301 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 realvalued.
Euler's formula states that, for any real number x,
Q2A 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]
31 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.
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 Three '10
 Pd
 Exponential Function, Complex number, Leonhard Euler, Euler's formula

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