Negative frequency in the Fourier Transform [duplicate]

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

What does negative frequency mean in Fourier transform?

Also, Noteworthy is the point that a negative frequency is the rotation vector in the opposite direction to the positive frequency. For example it is necessary to have a real (non-complex) signal. Then we have two vectors rotating in opposite directions.

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.

Why are there negative frequencies in FFT?

The reason is that the Fourier transform is symmetric about the y-axis, because the Fourier transform is mathematically defined on the interval (-Inf,Inf). The actual Fourier transform therefore has negative frequencies.

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.