Discrete Fourier transform with negative frequencies

1. What are negative frequencies in Fourier transform?
2. Can a Fourier transform have negative values?
3. Why do Fourier transforms have negative frequency?
4. Is it possible to have negative frequency?

What are negative frequencies in Fourier transform?

The 'negative frequencies' derive from the way the two-sided Fourier transform (as computed by fft) is characteristically depicted. The fft function returns a vector that appears to begin at the zero frequency and extends to the sampling frequency.

Can a Fourier transform have negative values?

Second, the real Fourier transform only deals with positive frequencies. That is, the frequency domain index, k, only runs from 0 to N/2. In comparison, the complex Fourier transform includes both positive and negative frequencies. This means k runs from 0 to N-1.

Why do Fourier transforms have negative frequency?

Negative frequency is the rotation vector in the opposite direction to the positive frequency. For example it is necessary to have a real (non-comlex) signal. Then we have two vectors rotating in opposite directions.

Is it possible to have negative frequency?

The meaning of negative frequencies is just mathematical(not physical) similarly to the imaginary part of a complex signal. In real world, the negative frequency does not exists and the spectral content on negative frequencies must be added to the spectral content at the positive frequencies, to save energy.