Example 2: Time Domain AliasingFigure 8.7 shows the effect of insufficient zero padding, which can be thought of as undersampling in the frequency domain. We will see aliasing in the time domain results.
The lowpass filter length is and the input signal consists of an impulse at times and , where the data frame length is . To avoid time aliasing (i.e., to implement acyclic convolution using an FFT), we must use an FFT size at least as large as . In the figure, the FFT sizes , , and are used. Thus, the first case is heavily time aliased, the second only slightly time aliased (involving only some of the filter's ``ringing'' after the second pulse), and the third is free of time aliasing altogether.
Example 1: Low-Pass Filtering by FFT Convolution