Re: [Discuss-gnuradio] Floating point FFT usage - suppress half of it?

[CEL]

Hi,
On Mon, 2018-03-19 at 22:29 -0400, Brad Hein wrote:
> 
> - Is it true then that if I have a 100-bin FFT, that each of the
> "left 50" equals the negative of its corresponding right-side bin? 
> 
No, it's their complex conjugate.

> - Is there any use for "negative frequencies" if my goal is to simply
> measure the ESD for each of the frequency bins?

In your case, they contain exactly the same energy as their positive
counterparts. That's the case because your signal is real. In the
general complex case, negative and positive frequencies carry
independent information!

> - If I want to get 48 usable frequency bands, each corresponding to a
> 0-1k, 1k-2k, 2k-3k, etc do I actually need a 96 bin FFT due to the
> mirroring?

Think of the DFT as converter from N time samples to N frequency
samples. So, if only half of them contain non-redundant information and
you need M, then N=2M.


> - Do the negative frequencies correspond to a phase difference
> compared to the positive frequencies - in other words if I have two
> 2600Hz signals that are out of phase by 180 degrees, would this be
> reflected in the negative vs positive bin associated with 2600Hz? 

not quite sure what you want to say. There's no "freedom" that your
signal has here: if it's real, then the negative DFT bins are the
conjugate of the positive ones, as said. 

Remember, the DFT gives you complex numbers, with an amplitude and a
phase. That phase represents your sinusoid's phase. It's as easy as
that – and as complicated as that.

At this point, I'd strongly recommend you get a good textbook intro to
signal theory; it's not like any of this is "random knowledge that only
very few expert have", it's written in any textbook that introduces the
DFT.

Best regards,
Marcus

smime.p7s
Description: S/MIME cryptographic signature