Lecture 9: Aliasing and Leakage
Schedule
::
The DFT
:: Aliasing & Leakage ::
Examples
::
The
FFT
::
Convolution
There are two effects that are introduced into the computation of the DFT.
 Aliasing
 Since when we compute we are necessarily dealing with a timelimited set of data, the signal cannot be bandlimited. The sampling process, with its incumbent spectral duplication, therefore introduces aliasing. This aliasing effect can be reduced by sampling faster.
 Leakage

If the function
is not really time limited, then
we truncate it in order to obtain a finite set of samples. As
viewed above, the mathematics sees the sampled signal as if it were
periodic in time. There are two ways of viewing what is going on.
First, if we have a function
, we can obtain a timetruncated version of it by
where is the truncated version and is a windowing function. In the frequency domain, the effect is to smear the spectrum out,
This smearing is spectral leakage. Another way of viewing the leakage is this: if we truncate a function then make it periodic, the resulting function is going to have additional frequency components in it that were not in the original function, due to the change from end to end. The only way this does not happen is if the the signal is periodic with respect to the number of samples already.Leakage can be reduced either by taking more samples (wider windows of data), i.e. increasing . It can also be reduced by choosing a different window function. However, it can never be completely eliminated for most functions.
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by the Contributing Authors.
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