Fourier Spectra Significance of the Negative Amplitude [duplicate]

1. What is the significance of negative frequencies?
2. What does a negative value in FFT mean?
3. Why there is negative frequency in Fourier transform?
4. Can Fourier transform have negative values?

What is the significance of negative frequencies?

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 does a negative value 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.

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.

Can Fourier transform have negative values?

The Fourier transform magnitude can be thought of as the length of the complex vector of X(e(j omega)) which is always a positive number.