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114_1_midterm_2008_Part2

114_1_midterm_2008_Part2 - p k K 1 = using the following...

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4 5. (20 points) LPC with modified calculation of the autocorrelation coefficients Five samples of a speech signal are given: s ( n ) = [ 4 0 -2 0 1], where the bold and underlined number represents s (0) and therefore s (2)=-2. The sampling frequency F s is given. Assuming the AR (auto-regressive) model of speech production, s ( n ) can be predicted by a linear combination of p previous sample values as = = p k k k n s a n s 1 ) ( ) ( ˆ . For this problem, we choose the model order p =2 . (a) Find the LPC coefficients k a , for
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Unformatted text preview: p k K 1 = , using the following formula to calculate the autocorrelation coefficients: ∑ = + ⋅ = 2 ) ( ) ( ) ( n s m n s n s m R , for p m K = . (b) Specify the vocal tract transfer function H ( z ) using the results in (a). (c) Calculate the poles of H(z) and plot them, together with the unit circle ( z =e j ω ), in the z-plane. Note: 7 . 5 . ≈ . (d) Are there formants present, and if yes, calculate their frequencies as a function of F s ?...
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