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Unformatted text preview: UCLA Dept. of Electrical Engineering EE 114, Winter 2009 Problem Set 3  Solutions 1. Figure 1 represents the spectrum of a steadystate vowel,  X ( ω )  . The approximated vocal tract transfer function  H ( ω )  is shown as a dashed line. Figure 1: The spectrum of a steadystate vowel. (a) Suppose the sampling rate is F s = 8 kHz. What is F 1 in Hz? (b) If a rectangular analysis window was used during spectral analysis, what is the dura tion of the window in seconds? (Assume that F s = 8 kHz.) (c) Suppose F 1 = 400 Hz, and you are not given the sampling rate. What is the pitch in Hz? Is the speaker more likely to be a male, female, or child? Why? Answer: (a) The discretedomain frequency of the first formant, F 1 , is approximated to be π 8 . This corresponds to: F 1 = ωF s 2 π = ( π/ 8)8000 2 π ⇒ F 1 = 500Hz . (b) The bandwidth of the main lobe of a rectangular window is known to be 4 π N w . The bandwidth of the analysis window used for the spectrum provided is approximately equal to the harmonic spacing, i.e....
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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.
 Spring '09
 VANDERSCHAAR
 Electrical Engineering

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