20111ee114_1_HW3

20111ee114_1_HW3 - m . What is the length of R x ( m )? 2....

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: m . What is the length of R x ( m )? 2. Consider the signal: x ( n ) = n for n (2) Using the autocorrelation method of linear prediction analysis, nd the 1 st order prediction coecient, 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...
View Full Document

Ask a homework question - tutors are online