Why is there eight possible even extensions of a real finite length sequence?
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Apparently there is many versions of the discrete cosine transforms (DCT) mainly because we can perform an even extension of a real finite length sequence :
$$~~~~~~~~~~~~~~~~~~~~~~~~~~~x(n) ~~~~~~~~~~~~~, ~~n:0,...N-1$$
In eight different ways , but the only ways I can possibly see is the obvious one concatenating : $~~x(2N-1-n)~~$ at the end of $~~x(n)$ . What about the other seven remaining options ?
sequences-and-series fourier-analysis
asked Dec 20 '18 at 12:23
HilbertHilbert
1649
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add a comment |
$begingroup$
Apparently there is many versions of the discrete cosine transforms (DCT) mainly because we can perform an even extension of a real finite length sequence :
$$~~~~~~~~~~~~~~~~~~~~~~~~~~~x(n) ~~~~~~~~~~~~~, ~~n:0,...N-1$$
In eight different ways , but the only ways I can possibly see is the obvious one concatenating : $~~x(2N-1-n)~~$ at the end of $~~x(n)$ . What about the other seven remaining options ?
sequences-and-series fourier-analysis
asked Dec 20 '18 at 12:23
HilbertHilbert
1649
$endgroup$
1
$begingroup$
Have you looked at the diagram in en.wikipedia.org/wiki/…?
$endgroup$
– Rahul
Dec 20 '18 at 12:27
add a comment |
$begingroup$
Apparently there is many versions of the discrete cosine transforms (DCT) mainly because we can perform an even extension of a real finite length sequence :
$$~~~~~~~~~~~~~~~~~~~~~~~~~~~x(n) ~~~~~~~~~~~~~, ~~n:0,...N-1$$
In eight different ways , but the only ways I can possibly see is the obvious one concatenating : $~~x(2N-1-n)~~$ at the end of $~~x(n)$ . What about the other seven remaining options ?
sequences-and-series fourier-analysis
asked Dec 20 '18 at 12:23
HilbertHilbert
1649
$endgroup$
Apparently there is many versions of the discrete cosine transforms (DCT) mainly because we can perform an even extension of a real finite length sequence :
$$~~~~~~~~~~~~~~~~~~~~~~~~~~~x(n) ~~~~~~~~~~~~~, ~~n:0,...N-1$$
In eight different ways , but the only ways I can possibly see is the obvious one concatenating : $~~x(2N-1-n)~~$ at the end of $~~x(n)$ . What about the other seven remaining options ?
sequences-and-series fourier-analysis
sequences-and-series fourier-analysis
asked Dec 20 '18 at 12:23
HilbertHilbert
1649
asked Dec 20 '18 at 12:23
HilbertHilbert
1649
asked Dec 20 '18 at 12:23
HilbertHilbert
1649
asked Dec 20 '18 at 12:23
HilbertHilbert
1649
asked Dec 20 '18 at 12:23
HilbertHilbert
1649
1649
1
$begingroup$
Have you looked at the diagram in en.wikipedia.org/wiki/…?
$endgroup$
– Rahul
Dec 20 '18 at 12:27
add a comment |
1
$begingroup$
Have you looked at the diagram in en.wikipedia.org/wiki/…?
$endgroup$
– Rahul
Dec 20 '18 at 12:27
1
1
$begingroup$
Have you looked at the diagram in en.wikipedia.org/wiki/…?
$endgroup$
– Rahul
Dec 20 '18 at 12:27
$begingroup$
Have you looked at the diagram in en.wikipedia.org/wiki/…?
$endgroup$
– Rahul
Dec 20 '18 at 12:27
add a comment |
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Have you looked at the diagram in en.wikipedia.org/wiki/…?
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– Rahul
Dec 20 '18 at 12:27