Question

The Fourier transform of a conjugate symmetric function is always
(A) imaginary (B) conjugate anti-symmetric
(C) real (D) conjugate symmetric

Answer 1

Hey there is your answer:-

C) real

I hope this answer is useful for you.

Answer 2

The correct answer is option (C), real.

Explanation

In time domain, the nature of the signal is conjugate symmetric. Now, we have to find the nature of signal in frequency domain.

For example - Consider the duality property. Lets take a rectangle rect(t). Here sinc(f) is the forehead transform. According to the duality property, we can interchange these two, that is for sinc(t), the forehead transform will be rect (f).

In a similar manner, according to the standard definition, whenever signal is real, the forehead transform is conjugate symmetric.  Now apply duality property on it, this means for conjugate symmetric function, the forehead transform is real.