Howtosignalprocessing
- Why is a square wave discontinuous?
- What is the Fourier transform of a square wave?
- What is odd square wave?
- What is meant by Gibbs phenomenon?
Why is a square wave discontinuous?
(Ideal) square waves are often drawn in a misleading way, because the vertical lines don't actually represent a signal value. The square wave actually jumps instantanously between two values, creating a discontinuity.
What is the Fourier transform of a square wave?
Example: Fourier Transform of Square Wave
n, below (in this case the coefficients are all real numbers - in the general case they would be complex). Using the result derived previously, the Fourier Transform of the function is. XT(ω)=+∞∑n=−∞cn2πδ(ω−nω0)=2π+∞∑n=−∞0.8sinc(0.8n)δ(ω−nω0)=1.6π+∞∑n=−∞sinc(0.8n)δ(ω−nω0)
What is odd square wave?
For an odd square wave, this means that all the an will be zero, and for an even square wave, all the bn will be zero. You can save yourself time and potential mistakes by exploiting this fact and only computing the coefficients that are nonzero.
What is meant by Gibbs phenomenon?
The Gibbs phenomenon is an overshoot (or "ringing") of Fourier series and other eigenfunction series occurring at simple discontinuities. It can be reduced with the Lanczos sigma factor. The phenomenon is illustrated above in the Fourier series of a square wave.
