Meaning of Real and Imaginary part of Fourier Transform of a signal

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.

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

What is the real part of a Fourier transform?

Fourier Transform of Complex Functions

Where, 𝑥_𝑟 (𝑡) and 𝑥_𝑖 (𝑡) are the real and imaginary parts of the function respectively.

What is real and imaginary part of signal?

In signal processing "real" denotes a signal component that is in phase with (i.e. has a 0° phase shift from) some reference signal. Imaginary denotes a signal component that is in quadrature with (i.e. has a 90° phase shift from) the same reference signal. The reference signal can come from a local oscillator.

Is the Fourier transform of a real function real?

Theorem 5.3 The Fourier transform of a real even function is real. Theorem 5.4 The Fourier transform of a real odd function is imaginary.