This set of Signals & Systems Multiple Choice Questions & Answers (MCQs) focuses on “Fourier Series Properties – 1″.

1. What are the properties of continuous time fourier series?

a) Linearity, time shifting

b) Linearity, time shifting, frequency shifting

c) Linearity, time shifting, frequency shifting, time reversal, time scaling, periodic convolution

d) Linearity, time shifting, frequency shifting, time reversal, time scaling, periodic convolution, multiplication, differentiation

2. Integration and conjugation are also followed by continuous time fourier series?

a) True

b) False

3. How do we represent a pairing of a periodic signal with its fourier series coefficients in case of continuous time fourier series?

a) x(t) ↔ X_{n}

b) x(t) ↔ X_{n+1}

c) x(t) ↔ X

d) x(n) ↔ X_{n}

4. If x(t) and y(t) are two periodic signals with coefficients X_{n} and Y_{n} then the linearity is represented as?

a) ax(t) + by(t) = aX_{n} + bY_{n}

b) ax (t) + by(t) = X_{n} + bY_{n}

c) ax(t) + by(t) = aX_{n} + Y_{n}

d) ax(t) + by(t) = X_{n} + Y_{n}

5. What is the frequency shifting property of continuous time fourier series?

a) Multiplication in the time domain by a real sinusoid

b) Multiplication in the time domain by a complex sinusoid

c) Multiplication in the time domain by a sinusoid

d) Addition in the time domain by a complex sinusoid

6. It does not depend whether the signal is odd or even, it is always reversal of the corresponding sequence of fourier series.

a) True

b) False

7. How is time shifting represented in case of periodic signal?

a) If x(t) is shifted to t_{0}, X_{n} is shifted to t_{0}

b) x(t-t_{0}), Y_{n} = X_{n} e^{-njwt0}

c) X_{n} = x(t-t_{0}), Y_{n} = X_{n} e^{-njwt0}

d) X_{n} = x(-t_{0}), Y_{n} = X_{n} e^{-njwt0}

8. What is the time reversal property of fourier series coefficients?

a) Time reversal of the corresponding sequence of fourier series

b) Time reversal of the last term of fourier series

c) Time reversal of the corresponding term of fourier series

d) Time reversal of the corresponding sequence

9. Why does the signal change while time scaling?

a) Because the frequency changes

b) Time changes

c) Length changes

d) Both frequency and time changes

10. What is the period of the signal when it is time shifted?

a) Changes according to the situation

b) Different in different situation

c) Remains the same

d) Takes the shifted value

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