Why MATLAB fft cos makes imaginary parts?

1. What do the real and imaginary parts of FFT represent?
2. Why is the FFT symmetric around the middle?
3. What is the complex part of a Fourier transform?
4. Why does FFT give NaN?

What do the real and imaginary parts of FFT represent?

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.

Why is the FFT symmetric around the middle?

Because both the positive and negative frequency sinusoids are 90 degrees out of phase and have the same magnitude, they will both respond to real signals in the same way.

What is the complex part of a Fourier transform?

The complex versions have a complex time domain signal and a complex frequency domain signal. The real versions have a real time domain signal and two real frequency domain signals. Both positive and negative frequencies are used in the complex cases, while only positive frequencies are used for the real transforms.

Why does FFT give NaN?

The ifft must be done on the unshifted fft result.) The values in the positive and negative frequencies must appear in complex-conjugate pairs. If you do not replace the NaN values with fillmissing, the entire ifft result will be NaN.