Is negative frequency important in calculating Spectral Moments

1. Why negative frequencies are needed in the spectrum?
2. What is the use of negative frequency?
3. What does negative frequency mean in Fourier transform?
4. What does a negative angular frequency mean?

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 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.

What does negative frequency mean in Fourier transform?

Negative frequency is the rotation vector in the opposite direction to the positive frequency. For example it is necessary to have a real (non-comlex) signal. Then we have two vectors rotating in opposite directions.

What does a negative angular frequency mean?

(This makes sense because the units of frequency are expressed in cycles, degrees, or radians per second). Hence a positive frequency (+ω) means that phase is increasing with time, while a negative frequency (−ω) implies that phase is decreasing with time.