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Test: The Complex Exponential - Electrical Engineering (EE) MCQ


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10 Questions MCQ Test Signals and Systems - Test: The Complex Exponential

Test: The Complex Exponential for Electrical Engineering (EE) 2024 is part of Signals and Systems preparation. The Test: The Complex Exponential questions and answers have been prepared according to the Electrical Engineering (EE) exam syllabus.The Test: The Complex Exponential MCQs are made for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: The Complex Exponential below.
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Test: The Complex Exponential - Question 1

 What is exp(ja) equal to, where j is the square root of unity?

Detailed Solution for Test: The Complex Exponential - Question 1

This is the corollary of DeMoivre/Euler’s Theorem.

Test: The Complex Exponential - Question 2

What is the magnitude of exp(2+3j)?

Detailed Solution for Test: The Complex Exponential - Question 2

exp(a+b) =exp(a) * exp(b), and |exp(3i)| = 1.

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Test: The Complex Exponential - Question 3

What is the fundamental frequency of exp(2pi*w*j)?

Detailed Solution for Test: The Complex Exponential - Question 3

Fundamental period = 2pi/w, hence fundamental frequency will be w.

Test: The Complex Exponential - Question 4

Total energy possessed by a signal exp(jwt) is?

Detailed Solution for Test: The Complex Exponential - Question 4

Energy possessed by a periodic signal is the integral of the square of the magnitude of the signal over a time period.

Test: The Complex Exponential - Question 5

 Sinusoidal signals multiplied by decaying exponentials are referred to as

Detailed Solution for Test: The Complex Exponential - Question 5

The decaying exponentials dampen the amplitudes of sinusoids. Hence, the term damped sinusoids.

Test: The Complex Exponential - Question 6

 What is the power possessed by a signal exp(jwt)?

Detailed Solution for Test: The Complex Exponential - Question 6

The power = Energy/Time period for a periodic signal. Hence, Power = 1.

Test: The Complex Exponential - Question 7

What is the period of exp(2+pi*j/4)t?

Detailed Solution for Test: The Complex Exponential - Question 7

The fundamental period = 2pi/(pi/4) = 8.

Test: The Complex Exponential - Question 8

exp(jwt) is periodic

Detailed Solution for Test: The Complex Exponential - Question 8

Any two instants, t and t + 2pi will be equal, hence the signal will be periodic with period 2pi.

Test: The Complex Exponential - Question 9

Define the fundamental period of the following signal x[n] = exp(2pi*j*n/3) + exp(3*pi*j*n/4)?

Detailed Solution for Test: The Complex Exponential - Question 9

The first signal, will repeat itself after 3 cycles. The second will repeat itself after 8 cycles. Thus, both of them together will repeat themselves only after LCM(8,3) = 24 cycles.

Test: The Complex Exponential - Question 10

 exp[jwn] is periodic

Detailed Solution for Test: The Complex Exponential - Question 10

Discrete exponentials are periodic only for a particular choice of the fundamental frequency.

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