# hmw9 - t u ( t ) h 2 ( t ) = sinc( t ) cos(8 πt ) (a)...

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Due March 31, 2010 BME 171, Spring 2010 - HOMEWORK #9 Frequency Response of FIR Filters; System Analysis Using Fourier Transform 1. Consider the FIR ﬁlter whose impulse response is: h [ n ] = { 1 , 2 , 2 , 1 } (a) Compute frequency response H (Ω) of this ﬁlter. (b) Determine formulas for the amplitude and phase responses of this ﬁlter. (c) If you were to plot the amplitude and phase responses of this ﬁlter, what range of the digital radian frequency Ω would you use and why? 2. Consider two systems, whose impulse responses are shown below: h 1 ( t ) = δ ( t ) - e -
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Unformatted text preview: t u ( t ) h 2 ( t ) = sinc( t ) cos(8 πt ) (a) Determine the frequency responses of these systems. (b) The signal x ( t ) = 4 + cos(4 πt )-cos(8 πt ) is an input to these two systems. Determine the signals we would see on the output. 3. Frequency response of an LTI system is H ( f ) = 2 + j 4 πf 4 + j 8 πf-(2 πf ) 2 . (a) If the response of the system is y = 2 te-2 t u ( t ), determine input x ( t ). (b) Determine impulse response h ( t ) of this system. (c) Determine the ODE governing this system....
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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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