How to plot Full spectrum with negative frequencies

1. What are negative frequencies in spectrum?
2. Why are there negative frequencies in fft?
3. Can we hear negative frequencies?
4. What do negative values in fft mean?

What are negative frequencies in spectrum?

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 we hear negative frequencies?

No. The frequency of a sound is the number of cycles per second. This can be so low as to beyond human hearing.

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.