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20111ee114_1_HW2_

20111ee114_1_HW2_ - tract transfer function j H j is shown...

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UCLA Dept. of Electrical Engineering EE 114, Winter 2011 Problem Set 2 Due: January 19, 2011 1. During spectral analysis of speech, a pre-emphasis fllter is generally used to boost higher frequencies, since they tend to contain discriminative information. A common form of the pre-emphasis fllter is: H ( z ) = 1 G 1 ¡ az ¡ 1 · (1) (a) If we want to design the fllter to have 5 times the gain at the Nyquist frequency relative to DC, i.e: j H ( ) j = 5 j H (0) j ; (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 fllter be unity, i.e.: 1 X n = ¡1 j h ( n ) j 2 = 1 ; (3) what should the parameter G be set to? 2. A 2 nd -order vocal tract transfer function is given by: H ( z ) = 1 1 ¡ 1 : 6 z ¡ 1 + 1 : 28 z ¡ 2 (4) Find the spectral location of F 1 (in Hz). Assume that F s = 8 kHz. 3. Transcribe the following sentence phonetically using the ARPABET (see handout): "My favorite subject is engineering." 4. Figure 1 represents the spectrum of a steady-state vowel, j X ( ! ) j . The approximated vocal
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Unformatted text preview: tract transfer function j H ( ! ) j is shown as a dashed line. (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 frequency in Hz? Is the speaker more likely to be a male, female, or child? Why? 1 Figure 1: The spectrum of a steady-state vowel. 5. The Fourier Transform can be expressed as: X n ( ! ) = a n ( ! ) ¡ jb n ( ! ) = j X n ( ! ) j e j± n ( ! ) (5) If x ( n ) is real, flnd the relationship between the following: (a) a n ( ! ) and a n ( ¡ ! ) (b) b n ( ! ) and b n ( ¡ ! ) (c) j X n ( ! ) j and j X / n ( ! ) j (d) ± n ( ! ) and ± n ( ¡ ! ) Also, express j X n ( ! ) j in terms of a n ( ! ) and b n ( ! ). 2...
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