What's the meaning of negative frequencies after taking the FFT in practice?

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

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.

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.

What do negative values in FFT mean?

Negative values in the real component of the result of a complex FFT correspond to a negative correlation with a cosine waveform (same as a 180 degree phase shift). If you want to check the energy at each frequency, graph the magnitude (sqrt(rere+imim)) of each complex FFT result bin.

What does negative Fourier transform mean?

A negative real component just means the correlation against that particular cosine wave is negative, e.g. the input waveform seems to wiggle in the opposite direction of the corresponding cosine function, goes mostly low when the cosine goes high and vice versa. Same for the imaginary component and the sine function.