Mathematicians of the 17th Century Jacob Bernoulli (also known as James or Jacques) (27 December 1654/6 January 1655 – 16 August 1705) was one of the many prominent mathematicians in the Bernoulli family. He became familiar with calculus through a correspondence with Gottfried Leibniz‚ then collaborated with his brother Johann on various applications‚ notably publishing papers ontranscendental curves (1696) and isoperimetry(1700‚ 1701). In 1690‚ Jacob Bernoulli became the first person to develop
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The Discrete Cosine Transform (DCT): Theory and Application 1 Syed Ali Khayam Department of Electrical & Computer Engineering Michigan State University March 10th 2003 1 This document is intended to be tutorial in nature. No prior knowledge of image processing concepts is assumed. Interested readers should follow the references for advanced material on DCT. ECE 802 – 602: Information Theory and Coding Seminar 1 – The Discrete Cosine Transform: Theory and Application 1. Introduction
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on this examination and that I have reported all such incidents observed by me in which unpermitted aid is given.” Signature Name Student ID Question 1: [4 points] Consider a linear time-invariant (LTI) system with impulse response h(t) whose Fourier transform is H(f ) = ∧(f ). Recall that ∧(f ) is non-zero only from f = −1 to f = +1. Find the output of the system if the input is: (a) x(t) = sin 0.5πt Solution: ∧(0.25) sin 0.5πt = 0.75 sin 0.5πt (b) x(t) = cos 10πt Solution: ∧(5) cos 10πt = 0
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1. Find the Fourier series expansion for the following function [pic] for [pic] [pic] Hence‚ deduce that [pic] 2. A periodic function of period [pic] is defined over one period by [pic] for [pic] Determine the Fourier series and illustrate graphically for [pic][pic] Then‚ deduce the value of [pic] 3. Find a Fourier series expansion of the periodic function
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20 80 Total 100 Credits 3 2 AS-402 Human 3 Behaviour (Including Human Sociology and Psychology) Basics of System 3 Modelling and Simulation Electronics Circuits Electromagnetic Field Theory Computer Architecture and Organisation Network Analysis and Synthesis Human Values and Professional Ethics General Proficiency 3 3 3 1 0 30 20 50 - 100 - 150 4 3 4 5 EC- 401 EC- 402 EC- 403
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basis of the applications for differential equations‚ Fourier series and Laplace transform in various branches of engineering and sciences. This course emphasizes the role of orthogonal polynomials in dealing with Sturm-Liouville problems. 2. Text Book: Simmons G.F.‚ Differential Equations with Applications and Historical Notes‚ TMH Edition 2003‚ Twelfth reprint 2008 Reference Book: 1. Kreider D.L. and Others: An Introduction to Linear Analysis‚ A.W.‚ 1966.
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Table of Contents Definitions of Even & Odd Functions 2 Algebraic Definition 2 Graphic Definition 4 Combining Even & Odd Functions 6 Multiplication 6 Addition 7 Integrals of Even & Odd Functions 7 Fourier Series: Even & Odd Functions 9 Arbitrary Period (2L) 9 Case of Period 2π 10 References 14 Algebraic Definitions 1) Even Function: 2) Odd Function: Algebraically You may be asked to "determine algebraically" whether a function is even or odd. To do
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Macro-environmental Analysis Children’s Market APPENDICEs Appendix 1.0 Expanded pestle analysis of children’s market An extensive pestle analysis was conducted to highlight the reasons changes have occurred in children’s market. The key issues that affect the market were recognised through thorough research and are talked about in more details below. Political factors • Increased legislation on marketing to children • Increased emphasis ethics and responsible
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PESTEL ANALYSIS Political factors - A government that is based on“A healthier you” strategy - Reporting of organic prices - Safety inspections Services ==> Positive impact Economic factors - Increase of 3.9% in the third quarter - Real Personal Consumption expenditures (increase of 3% in the third quarter) - Temporary Personal Income (increase of 6.1% in the third quarter) - European Markets : Weak dollar against Euro‚ increase in the interest rates. ==> Moderate impact Socio-cultural
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investments to accomplish its strategic goal and objectives. These external factors may include competition‚ ethical‚ legally and technical changes happening around the world which also includes economic and political environment. PESTLE PESTLE analysis (political‚ economic‚ socio-cultural‚ technological‚ legal and environmental) describes a framework of macro-environmental factors used in the environmental scanning component of strategic management. It is a strategic tool for understanding market
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