What is the physical significance of negative frequencies?

There's no physical significance of negative frequency. Because there cannot be a negative number of cycles per unit time. However, mathematically, it's a very helpful concept which greatly simplifies the frequency domain representation of signals using Fourier transforms.

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

What is the significance 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 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.