estimate the parameters in part b for a CT system with the following poles: 10 100 100 s-plane The unit-sample response of a second-order DT system has the form n h [ n ] = r 0 cos( n + ) u [ n ] where the parameters r , , and are related to the parameters of the characteristic polynomial for the system: z 2 + Dz + E . d. Determine expressions for r 0 and 0 (not ) in terms of D and E . e. Determine n the length of time required for the envelope r 0 of h [ n ] to diminish by a factor of e . the period of the oscillations in h [ n ], and the number of periods of oscillation in h [ n ] before it diminishes by a factor of e . Express your results as functions of D and E only. 2 6.003 Homework 6 / Spring 2010 . 938 . 149 z-plane f. Estimate the parameters in part e for a DT system with the following poles: 2. Maximum gain For each of the following systems, find the frequency m for which the magnitude of the gain is greatest....
View Full Document

This note was uploaded on 12/14/2011 for the course EECS 6.003 taught by Professor Dennism.freeman during the Spring '11 term at MIT.

Page1 / 8

MIT6_003S10_assn06 - 6.003 Homework 6 Due at the beginning...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online