Bandwidth

Abstract

Having wrapped a few chapters on the Fourier series and transform and being apt in visualizing and dealing with frequency spectrums, we turn to the important albeit not very well-defined topic of bandwidth. In simplest terms the bandwidth is the extent in frequency along which the spectrum of the function is nonzero. The two extremes are the time delta function which has an infinite frequency bandwidth and the DC function which has a zero frequency bandwidth (the Fourier transform being a delta function). On a more practical side the time pulse function of width 2t ₀ has a bandwidth to first order of π/t ₀—the point at which the first zero of the spectrum function takes place. Next we compare the spectrum of various pulse configurations, ranging from rectangular, to triangular and parabolic. In the process we observe that the bandwidth definition is to some extent subjective and not necessarily limited to the first zero of the Fourier transform. We refine our definition then that a signal has more BW than another if its spectrum (absolute-wise) extends deeper in frequency. The idea of a bandwidth is useful and in some simplifying situations a numerical one too. We wrap the chapter by examining the impact of unit step function edge rate on the corresponding spectrum. Extensive use of visualization is made use off in comparing the various frequency spectrums.