Example 2: Time Domain Aliasing
Figure 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.
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Example 1: Low-Pass Filtering by FFT Convolution