Discrete fourier transform negative frequencies

1. What are negative frequencies in Fourier transform?
2. Why do Fourier transforms have negative frequency?
3. Can a Fourier transform have negative values?
4. What does it mean when frequency is negative?

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.

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.

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.

What does it mean when frequency is negative?

Negative frequency is an idea associated with complex exponentials. A single sine wave can be broken down into two complex exponentials ('spinning numbers'), one with a positive exponent and one with a negative exponent. That one with the negative exponent is where you get the concept of a negative frequency.