Howtosignalprocessing
- Why there is negative frequency in Fourier transform?
- Can a Fourier transform have negative values?
- What does it mean when frequency is negative?
- Why we have negative frequencies needed in the spectrum?
Why there is negative frequency in Fourier transform?
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 a Fourier transform have negative values?
Second, the real Fourier transform only deals with positive frequencies. That is, the frequency domain index, k, only runs from 0 to N/2. In comparison, the complex Fourier transform includes both positive and negative frequencies. This means k runs from 0 to N-1.
What does it mean when frequency is negative?
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.
