Question

The Fourier transform of a real-valued time signal has

• A. odd symmetry
• B. even symmetry
• C. conjugate symmetry
• D. no symmetry

Hint:

Real signals always produce Fourier transforms with conjugate symmetry.

Answer 1

The Correct Option is C

Step 1: Consider a real-valued signal.
Let $x(t)$ be a real-valued time-domain signal with Fourier transform $X(\omega)$.
Step 2: Apply Fourier symmetry property.
For real signals, the Fourier transform satisfies the conjugate symmetry condition:
\[ X(-\omega) = X^*(\omega) \]
Step 3: Interpretation of symmetry.
This property is known as conjugate symmetry and is characteristic of real-valued signals.
Step 4: Eliminate incorrect options.
Odd or even symmetry alone is insufficient to describe $X(\omega)$.
Step 5: Final conclusion.
Therefore, the Fourier transform of a real-valued signal has conjugate symmetry.