250+ TOP MCQs on Fourier Series & Coefficients and Answers

Signals & Systems Multiple Choice Questions on “Fourier Series & Coefficients”.

1. What are fourier coefficients?
A. The terms that are present in a fourier series
B. The terms that are obtained through fourier series
C. The terms which consist of the fourier series along with their sine or cosine values
D. The terms which are of resemblance to fourier transform in a fourier series are called fourier series coefficients

Answer: C
Clarification: The terms which consist of the fourier series along with their sine or cosine values are called fourier coefficients. Fourier coefficients are present in both exponential and trigonometric fourier series.

2. Which are the fourier coefficients in the following?
A. a₀, a_n and b_n
B. a_n
C. b_n
D. a_n and b_n

Answer: A
Clarification: These are the fourier coefficients in a trigonometric fourier series.
a₀ = 1/T∫x(t)dt
a_n = 2/T∫x(t)cos(nwt)dt
b_n = 2/T∫x(t)sin(nwt)dt

3. Do exponential fourier series also have fourier coefficients to be evaluated.
A. True
B. False

Answer: A
Clarification: The fourier coefficient is : X_n = 1/T∫x(t)e^-njwtdt.

4. The fourier series coefficients of the signal are carried from –T/2 to T/2.
A. True
B. False

Answer: A
Clarification: Yes, the coefficients evaluation can be done from –T/2 to T/2. It is done for the simplification of the signal.

5. What is the polar form of the fourier series?
A. x(t) = c₀ + ∑cncos(nwt+ϕ_n)
B. x(t) = c₀ + ∑cncos(ϕ_n)
C. x(t) = ∑cncos(nwt+ϕ_n)
D. x(t) = c₀+ ∑cos(nwt+ϕ_n)

Answer: A
Clarification: x(t) = c₀ + ∑cncos(nwt+ϕ_n), is the polar form of the fourier series.
C₀=a₀ and c_n = √a2_n+ b2_n for n≥1
And ϕ_n = tan^-1 b_n/a_n .

6. What is a line spectrum?
A. Plot showing magnitudes of waveforms are called line spectrum
B. Plot showing each of harmonic amplitudes in the wave is called line spectrum
C. Plot showing each of harmonic amplitudes in the wave is called line spectrum
D. Plot showing each of harmonic amplitudes called line spectrum

Answer: B
Clarification: The plot showing each of harmonic amplitudes in the wave is called line spectrum. The line rapidly decreases for waves with rapidly convergent series.

7. Fourier series is not true in case of discrete time signals.
A. True
B. False

Answer: B
Clarification: Fourier series is also true in case of discrete time signals. They just need to follow the dirichlet’s conditions.

8. What is the disadvantage of exponential Fourier series?
A. It is tough to calculate
B. It is not easily visualized
C. It cannot be easily visualized as sinusoids
D. It is hard for manipulation

Answer: C
Clarification: The major disadvantage of exponential Fourier series is that it cannot be easily visualized as sinusoids. Moreover, it is easier to calculate and easy for manipulation leave aside the disadvantage.

9. Fourier series uses which domain representation of signals?
A. Time domain representation
B. Frequency domain representation
C. Both combined
D. Neither depends on the situation

Answer: B
Clarification: Fourier series uses frequency domain representation of signals. X(t)=1/T∑X_ne^jnwt. Here, the X(t) is the signal and X_n = 1/T∫x(t)e^-jwtn.

10. How does Fourier series make it easier to represent periodic signals?
A. Harmonically related
B. Periodically related
C. Sinusoidally related
D. Exponentially related

Answer: A
Clarification: Fourier series makes it easier to represent periodic signals as it is a mathematical tool that allows the representation of any periodic signals as the sum of harmonically related sinusoids.