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- ``Natural'' Basis:
- Normalized DFT Basis for
:
- Normalized Fourier Transform Basis:
- Normalized DTFT Basis:
(Find inner product
and reconstruction of
in terms
of
as an exercise.)
- Normalized STFT Basis:
- Overcomplete in general
- Orthonormal when
- (Hop size = Window length = DFT length)
Rectangular Window
-
,
i.e.,
for
,
and 0
otherwise
In this case,
- Continuous Wavelet Transform Basis:
scale parameter
-
maintains energy invariance
-
wavelet coefficients
mother wavelet
typically bandpass
- Qualitative example:
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Download JFB.pdf
Download JFB_2up.pdf
Download JFB_4up.pdf
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