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Which symmetry does the Fourier transform of a real valued time signal contain?

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BDL MT Electrical 17 April 2022 Official Paper
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  1. No symmetry
  2. Conjugate symmetry
  3. Odd symmetry
  4. Even symmetry

Answer (Detailed Solution Below)

Option 2 : Conjugate symmetry
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Detailed Solution

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The Fourier Transform of real valued signal is always of conjugate symmetry.

The Fourier Transform has two parts: Real and Imaginary.

The real part is of even nature while imaginary part is odd in nature.

Nature of Fourier Transform of various signal

Signal

Fourier Transform

Real

Conjugate symmetric

Imaginary

Conjugate anti-symmetric

Real + even

Real + even

Real + odd

Imaginary + odd

Imaginary + odd

Real + odd

Imaginary + even

Imaginary + even

Continuous + Periodic

Discrete + Aperiodic

Continuous + Aperiodic

Continuous + Aperiodic

Discrete + Periodic

Discrete + Periodic

Discrete + Aperiodic

Continuous + Periodic
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