Re: Complex to 2x real - how?

On Oct 12, 8:18 pm, Randy Yates <ya...@[EMAIL PROTECTED]
> wrote:

> If you simply take the real component and stuff zeros in every
> other sample to upsample to 2*Fs, you've got what's advertised,
> although without the "inversion". That is, you'll have a real signal
> that has the original content from 0 to Fs / 2 preserved in 0 to Fs / 2
> of the new signal, and the original content from -Fs / 2 to 0 preserved
> in Fs / 2 to Fs. Since the new sample rate is 2 * Fs, Fs is the highest
> frequency at the output rate.

Only partially true.

You will get what you've described where you've described it, but you
will also get the negative frequencies mirrored on top of the positive
ones, and the positive frequencies mirrored into the upper half on top
of the negative ones.

To avoid creating such an aliased mess, you will need a scheme that
does not "simply take the real component and..." but also take the
imaginery component as input to the proposed transformation.  It is
the use of both real *and* imaginery components that lets you tell the
positive and negative frequencies apart.

Also your scheme breaks the bandwidth in the middle and swaps the
pieces out of order.

The usual way to do it, which produces the result showin in the
GC1012's data sheet, is to interpolate (or already have twice the
needed sample rate) and then multiply (mix) by a complex signal at 1/4
the output sample rate, which offsets the whole thing into positive
frequency.

In effect, what you and Randy are proposing, when done right is like a
"2's complement" style of representation, wheras what is usually done
is an "offset binary" type of one.   Let me try to do this in ASCII
art....

original spectrum

ABCD!EFGH where !=0 frequency, half the bandwidth is negative and half
is positive

usual process is to interpolate and low pass filter, producing:

____ABCD!EFGH____  with the incresed sample rate now giving greater
alias-free bandwidth

And then ****ft all to positive frequency:

________!ABCDEFGH

At which point we can safely ignore the imaginery component as our 2x
real component is now sufficient to represent the entire bandwith
(there are is no power left in negative frequencies to be mistaken for
positive ones)

What Randy proposed would have given instead

!EFGHDCBA  which is non-contigous

And what Jerry just proposed gives

!EFGHDCBA with
    +
!DCBAEFGH aliased on top of it...