Numpy fft only positive frequencies

1. Why are there negative frequencies in FFT?
2. What do negative values in FFT mean?
3. Why negative frequencies are needed in the spectrum?
4. What is the difference between Numpy FFT and RFFT?

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 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.

Why negative frequencies are needed in the spectrum?

In real world, the negative frequency does not exists and the spectral content on negative frequencies must be added to the spectral content at the positive frequencies, to save energy. The concept of negative frequencies is used broad wide namely in this sense, in the connection with complex numbers.

What is the difference between Numpy FFT and RFFT?

fft returns a 2 dimensional array of shape (number_of_frames, fft_length) containing complex numbers. For np. fft. rfft returns a 2 dimensional array of shape (number_of_frames, ((fft_length/2) + 1)) containing complex numbers.