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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