HW_6(483)S09

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EE 483 – Introduction to Digital Signal Processing Spring 2009 Homework #6 – Due Wednesday, February 25, 2009 by 4:30 p.m. 6.1 An FIR LTI discrete-time system is described by the difference equation y [ n ] = a 1 x [ n ± m ] + a 2 x [ n ± m ± 1] + a 2 x [ n ± m ± 2] + a 1 x [ n + m ± 3]. where x [ n ] and y [ n ] denote, respectively, the input and output sequences. Determine the expression for the frequency response H ( e j ± ). For what values of the constant m will the system have a frequency response H ( e j ± ) that is a real function of ± . 6.2 An FIR filter of length 3 is characterized by a symmetric impulse response, i.e., h [0] = h[2]. Let the input to this filter be a sum of two cosine sequences of angular frequencies 0.4
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Unformatted text preview: rad/samples and 0.7 rad/samples, respectively. Determine the impulse response coefficients so that the filter passes only the high frequency component of the input. 6.3 Problem 7.36 of Text, Page 416. 6.4 Problem 7.43 of Text, Page 417. 6.5 A length-15 Type 3 real-coefficient FIR filter has the following zeros: z 1 = 0.1 ± j 0.6, z 2 = 0.3 + j 0.5, z 3 = ± 3. (a) Determine the locations of the remaining zeros. (b) What is the transfer function H ( z ) of this filter? 6.6 Problem 7.62, Part (b), Page 419. 6.7 Problem 7.72 of Text, Page 421. 6.8 Problem M7.5 of Text, Page 425....
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