# The Business Environment of Bp

## The Business Environment of Bp

EXAMINATION FOR THE DEGREES OF MASTER OF MATHEMATICAL SCIENCES AND OF ENGINEERING SCIENCE Semester 2 2004 BEAMFORMING AND ARRAY PROCESSING (ELEC ENG 7017 & 7025) Official Reading Time: Writing Time: Total Duration: 10 mins 180 mins 190 mins

Instructions: • This is an OPEN book examination • Attempt ALL SIX questions. • Marks are given in brackets where appropriate. • Begin each answer on a new page. • Examination materials must not be removed from the examination room. • ANSWERS TO QUESTIONS SHOULD BE EXPRESSED CLEARLY AND WRITTEN LEGIBLY. THESE ASPECTS OF PRESENTATION WILL BE TAKEN INTO ACCOUNT IN ASSESSMENT. Materials: • One Blue book • The use of calculators is permitted, this equipment to be supplied by the candidate. No pre-recorded material nor calculator instruction book is permitted, and calculators with remote communication links will be barred from the examination room.

DO NOT COMMENCE WRITING UNTIL INSTRUCTED TO DO SO

Question 1 begins on page 2.

2007, Signals and Systems II (Elec Eng 100273), Semester 2 2003 (contd)

Page 2

Question 1 : (a) Define and discuss what you understand by the beam pattern of an array of receivers. Use a diagram to illustrate the main features of the beam pattern of an array. [5 marks] (b) Consider the following two horizontal planar arrays. Based on the linear subarrays that constitute these arrays determine the positions and heights of the dominant sidelobes in the horizontal beam patterns for each array when steered at horizontal angles of 0 and 45 degrees with respect to the x-axis. What differences between the corresponding beam patterns of arrays (a) and (b) would you expect ? In both cases d = 0.5 where d is the separation of receivers in the linear subarrays.

λ

[8 marks]

(a) Question 2

(b)

x-axis

Consider an array of five omnidirectional receivers equi-spaced around the circumference of a circle of radius r as illustrated below.

y-axis

x-axis

(a) Write down the steering...