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Re: question about upsample

Posted by Scott Schaefer on December 20, 2004 at 16:48:27:

In Reply to: question about upsample posted by Wolfgang Geiss on December 15, 2004 at 13:00:45:

: on page 36 in the book, joe warren is talking
: about that he upsample the coefficient vector
: p(k-1) by introducing a new zero coefficient
: between each coefficient p(k-1).
: Further he says the generating funktion of the
: upsampled vector is exactly p(k-1)[x^2].

: My question is why is this the case ?

Joe thinks of the coefficient vectors as vectors of a polynomial. So the coefficients of the the polynomial p(k-1)[x] is exactly the vector p(k-1) that you refer to. Inserting a zero between each entry in p(k-1) then generates the coefficient vector p(k-1)[x^2]. Example,
p(k-1)[x]=1+2x+3x^2
p(k-1)[x^2]=1+2x^2+3x^4
Notice that the odd coefficients in p(k-1)[x^2] are zero. I hope that helps.

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: : on page 36 in the book, joe warren is talking : : about that he upsample the coefficient vector : : p(k-1) by introducing a new zero coefficient : : between each coefficient p(k-1). : : Further he says the generating funktion of the : : upsampled vector is exactly p(k-1)[x^2]. : : My question is why is this the case ? : Joe thinks of the coefficient vectors as vectors of a polynomial. So the coefficients of the the polynomial p(k-1)[x] is exactly the vector p(k-1) that you refer to. Inserting a zero between each entry in p(k-1) then generates the coefficient vector p(k-1)[x^2]. Example, : p(k-1)[x]=1+2x+3x^2 : p(k-1)[x^2]=1+2x^2+3x^4 : Notice that the odd coefficients in p(k-1)[x^2] are zero. I hope that helps.

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