20091ee114_1_PS2_Sol

20091ee114_1_PS2_Sol - UCLA Dept. of Electrical Engineering...

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Unformatted text preview: UCLA Dept. of Electrical Engineering EE 114, Winter 2009 Problem Set 2 Solutions 1. During spectral analysis of speech, a pre-emphasis filter is generally used to boost higher frequencies, since they tend to contain discriminative information. A common form of the pre-emphasis filter is: H ( z ) = 1 G 1- az- 1 (1) (a) If we want to design the filter to have 5 times the gain at the Nyquist frequency relative to DC, i.e: | H ( ) | = 5 | H (0) | , (2) what should the parameter a be set to? (Hint: a should lie in the range (0 , 1)). (b) If it is desired that the total energy of the filter be unity, i.e.: X n =- | h ( n ) | 2 = 1 , (3) what should the parameter G be set to? Answer: (a) The frequency response of the pre-emphasis filter is determined as: | H ( ) | 2 = H ( ) H * ( ) = 1 G 2 1- ae- jn 1- ae jn = 1 G 2 1 + a 2- 2 a cos( ) | H ( ) | = 1 G q 1 + a 2- 2 a cos( ) Using this expression: | H ( ) | | H (0) | = s 1 + a 2 + 2...
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This note was uploaded on 05/10/2010 for the course EE EE114 taught by Professor Vanderschaar during the Spring '09 term at UCLA.

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20091ee114_1_PS2_Sol - UCLA Dept. of Electrical Engineering...

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