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- We saw that a sinusoid at amplitude
, frequency
,
and phase
becomes a window transform shifted out to
frequency
, and scaled by
.
- Windowing in the time domain resulted in a `smearing'
or `smoothing' in the frequency domain.
We need to be aware of this if we are trying to resolve
sinusoids which are close together in frequency.
- Windowing also introduced side lobes.
This is important when we are trying to resolve low amplitude sinusoids
in the presence of higher amplitude signals.
When we look at specific windows, we will be
looking at this behavior.
- The window
can be thought of as the time-domain sampling kernel at time 0
- The window transform
is the corresponding frequency-domain sampling kernel at dc
- In ordinary sampling, we have
sinc
and its (rectangular) transform as the sampling kernels
There are many type of windows which serve various purposes and
exhibit various properties, as we shall see.
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Download Intro421.pdf
Download Intro421_2up.pdf
Download Intro421_4up.pdf
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