tut 3 complete sol - 3-0-1- Eulers identity (formula) is...

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3-0-1- Euler’s identity (formula) is known to be the most interesting formula in mathematics. Explain why? In simple terms explain the reasons for using Euler’s formula in manipulation of signals. Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that shows a deep relationship between the trigonometric functions and the complex exponential function. Euler's formula provides a powerful connection between analysis and trigonometry, and provides an interpretation of the sine and cosine functions as weighted sums of the exponential function. Also, Complex exponentials can simplify trigonometry, because they are easier to manipulate than their sinusoidal components. One technique is simply to convert sinusoids into equivalent expressions in terms of exponentials. After the manipulations, the simplified result is still real-valued. Euler's formula states that, for any real number x, Q2-A rotating phasor could have either a positive frequency or a negative frequency. What is the meaning of negative frequency and what distinguishes the negative from the positive frequency in a given rotating phasor. In Doppler radar, the usual convention is that objects moving toward the radar are considered to induce a positive (differential) frequency, and objects going away are considered to induce a negative frequency. If the value of w in e^jwt is a negative, frequency is negative. Otherwise, the frequency is positive. [2] 3-1- Periodic signals can be synthesized by adding two or more cosine waves that have harmonically related frequencies. What does this mean? Provide your answer by explanations and an example. Solution: Harmonically related frequencies means that the several frequencies of different signals must have a least common multiple as the fundamental frequency of the combined periodic signal. An example is three signals with frequencies of 100, 200 and 500 respectively having a fundamental frequency of 1000. 3-2- Spectrum is the collection of amplitude, phase and frequency information that
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This note was uploaded on 04/15/2010 for the course ECTE 906 taught by Professor Pd during the Three '10 term at University of Wollongong, Australia.

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tut 3 complete sol - 3-0-1- Eulers identity (formula) is...

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