Personal tools
  •  
You are here: Home Electrical and Computer Engineering Signals and Systems Lecture 4: Interpretation of the Smoothness of the Function

Lecture 4: Interpretation of the Smoothness of the Function

Document Actions
  • Content View
  • Bookmarks
  • CourseFeed
Schedule :: Periodic Signals :: Fourier Spectrum :: Symmetry :: Fundamental Frequency :: Smoothness of the Function :: Fourier Series :: Exponential Series :: Spectra :: Bandwidth :: Energy of Signals :: Geometric Viewpoint

Functions which are smooth (e.g. continuous) have most of their variations at lower frequencies. Functions which are not smooth have variations at higher frequencies. We can look at the rate of decay of the amplitude spectrum to determine something about the smoothness of the function.

For example, the square wave function has abrupt jumps and is not even continuous. The coefficients of the F.S. decay as $1/n$ .

By contrast, the sawtooth function we examined is smoother, since it is continuous. Its coefficients decay more quickly, decaying down as $1/n^2$ .

Copyright 2008, by the Contributing Authors. Cite/attribute Resource . admin. (2006, May 23). Lecture 4: Interpretation of the Smoothness of the Function. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Signals_and_Systems/4_5node5.html. This work is licensed under a Creative Commons License Creative Commons License