Why negative frequencies are needed in the spectrum

negative frequencies are needed in the spectrum so we can associate one direction to +ve frequencies and the other direction to -ve..

1. What is the use of negative frequency?
2. Why we have negative frequencies needed in the spectrum?
3. Why are there negative frequencies in FFT?
4. What does negative power spectrum mean?

What is the use of negative frequency?

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 we have negative frequencies needed in the spectrum?

Negative frequencies are just a mathematical construct to allow us to analyse real signals using a complex number framework, which is used when looking at double-sided spectra. A complex number can only be made real if you add to it its conjugate, e.g. (a+bj) + (a-bj) = 2a.

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 negative power spectrum mean?

All that negative values on a decibel scale mean is that the actual power is less than the reference power (because the ratio is less than one). The higher the decibel value, the more powerful the signal. Your signal has a major peak at about 4Hz, and lesser peaks at 28Hz and 39Hz.