ps4_fall09

ps4_fall09 - Department of Electrical and Computer...

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Department of Electrical and Computer Engineering Digital Speech Processing Homework No. 4 Problem 1 Consider the five N -point finite duration windows listed below: 1. Rectangular Window w R [ n ] = ( 1 0 n N - 1 0 otherwise 2. Triangular Window w T [ n ] = 2 n/ ( N - 1) 0 n ( N - 1) / 2 2 - 2 n/ ( N - 1) ( N - 1) / 2 n N - 1 0 otherwise 3. Hamming Window w H [ n ] = ( 0 . 54 - 0 . 46 cos(2 πn/ ( N - 1)) 0 n N - 1 0 otherwise 4. Hanning Window w H N [ n ] = ( 0 . 5 - 0 . 5 cos(2 πn/ ( N - 1)) 0 n N - 1 0 otherwise 5. Blackman Window w B [ n ] = ( 0 . 42 - 0 . 5 cos(2 πn/ ( N - 1)) + 0 . 08 cos(4 πn/ ( N - 1)) 0 n N - 1 0 otherwise (a) Using Matlab, with a value of N = 31, make a single plot showing the window time responses of all 5 windows over the region 0 n N - 1 (b) Using Matlab, again with a value of N = 31 and using a 1024-point FFT, calculate and make a single plot of the log magnitude responses of all 5 windows from 0 to F S / 2 (assume F S = 10000). (Be sure to normalize the peak of each
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ps4_fall09 - Department of Electrical and Computer...

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