Tone Search and correction for DC aliasing

[AlexA]

Hey,

I'm not sure if this is the right subforum. I'm in the process of trying to recreate the approach taken by the tone search algorithm in FPGA hardware. I've read through Alain Moriats 1999 presentation on the algorithm and spent a lot of time figuring out the maths myself, and finally googling a phenomenon that Alain makes note of, specifically, mirroring or wrapping round of the sinc (or Hanning modified sinc) envelope in the frequency domain off of DC and Nyquist.

My question is, what is the basis of this phenomenon? I can't find a reference to it in any literature so I was wondering if someone could illuminate by what mechanism the envelope is mirrored off DC and Nyquist?

Regards,

Alex

[crossrulz]

The frequency domain is made up of positive and negative frequencies. If a signal is real, then X(f) = X(-f). It's just the way the math works. Now since we are dealing with a digital signal, the spectrum repeats every Fs (sampling frequency). So if Fs is 1000Hz, you will see the spectrum that was centered around DC repeat at 1000Hz. If the spectrum bandwidth is greater than the Nyquist rate (Fs/2), then these negative frequencies that I mentioned earlier will show up in the band you are looking at. This phenomenon is called aliasing. So if you have a sine wave at 600Hz and Fs = 1000Hz, you will see a signal alias into the band at 400Hz (1000Hz + -600Hz). If you care about that 600Hz signal, then you need to up your sampling rate (and thereby increase your Nyquist rate). If you don't, filter it out before sampling.

[AlexA]

The frequency domain is made up of positive and negative frequencies. If a signal is real, then X(f) = X(-f). It's just the way the math works. Now since we are dealing with a digital signal, the spectrum repeats every Fs (sampling frequency). So if Fs is 1000Hz, you will see the spectrum that was centered around DC repeat at 1000Hz. If the spectrum bandwidth is greater than the Nyquist rate (Fs/2), then these negative frequencies that I mentioned earlier will show up in the band you are looking at. This phenomenon is called aliasing. So if you have a sine wave at 600Hz and Fs = 1000Hz, you will see a signal alias into the band at 400Hz (1000Hz + -600Hz). If you care about that 600Hz signal, then you need to up your sampling rate (and thereby increase your Nyquist rate). If you don't, filter it out before sampling.

Thanks, I managed to find a really helpful book after posting the OP. So if anyone wants help with DSP it seems to be a free online book.

http://www.dspguide.com/ch16/3.htm