Negative frequency in fourier transform

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

Why there is negative frequency in Fourier transform?

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.

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.

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.

Can there be a negative frequency?

Negative frequency is a vector that has the same mathematical meaning as the imaginary part of a complex signal. Negative frequencies do not exist in the actual world; hence the spectral content of negative frequencies must be added to the spectral content of positive frequencies in order to save energy.