20091ee114_1_PS3_sol

# 20091ee114_1_PS3_sol - UCLA Dept of Electrical Engineering...

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UCLA Dept. of Electrical Engineering EE 114, Winter 2009 Problem Set 3 - Solutions 1. Figure 1 represents the spectrum of a steady-state vowel, | X ( ω ) | . The approximated vocal tract transfer function | H ( ω ) | is shown as a dashed line. Figure 1: The spectrum of a steady-state 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 discrete-domain 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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