# hw16 - X : (i) The DFT Y of y = £ a b c 0 0 0 / T (ii) The...

This preview shows pages 1–2. Sign up to view the full content.

ENEE 241 02 * HOMEWORK ASSIGNMENT 16 Due Thu 04/16 The signal x = £ 0 0 0 0 0 0 a b c d 0 0 / T has DFT X given by X = £ D 0 D 1 D 2 D 3 D 4 D 5 D 6 D 7 D 8 D 9 D 10 D 11 / T The DFTs below should be expressed in terms of the entries of X . (i) (3 pts.) Determine the DFT X (1) of x (1) = £ a b c d 0 0 0 0 0 0 0 0 / T (ii) (4 pts.) Determine the DFT X (2) of x (2) = £ a b c d / T (iii) (4 pts.) Determine the DFT X (3) of x (3) = £ a b c d 0 0 / T (iv) (4 pts.) Determine the DFT X (4) of x (4) = £ a b c d a b c d / T (v) (5 pts.) Explain why the DFTs of x (5) = £ a b c d 0 0 0 0 / T and x (6) = £ a b 0 0 0 0 c d / T agree over all even-indexed entries, i.e., X (5) [ k ] = X (6) [ k ] for k = 0 , 2 , 4 , 6. Solved Examples S 16.1 ( P 3.26 in textbook). The twelve-point signal x = £ a b c 0 0 0 0 0 0 0 0 0 / T has DFT X given by X = £ X 0 X 1 X 2 X 3 X 4 X 5 X 6 X 7 X 8 X 9 X 10 X 11 / T Express the following DFT’s in terms of the entries of

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: X : (i) The DFT Y of y = £ a b c 0 0 0 / T (ii) The DFT S of s = £ a b c a b c a b c a b c / T S 16.2 ( P 3.27 in textbook). In MATLAB notation, consider the 4-point vector s = [a b c d].’ and its zero-padded extension x = [s ; zeros(12,1)] Let X denote the DFT of x . Express the DFT’s of the following vectors using the entries of X : x1 = s x2 = [ s ; s ] x3 = [ s ; s ; s ; s ; s ] % length=20 x4 = [ s ; z4 ] x5 = [ z4 ; s ] x6 = [ s ; z4 ; s ; z4 ] x7 = [ s ; s ; z4 ; z4 ] where z4 = zeros(4,1) ....
View Full Document

## This note was uploaded on 10/18/2011 for the course ENEE 241 taught by Professor Staff during the Spring '08 term at Maryland.

### Page1 / 2

hw16 - X : (i) The DFT Y of y = £ a b c 0 0 0 / T (ii) The...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online