Proving real and odd function has imaginary and odd Fourier Transform

1. Is the Fourier transform of an odd function odd?
2. What is real and imaginary part of Fourier transform?
3. Is the Fourier transform of a real function real?

Is the Fourier transform of an odd function odd?

Theorem 5.6 The Fourier transform of an odd function is odd. dt. = −F(−s). The Fourier transform of the even part (of a real function) is real (Theorem 5.3):

What is real and imaginary part of Fourier transform?

The real portion of an FFT result is how much each frequency component resembles a cosine wave, the imaginary component, how much each component resembles a sine wave.

Is the Fourier transform of a real function real?

Fourier transform of a real function is real.