Fourier Transform MCQs

Practice Fourier Transform MCQs with four options, answers and explanations for focused Electronics & Telecommunication Engineering revision.

Question 1

Signals & SystemsFourier Transform

Parseval’s relation for the Fourier transform connects signal energy with?

AIntegral of |X(jω)|² in frequency
BOnly X(0)
COnly signal period
DMaximum signal amplitude only

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Correct Answer: A. Integral of |X(jω)|² in frequency

Explanation: Parseval's relation expresses time-domain energy equivalently in terms of the integral of spectral magnitude squared, with the appropriate 1/(2π) factor.

Reference: Standard signals and systems: fourier transform

Question 2

Signals & SystemsFourier Transform

The continuous-time Fourier transform X(jω) of x(t) is defined as?

A∫x(t)e^(-jωt)dt over all time
B∫x(t)e^(jωt)dt from 0 to 1
Cx(t)e^(-jωt)
Ddx(t)/dt

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Correct Answer: A. ∫x(t)e^(-jωt)dt over all time

Explanation: The CTFT analysis equation is X(jω)=∫ from -∞ to ∞ x(t)e^(-jωt)dt.

Reference: Standard signals and systems: fourier transform

Question 3

Signals & SystemsFourier Transform

The Fourier transform of the unit impulse delta(t) is?

A0
B1
Cjω
D2πdelta(ω) only

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Correct Answer: B. 1

Explanation: Using the CTFT definition, ∫delta(t)e^(-jωt)dt=1.

Reference: Standard signals and systems: fourier transform

Question 4

Signals & SystemsFourier Transform

The Fourier transform of delta(t-t0) is?

Ae^(-jωt0)
Be^(jωt0)
Cdelta(ω-t0)
D1/(jω)

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Correct Answer: A. e^(-jωt0)

Explanation: The shifted impulse property gives delta(t-t0) ↔ e^(-jωt0).

Reference: Standard signals and systems: fourier transform

Question 5

Signals & SystemsFourier Transform

If x(t) ↔ X(jω), then x(t-t0) has Fourier transform?

AX(jω)e^(-jωt0)
BX(jω)e^(jωt0)
CX(j(ω-t0))
Dt0X(jω)

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Correct Answer: A. X(jω)e^(-jωt0)

Explanation: A time delay t0 introduces the linear phase factor e^(-jωt0).

Reference: Standard signals and systems: fourier transform

Question 6

Signals & SystemsFourier Transform

If x(t) ↔ X(jω), multiplication of x(t) by e^(jω0t) produces?

AX(j(ω-ω0))
BX(j(ω+ω0))
Cω0X(jω)
DX(jω)e^(-jω0)

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Correct Answer: A. X(j(ω-ω0))

Explanation: Time-domain modulation by e^(jω0t) shifts the spectrum by +ω0: X(j(ω-ω0)).

Reference: Standard signals and systems: fourier transform

Question 7

Signals & SystemsFourier Transform

Differentiation in time corresponds in the Fourier domain to?

ADivision by jω
BMultiplication by jω
CTime reversal only
DMultiplication by t

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Correct Answer: B. Multiplication by jω

Explanation: If x(t) ↔ X(jω), then dx(t)/dt ↔ jωX(jω), under standard conditions.

Reference: Standard signals and systems: fourier transform

Question 8

Signals & SystemsFourier Transform

Convolution in the time domain corresponds to what operation in the Fourier domain?

AAddition
BMultiplication
CDifferentiation only
DTime reversal

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Correct Answer: B. Multiplication

Explanation: The convolution theorem states x(t)*h(t) ↔ X(jω)H(jω).

Reference: Standard signals and systems: fourier transform