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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....
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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.
- Spring '11