19 - Window Functions for Reducing Side Lobes

Summary

We have learned that, in theory, a single frequency sinusoidal function in a time domain corresponds to an isolated line in the frequency domain. For multiple frequencies with linearly superimposed sinusoidal functions in time, the frequency domain representation is a series of lines (the so-called line spectrum). When finite sampling is performed, the isolated lines will be replaced by sinc functions centered on the locations of the lines in frequency. The lines are “smeared” to become continuous functions; each has a main lobe of finite width (), and side lobes or a series of decaying ringing toward both smaller and larger frequencies. This chapter discusses some techniques to reduce the ringing (side lobes) away from the main lobes. This is the windowing technique. This usually is done at a price: widening of the main lobe, which is sometimes acceptable in order to substantially reduce the side lobes.