20111ee114_1_HW3

# 20111ee114_1_HW3 - m What is the length of R x m 2 Consider...

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UCLA Dept. of Electrical Engineering EE 114, Winter 2011 Problem Set 3 Due: January 26, 2011 1. This question deals with properties of the autocorrelation function. Let X ( ! ) denote the Discrete-Time Fourier Transform (DTFT) of a real sequence x ( n ). The autocorrelation function is deﬂned as: R x ( m ) = 1 X n = ¡1 x ( n ) x ( n ¡ m ) (1) (a) Show that R x ( m ) is an even function. (b) Express the DTFT of R x ( m ), R ( ! ), in terms of the DTFT of x ( n ), X ( ! ). Show that R ( ! ) is real. (c) Suppose x ( n ) is nonzero only on the range [0 ;N ¡ 1]. Specify the minimum range over which the summation in Eq. 1 must be carried out for a given positive index
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Unformatted text preview: m . What is the length of R x ( m )? 2. Consider the signal: x ( n ) = ﬂ n for n ‚ (2) Using the autocorrelation method of linear prediction analysis, ﬂnd the 1 st order prediction coe–cient, i.e. a 1 . Find the corresponding error, E . 3. Consider the speech segment [3 ; 2 ; ¡ 1 ; 1]. Find the 2 nd order vocal tract transfer using linear predictive analysis using the autocorrelation method. 1...
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