Document Type

Conference Proceeding

Abstract

The phenomenon of aliasing is important when sampling analog signals. In cases where the signal is bandlimited, one can avoid aliasing by ensuring that the sampling rate is higher than the Nyquist rate . But in cases where the signal is not bandlimited , aliasing is unavoidable if the signal is not filtered before it is sampled. It is then crucial to understand the phenomenon in order to estimate the distortion generated when the signal is reconstructed from its samples. Using the software package MATLAB by MathWorks, Inc ., two examples are presented. The first is a pure sinusoid which is sampled at both higher and lower than the Nyquist rate , and the frequency spectrum of both sampled sinusoids are compared to illustrate the effect of aliasing. The second and more interesting case is a square wave which has an unlimited bandwidth. The square wave is a periodic wave that has Fourier expansion with odd harmonics only, the amplitudes of which drop as lin. A square wave is synthesized using MATLAB and its Fourier transform is presented graphically (The synthesized square wave inherently produces aliased components) . The odd harmonics and the aliased components seen on the graph are analyzed and compared to the predicted theoretical results. Graphs generated by MATLAB accompany the analysis for both signals.

 
 

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