Answer & Solution
Answer: Option
B
Solution:
Okay, let's break down this Fourier Transform question for beginners!
The question is asking what happens to the Fourier Transform (G(f)) of a signal g(t), when that signal is both real and odd-symmetric.
Let's define each part:
* Fourier Transform: Think of it as a way to see what frequencies make up a signal. It transforms a signal from the time domain (how it changes over time) to the frequency domain (how much of each frequency is present).
* Real Signal: A signal is real if its values are real numbers (no imaginary part). Most signals we deal with in the real world are real (e.g., sound waves, voltage).
* Odd Symmetry: A signal g(t) is odd-symmetric if g(-t) = -g(t). This means if you flip the signal around the y-axis and then flip it around the x-axis, you get the same signal back. A simple example is g(t) = t.
Now, here's the key concept:
The Fourier Transform has some properties related to symmetry.
Important Relationship: When g(t) is real and odd, its Fourier Transform G(f) will be purely imaginary.
Let's look at why the other options are incorrect.
* Option A: G(f) is complex: While *any* Fourier Transform *can* be complex, the combination of real and odd symmetry *simplifies* it.
* Option C: G(f) is real: A real and even signal in the time domain would give a real fourier transform.
* Option D: G(f) is real and non-negative: A real and non-negative time-domain signal doesn't guarantee the same characteristics in the frequency domain.
Therefore, the answer is Option B: G(f) is imaginary.
