Fourier Series MCQ’s

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This set of Signals & Systems Multiple Choice Questions & Answers (MCQs) focuses on “Fourier Series”.

1. Who discovered Fourier series?
a) Jean Baptiste de Fourier
b) Jean Baptiste Joseph Fourier
c) Fourier Joseph
d) Jean Fourier

2. Fourier series representation can be used in case of Non-periodic signals too. True or false?
a) True
b) False

3. What is Fourier series?
a) The representation of periodic signals in a mathematical manner is called a Fourier series
b) The representation of non periodic signals in a mathematical manner is called a Fourier series
c) The representation of non periodic signals in terms of complex exponentials or sinusoids is called a Fourier series
d) The representation of periodic signals in terms of complex exponentials or sinusoids is called a Fourier series

4. What are the conditions called which are required for a signal to fulfil to be represented as Fourier series?
a) Dirichlet’s conditions
b) Gibbs phenomenon
c) Fourier conditions
d) Fourier phenomenon

5. What are the two types of Fourier series?
a) Trigonometric and exponential
b) Trigonometric and logarithmic
c) Exponential and logarithmic
d) Trigonometric only

6. How is the exponential Fourier series represented?
a) X(t) = ∑Xnejnwt + wt
b) X(t) = 1/T∑Xnejnwt
c) X(t) = ∑Xnejnwt
d) X(t) = T*∑Xnejnwt

7. Choose the condition from below that is not a part of Dirichlet’s conditions?
a) If it is continuous then there are a finite number of discontinuities in the period T1
b) It has a finite average value over the period T
c) It has a finite number of positive and negative maxima in the period T
d) It is a periodic signal

8. How is a trigonometric Fourier series represented?
a) A0 +∑[ancos(w0t)+ ansin(w0t)]
b) ∑[ancos(w0t)+ ansin(w0t)]
c) A0 *∑[ancos(w0t)+ ansin(w0t)]
d) A0 +∑[ancos(w0t)+ ansin(w0t)] + sinwt

9. What is the equation – X(t)=∑Xnejnwt called?
a) Synthesis equation
b) Analysis equation
c) Frequency domain equation
d) Discrete equation

10. What is the equation – Xn=1/T∫x(t) ejwtn called?
a) Synthesis equation
b) Analysis equation
c) Frequency domain equation
d) Discrete equation

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