Interpolation and decimation in DFT...

On May 25, 1:51 pm, "Vista" <a...@gmai.com> wrote:
> "John Hadstate" <jh113...@hotmail.com> wrote in message
>
> news:1180094910.608568.259980@q75g2000hsh.googlegroups.com...
>
>
>
> > On May 25, 6:23 am, "Vista" <a...@gmai.com> wrote:
> >> Hi all,
>
> >> I have two blocks of samples of signals.
>
> >> x0, ..., x_{n-1},
>
> >> and
>
> >> y0, ..., y_{n-1},
>
> >> where DFT[x]= y.
>
> >> Suppose I want to interpolate {x} by a upsampling rate of 2, how to do
> >> that
> >> by operating on the {y} sequence, assuming {x} is not given so we can
> >> only
> >> modify {y}?
>
> > Divide y into two equal pieces (each having n/2 samples).  Insert n
> > zeroes between the first half of y and the last half of y.  IDFT the
> > new sequence.
>
> >> How about decimating {x} by a downsampling rate of 2?
>
> > Divide y into 4 equal pieces (each having n/4 samples).  Throw away
> > the middle two pieces.  IDFT the new sequence.
>
> Thanks John! Do you have any theorey/proof supporting your methods?

it's correct (we are assuming a real signal to start with which
corresponds to a complex conjugate symmetry in the other domain) and
well known those middle two sections correspond to the high frequency
half of the spectrum.  the only thing different i would do is call it
"N" instead of "n" and leave the small case letters for indices.

r b-j