# hmw6 - Due March 5, 2010 BME 171, Spring 2010 - HOMEWORK 6...

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Due March 5, 2010 BME 171, Spring 2010 - HOMEWORK 6 Frequency Response of LTI Systems 1. Frequency response of a linear, time-invariant system is H ( ω ) = 0 . 2 1 + j 0 . 5 ω (a) Show that the governing equation of this system is of the form: τ dy dt + y = α x. Determine the values of time constant τ and coe±cient α for the system char- acterized by H ( ω ) given above. (b) Determine formulas for amplitude and phase spectra of this system. Than make (by hand) a decent qualitative sketch of these spectra. Label all important features. (c) Consider signal x ( t ) = 4 - 2 cos(1 . 5 πt ). Write this signal in complex exponen- tial notation. Then determine and sketch the amplitude and phase spectra of this signal. (d) If x ( t ) is an input to the system considered above, what three frequencies will be represented in the output? (e) Use the table below to compute phasors of the response of this system to

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## This note was uploaded on 05/25/2010 for the course BME 171 taught by Professor Izatt during the Spring '08 term at Duke.

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hmw6 - Due March 5, 2010 BME 171, Spring 2010 - HOMEWORK 6...

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